CN108228938A - A kind of Time Domain Electromagnetic computational methods and device - Google Patents

A kind of Time Domain Electromagnetic computational methods and device Download PDF

Info

Publication number
CN108228938A
CN108228938A CN201611192392.1A CN201611192392A CN108228938A CN 108228938 A CN108228938 A CN 108228938A CN 201611192392 A CN201611192392 A CN 201611192392A CN 108228938 A CN108228938 A CN 108228938A
Authority
CN
China
Prior art keywords
grid
dimensional
mesh
asked
prism
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201611192392.1A
Other languages
Chinese (zh)
Inventor
买文鼎
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Huan Ding Technology Chengdu Co Ltd
Original Assignee
Huan Ding Technology Chengdu Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huan Ding Technology Chengdu Co Ltd filed Critical Huan Ding Technology Chengdu Co Ltd
Priority to CN201611192392.1A priority Critical patent/CN108228938A/en
Publication of CN108228938A publication Critical patent/CN108228938A/en
Pending legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention discloses a kind of Time Domain Electromagnetic computational methods and devices, are related to Numerical Calculation of Electromagnetic Fields field.The method includes：According to structural generation three-dimensional prism grid to be asked and planar polygons grid, every layer of prism grid corresponds to one layer of polygonal mesh；The basic function of prism grid and the basic function of polygonal mesh according to prism grid and polygonal mesh are set respectively, each basic function of polygonal mesh is made to be equal to each basic function that corresponding prism grid selects a bottom surface；Spacer step iteratively solves on time；Judge that each grid to be asked belongs to 3D region or 2 dimensional region；To each grid in 3D region using three-dimensional process, two-dimensional process is used to each grid in 2 dimensional region；To all grids, using being uniformly processed.Described device includes：Mesh module, setting basic function module, time iteration module, judgment module, computing module one, computing module two are set.The present invention can provide time-domain information, and applied widely, calculation amount is few.

Description

A kind of Time Domain Electromagnetic computational methods and device
Technical field
This disclosure relates to Numerical Calculation of Electromagnetic Fields field, more particularly to a kind of to carry out simulation calculation for Time Domain Electromagnetic Method and apparatus.
Background technology
For certain structure, if electric field is only primarily present in a direction, referred to as primary electrical direction, and in the direction Electric field value is basically unchanged, and magnetic field is only primarily present in the plane orthogonal with direction of an electric field, such as Fig. 1.Such magnetic distribution It can be expressed with two-dimensional grid come discrete approximation, it is possible to be calculated using two-dimentional algorithm.Compared to three-dimensional algorithm, two dimension is calculated Method unknown quantity is few, and calculation amount is small.But shortcoming is that applicability is narrow, to the restricted requirement of inside configuration magnetic distribution.
Three-dimensional algorithm frequently with tetrahedron as basic grid unit, suitable for various structures, to internal magnetic distribution There is no limit, but shortcoming is that unknown quantity is more, it is computationally intensive.
Document【1】Structure to be asked is divided into 3D region and 2 dimensional region solves respectively, so as to adaptable, unknown quantity It is few, but it is frequency domain method, it is impossible to time-domain information is provided.
Time Domain Electromagnetic emulation is capable of providing time-domain information, convenient for analysis time domain impulse, the electromagnetic response in frequency domain broadband, and And time varying media can be handled, there is its unique application advantage.
Time-domain finite element method (Finite Elements Time Domain, FETD) is using finite element method (Finite Element Method, FEM)【2】It is exported after zoning is divided into multiple units from governing equation and boundary condition Matrix equation simultaneously solves, then obtains time stepping formula by time discrete, so as to obtain time domain answer.
The slightly golden method (Discontinuous Galerkin Time Domain, DGTD) of the discontinuous character used in proper names and in rendering some foreign names of time domain can be regarded as The combination of time-domain finite volumetric method and time-domain finite element method.Similar time-domain finite volumetric method, the discontinuous character used in proper names and in rendering some foreign names Lve Jinfa of time domain are used Numerical value stream transmits data between different grids.So it can be seen as a kind of Domain Decomposition Method, each grid is one Independent region walks independent solution in current time, and unrelated with remaining current grid.Similar time-domain finite element method, it is adopted With unstructured grid, so the error of geometrical fit is small, and high-order basic function can be utilized to improve precision.Because time domain does not connect Continuous character used in proper names and in rendering some foreign names Lve Jinfa has the advantages of numerous, has been widely used.But for three-dimensional structure, however it remains unknown quantity is more, meter The shortcomings that calculation amount is big.
Bibliography：
【1】Y.J.Zhang et al.,“An Efficient Hybrid Finite-Element Analysis of Multiple Vias Sharing the Same Anti-Pad in an Arbitrarily Shaped Parallel- Plate Pair,”IEEE Trans.Microw.Theory Tech.,vol.63,no.3,pp.883–890,Mar.2015.
【2】J.-M.Jin,The finite element method in electromagnetics,Third edition.Hoboken.New Jersey:John Wiley&Sons Inc,2014.
Disclosure
During in order to solve to carry out time domain electromagnetic field computation to three-dimensional structure, two-dimentional algorithm applicability is narrow, and three-dimensional algorithm is unknown It measures the problem of more, the embodiment of the present disclosure provides a kind of method and apparatus of time domain electromagnetic field computation.The technical solution is as follows：
A kind of Time Domain Electromagnetic computational methods, including：
According to structural generation three-dimensional prism grid to be asked and planar polygons grid, wherein polygonal mesh is prism grid Straightforward face, corresponded with prism grid, every layer of prism grid corresponds to one layer of polygonal mesh；
The basic function of prism grid and the basic function of polygonal mesh are set respectively according to prism grid and polygonal mesh, Each basic function of polygonal mesh is made to be equal to each basic function that corresponding prism grid selects a bottom surface；
Spacer step iteratively solves on time；
Judge that each grid to be asked belongs to 3D region or 2 dimensional region；
To each grid in 3D region using three-dimensional process, each grid in 2 dimensional region is used at two dimension Reason；
To all grids, using being uniformly processed.
Advantage is to provide time-domain information, and applied widely, calculation amount is few.
In some embodiments, wherein
Three-dimensional process is to treat that grid is asked to carry out matrix fill-in using prismatic mesh time domain finite element method；
Two-dimensional process is to treat that the corresponding triangular mesh of grid is asked to use triangle time domain finite element method into row matrix Filling；
It is that the matrix simultaneous that the matrix that three-dimensional process generates is generated with two-dimensional process is unified into unified matrix to be uniformly processed It solves.
Advantage is to provide time-domain information, and applied widely, calculation amount is few.
In some embodiments, wherein
Three-dimensional process is to traverse the adjacent mesh of grid to be asked, if the adjacent mesh of grid to be asked belongs to space Domain is then treated and grid is asked directly to be solved using three-dimensional algorithm, if the adjacent mesh of grid to be asked has grid to belong to 2 dimensional region, Then the two-dimensional grid electromagnetic field value of the previous time step of the grid is converted into treat again after three-dimensional grid electromagnetic field value and seeks grid It is solved using three-dimensional algorithm；Wherein three-dimensional algorithm uses prism grid；The electromagnetism to be asked of any net region of a time step in office Field value is only determined by the electromagnetic field value of previous this grid of time step and adjacent mesh, and the electromagnetism of other grids is walked with current time Field value is unrelated, and the electromagnetic field value of each grid is solved independently respectively in current time step；
Two-dimensional process is to traverse the adjacent mesh of grid to be asked, if the adjacent mesh of grid to be asked belongs to two-dimentional area Domain is then treated and grid is asked directly to be solved using two-dimentional algorithm, if the adjacent mesh of grid to be asked has grid to belong to 3D region, Then the three-dimensional grid electromagnetic field value of the previous time step of the grid is converted into treat again after two-dimensional grid electromagnetic field value and seeks grid It is solved using two-dimentional algorithm；Wherein two-dimentional algorithm uses polygonal mesh；The electromagnetic field to be asked of any grid of a time step in office Value is only determined by the electromagnetic field value of previous this grid of time step and adjacent mesh, and the electromagnetic field of other grids is walked with current time It is worth unrelated, the electromagnetic field value of each grid is solved independently respectively in current time step；
No operation is uniformly processed.
Advantage is to provide time-domain information, is easy to parallel computation, applied widely, calculation amount is few.
In some embodiments, wherein
Prism grid is prismatic mesh, and three-dimensional algorithm is solved using the slightly golden algorithm of the discontinuous character used in proper names and in rendering some foreign names of DGTD time domains；
Polygonal mesh is triangular mesh, and two-dimentional algorithm is solved using the slightly golden algorithm of the discontinuous character used in proper names and in rendering some foreign names of DGTD time domains.
Advantage is to provide time-domain information, is easy to parallel computation, applied widely, calculation amount is few.
In some embodiments, wherein two-dimensional process, if there is the multilayer formed by the stretching of same polyhedron in grid Prism grid, and each layer prism grid belongs to 2 dimensional region, then the multi-layer net is reduced to single layer mesh.
Advantage is to provide time-domain information, and applied widely, calculation amount is few.
A kind of Time Domain Electromagnetic computing device, including：
Mesh module is set：According to structural generation three-dimensional prism grid to be asked and planar polygons grid, wherein polygon Grid is the straightforward face of prism grid, is corresponded with prism grid, and every layer of prism grid corresponds to one layer of polygonal mesh；
Basic function module is set：The basic function of prism grid and polygon is set according to prism grid and polygonal mesh respectively The basic function of shape grid makes each basic function of polygonal mesh be equal to each basic function that corresponding prism grid selects a bottom surface；
Time iteration module：Spacer step iteratively solves on time；
Judgment module：Judge that each grid to be asked belongs to 3D region or 2 dimensional region；
Computing module one：To each grid in 3D region using three-dimensional process, to each grid in 2 dimensional region Using two-dimensional process；
Computing module two：To all grids, using being uniformly processed.
Advantage is to provide time-domain information, and applied widely, calculation amount is few.
In some embodiments, wherein
Three-dimensional process in computing module one is to treat that grid is asked to carry out square using prismatic mesh time domain finite element method Battle array filling；
Two-dimensional process in computing module one is to treat that the corresponding triangular mesh of grid is asked to use triangle time-domain finite First method carries out matrix fill-in；
Being uniformly processed in computing module two is the matrix for generating three-dimensional process and the matrix simultaneous of two-dimensional process generation Into unified matrix Unified Solution.
Advantage is to provide time-domain information, and applied widely, calculation amount is few.
In some embodiments, wherein
Three-dimensional process in computing module one is to traverse the adjacent mesh of grid to be asked, if the adjacent mesh of grid to be asked 3D region is belonged to, then treats and grid is asked directly to be solved using three-dimensional algorithm, if the adjacent mesh of grid to be asked has grid Belong to 2 dimensional region, then the two-dimensional grid electromagnetic field value of the previous time step of the grid is converted into after three-dimensional grid electromagnetic field value It treats again and grid is asked to be solved using three-dimensional algorithm；
Wherein three-dimensional algorithm uses prism grid；The electromagnetic field value to be asked of any net region of a time step in office is only by preceding One time step Home Network lattice and the electromagnetic field value of adjacent mesh determine, and the electromagnetic field value that other grids are walked with current time is unrelated, The electromagnetic field value of each grid is solved independently respectively in current time step；
Two-dimensional process in computing module one is to traverse the adjacent mesh of grid to be asked, if the adjacent mesh of grid to be asked 2 dimensional region is belonged to, then treats and grid is asked directly to be solved using two-dimentional algorithm, if the adjacent mesh of grid to be asked has grid Belong to 3D region, then the three-dimensional grid electromagnetic field value of the previous time step of the grid is converted into after two-dimensional grid electromagnetic field value It treats again and grid is asked to be solved using two-dimentional algorithm；
Wherein two-dimentional algorithm uses polygonal mesh；The electromagnetic field value to be asked of any grid of a time step in office is only by previous This grid of time step and the electromagnetic field value of adjacent mesh determine, and the electromagnetic field value that other grids are walked with current time is unrelated, often The electromagnetic field value of a grid is solved independently respectively in current time step；
No operation is uniformly processed in computing module two.
Advantage is to provide time-domain information, is easy to parallel computation, applied widely, calculation amount is few.
In some embodiments, wherein
Prism grid is prismatic mesh, and three-dimensional algorithm is solved using the slightly golden algorithm of the discontinuous character used in proper names and in rendering some foreign names of DGTD time domains；
Polygonal mesh is triangular mesh, and two-dimentional algorithm is solved using the slightly golden algorithm of the discontinuous character used in proper names and in rendering some foreign names of DGTD time domains.
Advantage is to provide time-domain information, is easy to parallel computation, applied widely, calculation amount is few.
In some embodiments, wherein two-dimensional process, if there is the multilayer formed by the stretching of same polyhedron in grid Prism grid, and each layer prism grid belongs to 2 dimensional region, then the multi-layer net is reduced to single layer mesh.
Advantage is to provide time-domain information, and applied widely, calculation amount is few.
Description of the drawings
Fig. 1 is 2 dimensional region magnetic distribution schematic diagram, wherein, 101 be electric field line, and 102 be magnetic field line.
Fig. 2 is the flow chart for the Time Domain Electromagnetic computational methods that the embodiment of the present disclosure 1 provides.
Fig. 3 is the Waveguide coaxial exchanging structure schematic diagram to be asked of the embodiment of the present disclosure 2, wherein, 301 be 2 dimensional region, 302 For 3D region.
Fig. 4 is a kind of FETD mono- based on triangular prism and corresponding bottom surface triangular mesh that the embodiment of the present disclosure 2 provides Rank seamed edge magnetic field basic function position view, wherein, 401 be FETD triangular prisms magnetic field single order seamed edge basic function, and 402 be FETD tri- Angular magnetic field single order seamed edge basic function, the 403 delta field single order seamed edge basic functions simplified for FETD.
Fig. 5 is in 2 dimensional region, and the FETD triangular prisms of two layers of prismatic mesh formed are stretched by same triangular mesh Magnetic field single order seamed edge basic function, wherein the 501 FETD triangular prisms magnetic field single order seamed edge basic function for two layers of prismatic mesh, 502 FETD triangular prisms magnetic field single order seamed edge basic function for simplified individual layer prismatic mesh.
Electric field distribution situation when Fig. 6 is the 0.281ns that the embodiment of the present disclosure 2 is calculated, wherein, 601 be 2 dimensional region, 602 be 3D region.
Fig. 7 is the parallel-plate structure schematic diagram to be asked of the embodiment of the present disclosure 3, wherein, 701 be vertical view, and 702 be head-up Figure, 703 be separator, and 704 be guide hole, 705 be empirical value apart from criterion, 706 be 3D region, and 707 be 2 dimensional region.
Fig. 8 is a kind of single order rib based on triangular prism with corresponding lower top surface triangular mesh that the embodiment of the present disclosure 3 provides Side basic function position view, wherein, 801 be triangular prism single order seamed edge basic function, and 802 be triangle single order seamed edge basic function, 803 be simplified triangle single order seamed edge basic function.
Fig. 9 is a kind of single order seamed edge based on cuboid with corresponding lower top surface rectangular mesh that the embodiment of the present disclosure 3 provides Basic function position view, wherein, 901 be cuboid single order seamed edge basic function, and 902 be rectangle single order seamed edge basic function, and 903 are Simplified rectangle single order seamed edge basic function.
Figure 10 is that the embodiment of the present disclosure 3 provides, in 2 dimensional region, two layers three formed by the stretching of same triangular mesh The triangular prism single order seamed edge basic function of prism grid, wherein the 1001 triangular prism single order seamed edge base letter for two layers of prismatic mesh Number, the 1002 triangular prism single order seamed edge basic function for simplified individual layer prismatic mesh.
Figure 11 is a kind of single order section based on triangular prism with corresponding lower top surface triangular mesh that the embodiment of the present disclosure 4 provides Point basic function position view, wherein, 1101 be triangular prism single order node basic function, and 1102 be triangle single order node base letter Number, 1103 be simplified triangle single order node basic function.
Figure 12 is a kind of single order node based on cuboid with corresponding lower top surface rectangular mesh that the embodiment of the present disclosure 4 provides Basic function position view, wherein, 1201 be cuboid single order node basic function, and 1202 be rectangle single order node basic function, 1203 be simplified rectangle single order node basic function.
Figure 13 is a kind of second order section based on triangular prism with corresponding lower top surface triangular mesh that the embodiment of the present disclosure 4 provides Point basic function position view, wherein, 1301 be triangular prism second order node basic function, and 1302 be triangle second order node base letter Number, 1303 be simplified triangle second order node basic function.
Figure 14 is that the embodiment of the present disclosure 4 provides, in 2 dimensional region, two layers three formed by the stretching of same triangular mesh The triangular prism single order node basic function of prism grid, wherein the 1401 triangular prism single order node base letter for two layers of prismatic mesh Number, the 1402 triangular prism single order node basic function for simplified individual layer prismatic mesh.
Figure 15 is the block diagram for the Time Domain Electromagnetic computing device that the embodiment of the present disclosure 5 provides.
Figure 16 is the block diagram of Time Domain Electromagnetic computing device that the another embodiment of the disclosure provides.
Specific embodiment
Purpose, technical scheme and advantage to make the disclosure are clearer, below in conjunction with attached drawing to disclosure embodiment party Formula is described in further detail.
Embodiment 1
Referring to Fig. 2, a kind of method of time domain electromagnetic field computation is present embodiments provided, including：
201 according to structural generation three-dimensional prism grid to be asked and planar polygons grid, and wherein polygonal mesh is prism The straightforward face of grid is corresponded with prism grid, and every layer of prism grid corresponds to one layer of polygonal mesh；
202 set the base letter of the basic function of prism grid and polygonal mesh according to prism grid and polygonal mesh respectively Number makes each basic function of polygonal mesh be equal to each basic function that corresponding prism grid selects a bottom surface；
203 spacer step iterative solutions on time；
204 judge that each grid to be asked belongs to 3D region or 2 dimensional region；
Each grid in 205 pairs of 3D regions is using three-dimensional process, to each grid in 2 dimensional region using two dimension Processing；
206 pairs of all grids, using being uniformly processed.
In wherein 201 setting grids, prism mesh shape is polygon prism, including but not limited to triangular prism, cube etc.； Wherein polygonal mesh shape is polygon, including but not limited to triangle, rectangle etc., and the embodiment of the present disclosure, which does not do this, to be had Body limits.
In wherein 202 setting basic functions, basic function can be seamed edge basic function or node basic function；Basic function Can be low order basic function or high-order basic function, the embodiment of the present disclosure are not specifically limited this.
The iteration sides such as including but not limited to explicit iteration, implicit iterative may be used in wherein 203 spacer step iterative solutions on time Formula, the embodiment of the present disclosure are not specifically limited this.
Wherein each prism grid is handled can be each grid is handled one by one or multiple grids simultaneously Row processing, the embodiment of the present disclosure are not specifically limited this.
Wherein 204 judge that grid to be asked belongs to 3D region or 2 dimensional region and can be realized by experience, can also be by algorithm Design realizes that the embodiment of the present disclosure is not specifically limited this.From physical significance, partitioning standards are：For certain structure, such as Fruit electric field is only primarily present in a direction, referred to as primary electrical direction, and electric field intensity values are basically unchanged in the direction, and magnetic field is only It is primarily present in the plane orthogonal with primary electrical direction, such as Fig. 1.Of this sort magnetic distribution can use two-dimensional grid Discrete approximation is expressed, so being divided into 2 dimensional region, other regions are then divided into 3D region.The sequence of 204 steps can With adjustment, as long as being completed before 205 steps.
Including but not limited to time domain may be used in three-dimensional process in wherein 205, being uniformly processed in two-dimensional process and 206 Slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of mode, time domain of finite element etc., the embodiment of the present disclosure is not specifically limited this.
The above method provided in this embodiment handles meter respectively by the way that three-dimensional structure is divided into 3D region and 2 dimensional region It calculates, in the physical characteristic that magnetic distribution is utilized in 2 dimensional region to reduce unknown quantity, time-domain information, the scope of application can be provided Extensively, calculation amount is few.
Embodiment 2
Referring to the waveguide shaped like Fig. 3, coaxial mixed structure, the embodiment of the present disclosure, should using this structure as a specific embodiment Structure is not used as the limitation disclosure.The embodiment of the present disclosure provides a kind of method of time domain electromagnetic field computation, flow chart referring to Fig. 2, the embodiment of the present disclosure with
Grid uses triangular prism and corresponding triangular mesh；
Basic function uses magnetic field single order seamed edge basic function corresponding with grid；
It three-dimensional process, two-dimensional process and is uniformly processed using time-Domain FEM mode；
For illustrate, specifically include：
201 according to structural generation three-dimensional prism grid to be asked and planar polygons grid, and wherein polygonal mesh is prism The straightforward face of grid is corresponded with prism grid, and every layer of prism grid corresponds to one layer of polygonal mesh；
202 set the base letter of the basic function of prism grid and polygonal mesh according to prism grid and polygonal mesh respectively Number makes each basic function of polygonal mesh be equal to each basic function that corresponding prism grid selects a bottom surface；
203 spacer step iterative solutions on time；
204 judge that each grid to be asked belongs to 3D region or 2 dimensional region；
Each grid in 205 pairs of 3D regions is using three-dimensional process, to each grid in 2 dimensional region using two dimension Processing；
206 pairs of all grids, using being uniformly processed.
In wherein 201 setting grids, the embodiment of the present disclosure is using prismatic mesh and corresponding triangular mesh as one Kind of preferred embodiment, not limiting the disclosure.
In wherein 202 setting basic functions, the embodiment of the present disclosure provides a kind of and triangular prism, rectangular parallelepiped grid and corresponding three A kind of angular, the corresponding single order seamed edge magnetic field basic function of rectangular mesh is as a kind of preferred embodiment, not limiting this public affairs It opens.
Referring to Fig. 4, the embodiment of the present disclosure provides a kind of single order based on triangular prism and corresponding bottom surface triangular mesh Seamed edge magnetic field basic function：
Wherein Li(i=1:6) to be defined on【2】In, the node basic function on i-th of vertex, c is triangular prism height, z-axis It is parallel with incline, ezFor z units direction.
In Fig. 4,401 be triangular prism single order seamed edge basic function, and 402 be corresponding bottom surface triangle single order seamed edge basic function. Due to using magnetic field basic function, and in 2 dimensional region, magnetic field is mainly existed only in the plane orthogonal with incline, so base letter Number N7, N8, N9Coefficient be zero, only N1, N2, N3Coefficient for unknown quantity to be asked, compared with the prismatic mesh base letter of 3D region Number is few.
Wherein 203 steps of spacer step iterative solution on time can include explicit iteration, implicit iterative etc., the embodiment of the present disclosure Using one kind of implicit iterative mode, Newmark modes【2】It is iterated, not limiting the disclosure.
Wherein each prism grid is handled can be each grid is handled one by one or multiple grids simultaneously Row processing, the embodiment of the present disclosure by the way of handling one by one, not limiting the disclosure.
Wherein 204 judge that each grid to be asked belongs to 3D region or 2 dimensional region, which can be realized by experience, Can also be designed and realized by algorithm, the embodiment of the present disclosure to this using experience realization, not limiting the disclosure.Specifically, Fig. 2 structures are divided into structure 1,2 Waveguide coaxial adapter structure of waveguiding structure and structure by the embodiment of the present disclosure.By experience, knot It is mainly the magnetic distribution of TE10 patterns in structure 1, meets two dimension and solve requirement, therefore 1 region of structure is divided into two dimension 2 region of structure is divided into 3D region by region.The sequence of 204 steps can adjust, as long as being completed before 205 steps .
In three-dimensional process in wherein 205, matrix fill-in is carried out using prismatic mesh time domain finite element method.The disclosure Embodiment provides a kind of preferred embodiment of its three-dimensional matrice, not limiting the disclosure：
Several submatrixs therein are：
It brings the basic function in 202 into above-mentioned matrix expression, that is, completes three-dimensional process.
In two-dimensional process in wherein 205, matrix fill-in is carried out using triangular mesh time domain finite element method.The disclosure Embodiment provides a kind of preferred embodiment of its two-dimensional matrix, not limiting the disclosure：
It brings the basic function in 202 into above-mentioned matrix expression, that is, completes two-dimensional process.
Optionally, the embodiment of the present disclosure proposes an optional step, in two-dimensional process, if existed in grid by same more The multilayer prism grid that face body stretching forms, and each layer prism grid belongs to 2 dimensional region, then by multi-layer net letter Single layer mesh is turned to, two-dimensional process is used to the single layer mesh.
Specifically, referring to Fig. 5, such as have two layers of prismatic mesh by being stretched, and all belong to by same triangular mesh In 2 dimensional region, such as 501.
Then simplified two-dimensional grid is such as 502：
By this optional step, unknown quantity to be asked can be further reduced.
During wherein 209 pairs of all grids are uniformly processed, the embodiment of the present disclosure proposes a kind of by three-dimensional matrice and Two-Dimensional Moment The mode of the unified matrix Unified Solution of battle array simultaneous, not to limit the disclosure, includes the following steps as preferred embodiment：
1. the seamed edges parallel with incline all in 2 dimensional region are rejected from global matrix；Prismatic mesh in 2 dimensional region The corresponding seamed edge of upper bottom surface is all using same number, i.e., the seamed edge number of two-dimentional triangular mesh；
2. resulting unified matrix is solved according to time domain finite element method.
The comparison display of the present embodiment result of calculation：To structure shown in the present embodiment, using complete three-dimensional triangular prism structure every One time step has 1681 unknown quantitys, and using embodiment of the present disclosure method, each time step only has 756 unknown quantitys, reduces Unknown quantity.Fig. 6 gives shown structure and increases this excitation in same shaft end, electric field distribution during 0.281ns, such time-domain information It is document【1】Algorithm cannot provide.
The above method provided in this embodiment, by by three-dimensional structure be divided into 3D region and 2 dimensional region handle respectively into The physical characteristic of magnetic distribution is utilized in 2 dimensional region to reduce unknown quantity in row time-domain calculation.In the present embodiment, grid is adopted With prismatic mesh and the magnetic field single order seamed edge basic function to triangular mesh, three-dimensional process, two-dimensional process and being uniformly processed is adopted With time-Domain FEM mode.Method provided in this embodiment can provide time-domain information, and applied widely, calculation amount is few.
Embodiment 3
Referring to more guide hole parallel-plate structures shaped like Fig. 7, the embodiment of the present disclosure is using this structure as a specific embodiment, the knot Structure is not used as the limitation disclosure.The embodiment of the present disclosure provides a kind of method of time domain electromagnetic field computation, and flow chart is referring to figure 2.The embodiment of the present disclosure with
Triangular prism, rectangular parallelepiped grid and corresponding triangle, rectangular mesh is respectively adopted in grid；
Basic function uses seamed edge basic function；
It three-dimensional process, two-dimensional process and is uniformly processed using the slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain
For illustrate, specifically include：
201 according to structural generation three-dimensional prism grid to be asked and planar polygons grid, and wherein polygonal mesh is prism The straightforward face of grid is corresponded with prism grid, and every layer of prism grid corresponds to one layer of polygonal mesh；
202 set the base letter of the basic function of prism grid and polygonal mesh according to prism grid and polygonal mesh respectively Number makes each basic function of polygonal mesh be equal to each basic function that corresponding prism grid selects a bottom surface；
203 spacer step iterative solutions on time；
204 judge that each grid to be asked belongs to 3D region or 2 dimensional region；
Each grid in 205 pairs of 3D regions is using three-dimensional process, to each grid in 2 dimensional region using two dimension Processing；
206 pairs of all grids, using being uniformly processed.
In wherein 201 setting grids, triangular prism, rectangular parallelepiped grid and corresponding triangle is respectively adopted in the embodiment of the present disclosure Shape, rectangular mesh are as preferred embodiment, not limiting the disclosure.
In wherein 202 setting basic functions, the embodiment of the present disclosure provides a kind of based on triangular prism, rectangular parallelepiped grid and right respectively The triangle answered, the single order seamed edge basic function of rectangular mesh are as preferred embodiment, not limiting the disclosure：
Referring to Fig. 8, present embodiments provide a kind of for prismatic mesh and the single order of corresponding bottom surface triangular mesh Seamed edge basic function：
Wherein Li(i=1:6) to be defined on【2】In i-th of vertex node basic function,Along incline from 1 linear change To 0.
In Fig. 8,801 position for prismatic mesh and its single order seamed edge basic function, 802 be corresponding bottom surface triangle Grid and its single order seamed edge basic function position.Basic function NiPreceding coefficient eiOr hiThe basic function is represented respectively for characterizing electric field Or magnetic field.Since in 2 dimensional region, electric field mainly exists only in the direction parallel with incline, magnetic field mainly exists only in and side The orthogonal direction of rib, so N7, N8, N9Magnetic field coefficient h7、h8、h9It is zero, N1, N2, N3Electric field coefficient e1、e2、e3It is zero, by This obtains 803, simplified triangle single order Basis Function.
Referring to Fig. 9, the present embodiment additionally provides a kind of for rectangular parallelepiped grid and the single order of corresponding bottom surface rectangular mesh Seamed edge basic function：
WhereinRespectively rectangular parallelepiped grid x, y, z direction length,Respectively cuboid net The x, y, z direction coordinate at lattice center.
In Fig. 9,901 position for rectangular parallelepiped grid and its single order seamed edge basic function, 902 be corresponding bottom surface rectangle net Lattice and its single order seamed edge basic function position.Basic function NiPreceding coefficient eiOr hiRepresent respectively the basic function for characterize electric field or Magnetic field.Since in 2 dimensional region, electric field mainly exists only in the direction parallel with incline, magnetic field mainly exists only in and incline Orthogonal direction, so N9、N10、N11、N12Magnetic field coefficient h9、h10、h11、h12It is zero, N1、N2、N3、N4Electric field coefficient e1、 e2、e3、e4It is zero, thus obtains 903, simplified rectangle single order Basis Function.
Wherein 203 steps of spacer step iterative solution on time can include explicit iteration, implicit iterative etc., the embodiment of the present disclosure This is not specifically limited.
Can each grid be handled one by one or multiple grid parallel computations wherein to the processing of each prism grid Processing, the embodiment of the present disclosure are handled using multiple grid parallel computations, do not limit the disclosure with this.
Wherein 204 judge that the grid belongs to 3D region or 2 dimensional region, which can be realized by experience, can also It is designed and realized by algorithm.The embodiment of the present disclosure is realized using a kind of algorithm design of range estimation is used as a preferred embodiment, and Not limiting the disclosure.
Specifically, when 204 judge that grid belongs to 3D region or 2 dimensional region, if the grid belongs to separator knot The mesh generation is then 3D region by structure；
If the grid is not belonging to isolation dish structure, each grid is detected with the distance of dish structure is isolated：
It is space by the mesh generation if grid is outer peripheral apart from small Mr. Yu's empirical value criterion with separator Domain；
Otherwise it is 2 dimensional region by the mesh generation.
Wherein certain empirical value criterion can be provided by experience, and general value is greater than or equal to 0.The embodiment of the present disclosure is respectively adopted 0mm and 0.381mm is as preferred embodiment, not limiting the disclosure.
The sequence of 204 steps can adjust, as long as being completed before 205 steps.
Wherein, the three-dimensional process in 205 steps is：
The adjacent mesh of grid to be asked is traversed, if the adjacent mesh of grid to be asked belongs to 3D region, treats and asks Grid is directly solved using three-dimensional algorithm, if the adjacent mesh of grid to be asked has grid to belong to 2 dimensional region, by the grid The two-dimensional grid electromagnetic field value of previous time step, which is converted into after the three-dimensional grid electromagnetic field value of 3D region to treat again, seeks grid It is solved using three-dimensional algorithm.
Two-dimensional grid electromagnetic field value is wherein converted into three-dimensional grid electromagnetic field value, following manner can be used as preferable real Example is applied, is not used as the limitation disclosure：
To triangular prism and corresponding triangular mesh：
e3D 1:6=0；
e3D 7:9=e2D 7:9；
h3D 1:3And h3D 4:6=h2D 1:3；
h3D 7:9=0；
To cuboid and corresponding rectangular mesh：
e3D 1:8=0；
e3D 9:12=e2D 9:12；
h3D 1:4And h3D 5:8=h2D 1:4；
h3D 9:12=0；
Wherein eiAnd hiCoefficient before respectively i-th of electric field and magnetic field basic function, superscript 3D, 2D represent this respectively Coefficient is used for three-dimensional grid and two-dimensional grid.
Wherein three-dimensional algorithm, the present embodiment is using the slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain.The slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain can It is realized in a manner of using various numerical value streams such as including but not limited to windward set, center streams.The embodiment of the present disclosure uses seamed edge base Function, windward set are as preferred embodiment, not limiting the disclosure.
The embodiment of the present disclosure provides a kind of three-dimensional algorithm to seamed edge basic function, windward set as a preferred embodiment, Not limiting the disclosure：
I-th of prism grid solves required matrix equation：
Wherein equation right endAll grid js adjacent with i, electric field, magnetic in previous time step are represented respectively ；Each submatrix expression formula in equation is：
Wherein Z and Y is respectively characteristic impedance and characteristic admittance,For electric field basic function,For magnetic field basic function.
The seamed edge basic function that 202 steps obtain is substituted into above-mentioned matrix equation and is solved, that is, completes three-dimensional process.
Wherein, the two-dimensional process in 205 steps is：
The adjacent mesh of grid to be asked is traversed, if the adjacent mesh of grid to be asked belongs to 2 dimensional region, treats and asks Grid is directly solved using two-dimentional algorithm, if the adjacent mesh of grid to be asked has grid to belong to 3D region, by the grid The three-dimensional grid electromagnetic field value of previous time step, which is converted into after two-dimensional grid electromagnetic field value to treat again, asks grid to be calculated using two dimension Method solves.
Three-dimensional grid electromagnetic field value is wherein converted into two-dimensional grid electromagnetic field value, following manner can be used as preferable real Example is applied, is not used as the limitation disclosure：
To triangular prism and corresponding triangular mesh：
e2D 7:9=e3D 7:9；
h2D 1:3=h3D 4:6Or h3D 1:3；
To cuboid and corresponding rectangular mesh：
e2D 9:12=e3D 9:12；
h2D 1:4=h3D 5:8Or h3D 1:4；
Wherein eiAnd hiCoefficient before respectively i-th of electric field and magnetic field basic function, superscript 3D, 2D represent this respectively Coefficient is used for three-dimensional grid and two-dimensional grid.
Wherein two-dimentional algorithm, the present embodiment is using the slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain.The slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain can It is realized in a manner of using various numerical value streams such as including but not limited to windward set, center streams.The embodiment of the present disclosure uses seamed edge base Function, windward set are as preferred embodiment, not limiting the disclosure.
The embodiment of the present disclosure provides a kind of two-dimentional algorithm to seamed edge basic function, windward set as a preferred embodiment, Not limiting the disclosure：
I-th of prism grid solves required matrix equation：
The wherein e of equation right endj、hjAll grid js adjacent with i are represented respectively, in the electric field magnetic field of previous time step； Submatrix expression formula in equation is identical with the expression formula in three-dimensional process mode in the present embodiment.Although two-dimensional process and three-dimensional Processing array equation is identical with matrix expression form, but boundary integral is respectively adopted two-dimensional curve integration and three-dimension curved surface Integration, so it is different to obtain matrix.
The seamed edge basic function that 202 steps obtain is substituted into above-mentioned matrix equation and is solved, that is, completes two-dimensional process.
Optionally, the embodiment of the present disclosure proposes a kind of optional step, in two-dimensional process, if existed in grid by same The multilayer prism grid that polyhedron stretching forms, and each layer prism grid belongs to 2 dimensional region, then by the multi-layer net Single layer mesh is reduced to, two-dimensional process is used to the single layer mesh.
Specifically, referring to Figure 10, such as have two layers of prismatic mesh by being stretched, and all belong to by same triangular mesh In 2 dimensional region, such as 1001, then single layer mesh processing, such as 1002 are reduced to.
Above-mentioned two-dimensional grid electromagnetic field value is converted into three-dimensional grid electromagnetic field value step and can be changed to：
To stretching each prismatic mesh in the multilayer prismatic mesh formed by same triangle,
e3D 1:6=0；
e3D 7:9=e2D 7:9；
h3D 1:3And h3D 4:6=h2D 1:3；
h3D 7:9=0；
Three-dimensional grid electromagnetic field value is converted into two-dimensional grid electromagnetic field value step and can be changed to：
An optional prismatic mesh in the multilayer prismatic mesh formed from the stretching of same triangle so that
e2D 7:9=e3D 7:9；
h2D 1:3=h3D 4:6Or h3D 1:3；
By this optional step, unknown quantity to be asked can be further reduced.
Wherein no operation is uniformly processed in 206 pairs of all grids.
Above-mentioned two dimension algorithm, three-dimensional algorithm although only with being illustrated for the slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain, Those skilled in the art is it will be noted that in progress two-dimensional process and three-dimensional process, and make 2 dimensional region and 3D region respectively During linking up, the following property of the slightly golden method of the discontinuous character used in proper names and in rendering some foreign names of time domain is only utilized in the embodiment of the present disclosure, i.e.,：
For wherein three-dimensional algorithm using prism grid, two-dimentional algorithm uses triangular mesh.Three-dimensional algorithm and triangular prism algorithm The electromagnetic field value to be asked of any net region of a time step in office is only by previous this grid of time step and the electromagnetic field of adjacent mesh Value determines, and the electromagnetic field value that other grids are walked with current time is unrelated, and the electromagnetic field value of each grid is in current time step point It is not solved independently.
So being enough rationally to infer according to the present embodiment, the discontinuous character used in proper names and in rendering some foreign names of time domain that includes but not limited to above-mentioned property omits The method that other algorithms of golden mode are equally applicable to embodiment of the present disclosure proposition.The embodiment of the present disclosure uses the discontinuous character used in proper names and in rendering some foreign names of time domain Slightly golden mode is as a kind of preferred embodiment, not limiting the disclosure.
The above method provided in this embodiment handles meter respectively by the way that three-dimensional structure is divided into 3D region and 2 dimensional region It calculates, the physical characteristic of magnetic distribution is utilized in 2 dimensional region to reduce unknown quantity.Table below is listed using the disclosure Embodiment method and the comparison used for calculating the time of pure three-dimensional method, it can be seen that since unknown quantity is few, this method improves meter Calculate speed.
Empirical value criterion in table is only used as preferred embodiment, not limiting the disclosure.
In the present embodiment, grid is using prism grid and the seamed edge basic function of corresponding polygonal mesh, three-dimensional process, two dimension It handles and is uniformly processed using the slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain.Method provided in this embodiment can provide time-domain information, be applicable in Range is wide, and calculation amount is few.Since each grid can be solved independently, convenient for parallel computation, node base is compared using seamed edge basic function Function unknown quantity is few.
Embodiment 4
Referring to more guide hole parallel-plate structures shaped like Fig. 7, the embodiment of the present disclosure is using this structure as a specific embodiment, the knot Structure is not used as the limitation disclosure.The embodiment of the present disclosure provides a kind of method of time domain electromagnetic field computation, and flow chart is referring to figure 2.The embodiment of the present disclosure with
Grid is using triangular prism, rectangular parallelepiped grid and corresponding triangle, rectangular mesh；
Basic function is using single order, second order node basic function；
It three-dimensional process, two-dimensional process and is uniformly processed using the slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain
For illustrate, specifically include：
201 according to structural generation three-dimensional prism grid to be asked and planar polygons grid, and wherein polygonal mesh is prism The straightforward face of grid is corresponded with prism grid, and every layer of prism grid corresponds to one layer of polygonal mesh；
202 set the base letter of the basic function of prism grid and polygonal mesh according to prism grid and polygonal mesh respectively Number makes each basic function of polygonal mesh be equal to each basic function that corresponding prism grid selects a bottom surface；
203 spacer step iterative solutions on time；
204 judge that each grid to be asked belongs to 3D region or 2 dimensional region；
Each grid in 205 pairs of 3D regions is using three-dimensional process, to each grid in 2 dimensional region using two dimension Processing；
206 pairs of all grids, using being uniformly processed.
In wherein 201 setting grids, triangular prism, rectangular parallelepiped grid and corresponding triangle is respectively adopted in the embodiment of the present disclosure Shape, rectangular mesh are as preferred embodiment, not limiting the disclosure.
In wherein 202 setting basic functions, the embodiment of the present disclosure provides a kind of based on triangular prism, rectangular parallelepiped grid and right respectively The triangle answered, the single order of rectangular mesh, second order node basic function are as preferred embodiment, not limiting the disclosure：
Referring to Figure 11, present embodiments provide a kind of for prismatic mesh and the single order of corresponding bottom surface triangular mesh Node basic function：
Wherein Li(i=1:6) to be defined on【2】In, the node basic function on i-th of vertex,Along incline from 1 linear change To 0.
In Figure 11,1101 position for prismatic mesh and its single order node basic function, 1102 be corresponding bottom surface three Hexagonal lattice and its single order node basic function position.Basic function NiPreceding coefficient eiOr hiThe basic function is represented respectively for characterizing Electric field or magnetic field.Basic function Ni(x, y, z) afterwards represents that the node basic function is respectively provided with the component in x, y, z direction.Due to In 2 dimensional region, electric field mainly exists only in the direction parallel with incline, and magnetic field mainly exists only in the side orthogonal with incline To so magnetic field h1、h2、h3It is zero in z directions, electric field e1、e2、e3It is zero in x and y directions, thus obtains 1103, three simplified Angular single order node basic function.
Referring to Figure 12, the present embodiment additionally provides a kind of for rectangular parallelepiped grid and the single order of corresponding bottom surface rectangular mesh Node basic function：
Wherein Li(i=1:6) to be defined on【2】In, the node basic function on i-th of vertex,Along incline from 1 linear change To 0.
In Figure 12,1201 position for prismatic mesh and its single order node basic function, 1202 be corresponding bottom surface three Hexagonal lattice and its single order node basic function position.Basic function NiPreceding coefficient eiOr hiThe basic function is represented respectively for characterizing Electric field or magnetic field.Basic function Ni(x, y, z) afterwards represents that the node basic function is respectively provided with the component in x, y, z direction.Due to In 2 dimensional region, electric field mainly exists only in the direction parallel with incline, and magnetic field mainly exists only in the side orthogonal with incline To so magnetic field h1、h2、h3、h4It is zero in z directions, electric field e1、e2、e3、e4It is zero in x and y directions, thus obtains 1203, letter The triangle single order node basic function of change.
Referring to Figure 13, the present embodiment additionally provides a kind of for the two of prismatic mesh and corresponding bottom surface triangular mesh Rank node basic function：
Wherein Li(i=1:6) to be defined on【2】In, the node basic function on i-th of vertex,Along incline from 1 linear change To 0.
In Figure 13,1301 position for prismatic mesh and its second order node basic function, 1302 be corresponding bottom surface three Hexagonal lattice and its second order node basic function position.Basic function NiPreceding coefficient eiOr hiThe basic function is represented respectively for characterizing Electric field or magnetic field.Basic function Ni(x, y, z) afterwards represents that the node basic function is respectively provided with the component in x, y, z direction.Due to In 2 dimensional region, electric field mainly exists only in the direction parallel with incline, and magnetic field mainly exists only in the side orthogonal with incline To so magnetic field h1、h2、h3、h4、h5、h6It is zero in z directions, electric field e1、e2、e3、e4、e5、e6It is zero in x and y directions, thus 1303 are obtained, simplified triangle second order node basic function.
Wherein 203 on time spacer step iterative solution step can include explicit iteration, implicit iterative etc..The embodiment of the present disclosure Using one kind of display iteration, second order leapfrogs mode as a kind of preferred embodiment, not limiting the disclosure.
Can be wherein each grid to be handled one by one or at multiple grid parallel computations to the processing of each grid Reason.The embodiment of the present disclosure, which uses to solve multiple grid parallel computations, is used as a kind of preferred embodiment, not limiting the disclosure.
Wherein 204 to judge that the grid belongs to 3D region or the foundation of 2 dimensional region be 3D region and 2 dimensional region It divides.The division can be realized by experience, can also be designed and realized by algorithm, and the embodiment of the present disclosure is judged using a kind of value Algorithm design realized as a preferred embodiment, not limiting the disclosure.
Specifically, before original flow chart 204 traverses each prism grid, increase a step, to each grid Electricity, magnetic field basic function coefficient detect.By taking triangular prism and triangular mesh as an example：
If the grid electromagnetic field value meets
It is then 2 dimensional region by the mesh generation；
Otherwise it is 3D region by the mesh generation；
WhereinFor wave impedance, α is the value of zero empirically set, and α is set as 1e by the embodiment of the present disclosure-8As A kind of preferred embodiment, not limiting the disclosure.The sequence of 204 steps can adjust, as long as being completed before 205 steps It can be with.
Wherein, the three-dimensional process in 205 steps is：
The adjacent mesh of grid to be asked is traversed, if the adjacent mesh of grid to be asked belongs to 3D region, treats and asks Grid is directly solved using three-dimensional algorithm, if the adjacent mesh of grid to be asked has grid to belong to 2 dimensional region, by the grid The two-dimensional grid electromagnetic field value of previous time step, which is converted into after the three-dimensional grid electromagnetic field value of 3D region to treat again, seeks grid It is solved using three-dimensional algorithm.
Two-dimensional grid electromagnetic field value is wherein converted into three-dimensional grid electromagnetic field value in the following way：
To triangular prism and corresponding triangular mesh single order node basic function：
e3D 1:6(x, y)=0；
e3D 1:3(z) and e3D 4:6(z)=e2D 1:3(z)；
h3D 1:3(x, y) and h3D 4:6(x, y)=h2D 1:3(x,y)；
h3D 1:6(z)=0；
To cuboid and corresponding rectangular mesh single order node basic function：
e3D 1:8(x, y)=0；
e3D 1:4(z) and e3D 8:8(z)=e2D 1:4(z)；
h3D 1:4(x, y) and h3D 5:8(x, y)=h2D 1:4(x,y)；
h3D 1:8(z)=0；
To triangular prism and corresponding triangular mesh second order node basic function：
e3D 1:12(x, y)=0；
e3D 1:6(z) and e3D 7:12(z)=e2D 1:6(z)；
h3D 1:6(x, y) and h3D 7:12(x, y)=h2D 1:6(x,y)；
h3D 1:12(z)=0；
Wherein eiAnd hiCoefficient before respectively i-th of electric field and magnetic field basic function, superscript 3D, 2D represent this respectively Coefficient is used for three-dimensional grid and two-dimensional grid, and the x, y, z in bracket represents that the coefficient corresponds to x, y, z durection component respectively.
Wherein three-dimensional algorithm, the present embodiment is using the slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain.The slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain can It is realized in a manner of using various numerical value streams such as including but not limited to windward set, center streams.The embodiment of the present disclosure uses node base Function, center stream are as preferred embodiment, not limiting the disclosure.
The embodiment of the present disclosure provides a kind of three-dimensional process mode to node basic function, center stream：
I-th of prism grid solves required matrix equation：
Submatrix expression formula therein is：
Wherein, nijx、nijy、nijzRespectively fijX, y, z component in boundary face, M and s-matrix are in grid i inner volumes Point, F matrix is in grid i and grid j interface areas point.
The seamed edge basic function that 202 steps obtain is substituted into above-mentioned matrix equation and is solved, that is, completes three-dimensional process.
Wherein, the two-dimensional process in 205 steps is：
The adjacent mesh of grid to be asked is traversed, if the adjacent mesh of grid to be asked belongs to 2 dimensional region, treats and asks Grid is directly solved using two-dimentional algorithm, if the adjacent mesh of grid to be asked has grid to belong to 3D region, by the grid The three-dimensional grid electromagnetic field value of previous time step be converted into after the two-dimensional grid electromagnetic field value of 2 dimensional region to treat again and seek net Lattice are solved using two-dimentional algorithm.
Three-dimensional grid electromagnetic field value is wherein converted into two-dimensional grid electromagnetic field value in the following way：
To triangular prism and corresponding triangular mesh single order node basic function：
e2D 1:3(z)=e3D 1:3(z) or e3D 4:6(z)；
h2D 1:3(x, y)=h3D 1:3(x, y) or h3D 4:6(x,y)；
To cuboid and corresponding rectangular mesh single order node basic function：
e2D 1:4(z)=e3D 1:4(z) or e3D 5:8(z)；
h2D 1:4(x, y)=h3D 1:4(x, y) or h3D 5:8(x,y)；
To triangular prism and corresponding triangular mesh second order node basic function：
e2D 1:6(z)=e3D 1:6(z) or e3D 7:12(z)；
h2D 1:6(x, y)=h3D 1:6(x, y) or h3D 7:12(x,y)；
Wherein eiAnd hiCoefficient before respectively i-th of electric field and magnetic field basic function, superscript 3D, 2D represent this respectively Coefficient is used for three-dimensional grid and two-dimensional grid, and the x, y, z in bracket represents that the coefficient corresponds to x, y, z durection component respectively.
Wherein two-dimentional algorithm, the present embodiment is using the slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain.The slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain can It is realized in a manner of using various numerical value streams such as including but not limited to windward set, center streams.The embodiment of the present disclosure uses node base Function, center stream are as preferred embodiment, not limiting the disclosure.
The embodiment of the present disclosure provides a kind of two-dimentional algorithm to node basic function, center stream：
I-th of prism grid solves required matrix equation：
Submatrix expression formula therein is identical with the submatrix expression formula in algorithm three-dimensional in the present embodiment.But M and s-matrix To be integrated in grid i inner faces, F matrix is to be integrated in grid i and grid j intersections curve.
The seamed edge basic function that 202 steps obtain is substituted into above-mentioned matrix equation and is solved, that is, completes two-dimensional process.
Optionally, the embodiment of the present disclosure proposes a kind of optional step, in two-dimensional process, if existed in grid by same The multilayer prism grid that polyhedron stretching forms, and each layer prism grid belongs to 2 dimensional region, then by the multi-layer net Single layer mesh is reduced to, two-dimensional process is used to the single layer mesh.
Specifically, referring to Figure 14, such as have two layers of prismatic mesh by being stretched, and all belong to by same triangular mesh In 2 dimensional region, such as 1401, then single layer mesh processing, such as 1402 are reduced to.
To stretching each prismatic mesh in the multilayer prismatic mesh formed by same triangle,
e3D 1:6(x, y)=0；
e3D 1:3(z) and e3D 4:6(z)=e2D 1:3(z)；
h3D 1:3(x, y) and h3D 4:6(x, y)=h2D 1:3(x,y)；
h3D 1:6(z)=0；
Three-dimensional grid electromagnetic field value is converted into two-dimensional grid electromagnetic field value step and is changed to：
An optional prismatic mesh in the multilayer prismatic mesh formed from the stretching of same triangle so that
e2D 1:3(z)=e3D 1:3(z) or e3D 4:6(z)；
h2D 1:3(x, y)=h3D 1:3(x, y) or h3D 4:6(x,y)；
By this optional step, unknown quantity to be asked can be further reduced.
Wherein no operation is uniformly processed in 209 pairs of all grids.
Above-mentioned two dimension algorithm, three-dimensional algorithm although only with being illustrated for the slightly golden mode of the discontinuous character used in proper names and in rendering some foreign names of time domain, It will be noted that carrying out two-dimensional process and three-dimensional process respectively, and the engineering that 2 dimensional region is made to be linked up with 3D region In, the following property of the slightly golden method of the discontinuous character used in proper names and in rendering some foreign names of time domain is only utilized in the embodiment of the present disclosure, i.e.,：
For wherein three-dimensional algorithm using prism grid, two-dimentional algorithm uses polygonal mesh；Any grid of a time step in office The electromagnetic field value to be asked in region is only determined by the electromagnetic field value of previous this grid of time step and adjacent mesh, and is walked with current time The electromagnetic field value of other grids is unrelated, and the electromagnetic field value of each grid is solved independently respectively in current time step.
So being enough rationally to infer according to the present embodiment, the discontinuous character used in proper names and in rendering some foreign names of time domain that includes but not limited to above-mentioned property omits Other algorithms of golden mode are equally applicable to the method that the disclosure is proposed.The embodiment of the present disclosure is slightly golden using the discontinuous character used in proper names and in rendering some foreign names of time domain Mode is as a kind of preferred embodiment, not limiting the disclosure.
The above method provided in this embodiment handles meter respectively by the way that three-dimensional structure is divided into 3D region and 2 dimensional region It calculates, the physical characteristic of magnetic distribution is utilized in 2 dimensional region to reduce unknown quantity.In the present embodiment, grid uses prism net Lattice and the seamed edge basic function to polygonal mesh, three-dimensional process, two-dimensional process and are uniformly processed slightly golden using the discontinuous character used in proper names and in rendering some foreign names of time domain Mode.Method provided in this embodiment can provide time-domain information, and applied widely, calculation amount is few.Since each grid can be only It is vertical to solve, convenient for parallel computation, high-order basic function is easily achieved using node basic function.
Embodiment 5
Referring to Figure 15, a kind of device of time domain electromagnetic field computation is present embodiments provided, including：
1501 setting mesh modules：According to structural generation three-dimensional prism grid to be asked and planar polygons grid, wherein more Side shape grid is the straightforward face of prism grid, is corresponded with prism grid, and every layer of prism grid corresponds to one layer of polygonal mesh；
1502 setting basic function modules：According to prism grid and polygonal mesh set respectively prism grid basic function and The basic function of polygonal mesh makes each basic function of polygonal mesh be equal to each base letter that corresponding prism grid selects a bottom surface Number；
1503 time iteration modules：Spacer step iteratively solves on time；
1504 judgment modules：Judge that each grid to be asked belongs to 3D region or 2 dimensional region；
1504 computing modules one：To each grid in 3D region using three-dimensional process, to each in 2 dimensional region Grid uses two-dimensional process；
1506 computing modules two：To all grids, using being uniformly processed.
In wherein 1501 setting mesh modules, prism mesh shape is polygon prism, including but not limited to triangular prism, cube Etc.；Wherein polygonal mesh shape is polygon, including but not limited to triangle, rectangle etc., and the embodiment of the present disclosure is to this It is not specifically limited.
In wherein 1502 setting basic function modules, basic function can be seamed edge basic function or node basic function；Base Function can be low order basic function or high-order basic function, the embodiment of the present disclosure are not specifically limited this.
Wherein 1503 on time spacer step iterative solution module may be used including but not limited to explicit iteration, implicit iterative etc. repeatedly For mode, the embodiment of the present disclosure is not specifically limited this.
Can each grid be handled one by one or multiple grids wherein to the processing of each prism mesh module Parallel processing, the embodiment of the present disclosure are not specifically limited this.
Wherein 1504 judgment modules judge that grid to be asked belongs to 3D region or 2 dimensional region, which can be by elder generation Knowledge realization is tested, can also be designed and realized by algorithm, the embodiment of the present disclosure is not specifically limited this.From physical significance, draw Foundation is divided to be：For certain structure, if electric field is only primarily present in a direction, referred to as primary electrical direction, and along the party It is basically unchanged to electric field intensity values, magnetic field is only primarily present in the plane orthogonal with primary electrical direction, such as Fig. 1.It is of this sort Magnetic distribution can use two-dimensional grid discrete approximation express, so being divided into 2 dimensional region, other regions then divide For 3D region.The position of 1504 judgment modules can adjust, as long as completing to judge before 1505 computing modules one.
Three-dimensional process in wherein 1505 computing modules one, being uniformly processed in two-dimensional process and 1506 computing modules two can By using include but not limited to time-Domain FEM in a manner of, the discontinuous character used in proper names and in rendering some foreign names of time domain slightly gold in the way of etc. modes, the embodiment of the present disclosure This is not specifically limited.
Above device provided in this embodiment handles meter respectively by the way that three-dimensional structure is divided into 3D region and 2 dimensional region It calculates, the physical characteristic of magnetic distribution is utilized to reduce unknown quantity in 2 dimensional region, it is applied widely, reduce calculation amount.
It will be understood by those skilled in the art that embodiment of the disclosure can be provided as method, apparatus (equipment) or computer Program product.Therefore, in terms of the disclosure can be used complete hardware embodiment, complete software embodiment or combine software and hardware Embodiment form.Moreover, the meter for wherein including computer usable program code in one or more can be used in the disclosure The computer that calculation machine usable storage medium is implemented on (including but not limited to magnetic disk storage, system CD, optical memory etc.) The form of program product.
The disclosure is to realize flow with reference to according to the method, apparatus (equipment) and computer program instructions of the embodiment of the present disclosure Figure and/or block diagram describe.It should be understood that it can be realized by computer program instructions every first-class in flowchart and/or the block diagram The combination of flow and/or box in journey and/or box and flowchart and/or the block diagram.These computer programs can be provided The processor of all-purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices is instructed to produce A raw machine so that the instruction performed by computer or the processor of other programmable data processing devices is generated for real The dress of function specified in a present flow of flow chart or one box of multiple flows and/or block diagram or multiple boxes It puts.
These computer program instructions, which may also be stored in, can guide computer or other programmable data processing devices with spy Determine in the computer-readable memory that mode works so that the instruction generation being stored in the computer-readable memory includes referring to Enable the manufacture of device, the command device realize in one flow of flow chart or multiple flows and/or one box of block diagram or The function of being specified in multiple boxes.
These computer program instructions can be also loaded into computer or other programmable data processing devices so that counted Series of operation steps are performed on calculation machine or other programmable devices to generate computer implemented processing, so as in computer or The instruction offer performed on other programmable devices is used to implement in one flow of flow chart or multiple flows and/or block diagram one The step of function of being specified in a box or multiple boxes.
Although preferred embodiment of the present disclosure has been described, those skilled in the art once know basic creation Property concept, then can make these embodiments other change and modification.Include preferably so appended claims are intended to explain Embodiment and all change and modification for falling into disclosure range.
Obviously, those skilled in the art can carry out the disclosure essence of the various modification and variations without departing from the disclosure Refreshing range.If in this way, these modifications and variations of the disclosure belong to disclosure claim and its equivalent technologies range it Interior, the disclosure is also intended to include these modifications and variations.

Claims (10)

1. a kind of Time Domain Electromagnetic computational methods, including：
According to structural generation three-dimensional prism grid to be asked and planar polygons grid, wherein polygonal mesh is the straight of prism grid Section is corresponded with prism grid, and every layer of prism grid corresponds to one layer of polygonal mesh；
The basic function of prism grid and the basic function of polygonal mesh according to prism grid and polygonal mesh are set respectively, made more Each basic function of side shape grid is equal to each basic function that corresponding prism grid selects a bottom surface；
Spacer step iteratively solves on time；
Judge that each grid to be asked belongs to 3D region or 2 dimensional region；
To each grid in 3D region using three-dimensional process, two-dimensional process is used to each grid in 2 dimensional region；
To all grids, using being uniformly processed.
2. Time Domain Electromagnetic computational methods according to claim 1, which is characterized in that
The three-dimensional process is to treat that grid is asked to carry out matrix fill-in using prismatic mesh time domain finite element method；
The two-dimensional process is to treat that the corresponding triangular mesh of grid is asked to use triangle time domain finite element method into row matrix Filling；
Described be uniformly processed is that the matrix simultaneous that the matrix that three-dimensional process generates is generated with two-dimensional process is unified into unified matrix It solves.
3. Time Domain Electromagnetic computational methods according to claim 1, which is characterized in that
The three-dimensional process is to traverse the adjacent mesh of grid to be asked, if the adjacent mesh of grid to be asked belongs to space Domain is then treated and grid is asked directly to be solved using three-dimensional algorithm, if the adjacent mesh of grid to be asked has grid to belong to 2 dimensional region, Then the two-dimensional grid electromagnetic field value of the previous time step of the grid is converted into treat again after three-dimensional grid electromagnetic field value and seeks grid It is solved using three-dimensional algorithm；
Wherein three-dimensional algorithm uses prism grid；Any net region of a time step in office wait ask electromagnetic field value only by it is previous when This grid of spacer step and the electromagnetic field value of adjacent mesh determine, and the electromagnetic field value that other grids are walked with current time is unrelated, each The electromagnetic field value of grid is solved independently respectively in current time step；
The two-dimensional process is to traverse the adjacent mesh of grid to be asked, if the adjacent mesh of grid to be asked belongs to two-dimentional area Domain is then treated and grid is asked directly to be solved using two-dimentional algorithm, if the adjacent mesh of grid to be asked has grid to belong to 3D region, Then the three-dimensional grid electromagnetic field value of the previous time step of the grid is converted into treat again after two-dimensional grid electromagnetic field value and seeks grid It is solved using two-dimentional algorithm；
Wherein two-dimentional algorithm uses polygonal mesh；The electromagnetic field value to be asked of any grid of a time step in office is only by the previous time The electromagnetic field value for walking this grid and adjacent mesh determines, and the electromagnetic field value that other grids are walked with current time is unrelated, each net The electromagnetic field value of lattice is solved independently respectively in current time step；
It is described that no operation is uniformly processed.
4. Time Domain Electromagnetic computational methods according to claim 3, which is characterized in that
The prism grid is prismatic mesh, and the three-dimensional algorithm is solved using the slightly golden algorithm of the discontinuous character used in proper names and in rendering some foreign names of DGTD time domains；
The polygonal mesh is triangular mesh, and the two dimension algorithm is solved using the slightly golden algorithm of the discontinuous character used in proper names and in rendering some foreign names of DGTD time domains.
5. the Time Domain Electromagnetic computational methods according to any claim in Claims 1-4, which is characterized in that described Two-dimensional process, if there is the multilayer prism grid formed by the stretching of same polyhedron in grid, and each layer prism grid 2 dimensional region is belonged to, then the multi-layer net is reduced to single layer mesh.
6. a kind of Time Domain Electromagnetic computing device, including：
Mesh module is set：According to structural generation three-dimensional prism grid to be asked and planar polygons grid, wherein polygonal mesh It is the straightforward face of prism grid, is corresponded with prism grid, every layer of prism grid corresponds to one layer of polygonal mesh；
Basic function module is set：The basic function and polygon latticed of prism grid are set respectively according to prism grid and polygonal mesh The basic function of lattice makes each basic function of polygonal mesh be equal to each basic function that corresponding prism grid selects a bottom surface；
Time iteration module：Spacer step iteratively solves on time；
Judgment module：Judge that each grid to be asked belongs to 3D region or 2 dimensional region；
Computing module one：To each grid in 3D region using three-dimensional process, each grid in 2 dimensional region is used Two-dimensional process；
Computing module two：To all grids, using being uniformly processed.
7. Time Domain Electromagnetic computing device according to claim 6, which is characterized in that
Three-dimensional process in the computing module one is to treat that grid is asked to carry out square using prismatic mesh time domain finite element method Battle array filling；Two-dimensional process in the computing module one is to treat that the corresponding triangular mesh of grid is asked using triangle time domain to have The first method of limit carries out matrix fill-in；
Being uniformly processed in the computing module two is the matrix for generating three-dimensional process and the matrix simultaneous of two-dimensional process generation Into unified matrix Unified Solution.
8. Time Domain Electromagnetic computing device according to claim 6, which is characterized in that
Three-dimensional process in the computing module one is to traverse the adjacent mesh of grid to be asked, if the adjacent mesh of grid to be asked 3D region is belonged to, then treats and grid is asked directly to be solved using three-dimensional algorithm, if the adjacent mesh of grid to be asked has grid Belong to 2 dimensional region, then the two-dimensional grid electromagnetic field value of the previous time step of the grid is converted into after three-dimensional grid electromagnetic field value It treats again and grid is asked to be solved using three-dimensional algorithm；
Wherein three-dimensional algorithm uses prism grid；Any net region of a time step in office wait ask electromagnetic field value only by it is previous when This grid of spacer step and the electromagnetic field value of adjacent mesh determine, and the electromagnetic field value that other grids are walked with current time is unrelated, each The electromagnetic field value of grid is solved independently respectively in current time step；
Two-dimensional process in the computing module one is to traverse the adjacent mesh of grid to be asked, if the adjacent mesh of grid to be asked 2 dimensional region is belonged to, then treats and grid is asked directly to be solved using two-dimentional algorithm, if the adjacent mesh of grid to be asked has grid Belong to 3D region, then the three-dimensional grid electromagnetic field value of the previous time step of the grid is converted into after two-dimensional grid electromagnetic field value It treats again and grid is asked to be solved using two-dimentional algorithm；
Wherein two-dimentional algorithm uses polygonal mesh；The electromagnetic field value to be asked of any grid of a time step in office is only by the previous time The electromagnetic field value for walking this grid and adjacent mesh determines, and the electromagnetic field value that other grids are walked with current time is unrelated, each net The electromagnetic field value of lattice is solved independently respectively in current time step；
No operation is uniformly processed in the computing module two.
9. Time Domain Electromagnetic computing device according to claim 8, which is characterized in that
The prism grid is prismatic mesh, and the three-dimensional algorithm is solved using the slightly golden algorithm of the discontinuous character used in proper names and in rendering some foreign names of DGTD time domains；
The polygonal mesh is triangular mesh, and the two dimension algorithm is solved using the slightly golden algorithm of the discontinuous character used in proper names and in rendering some foreign names of DGTD time domains.
10. the Time Domain Electromagnetic computational methods according to any claim in claim 6 to 10, which is characterized in that institute Two-dimensional process is stated, if there is the multilayer prism grid formed by the stretching of same polyhedron in grid, and each layer prism net Lattice belong to 2 dimensional region, then the multi-layer net are reduced to single layer mesh.
CN201611192392.1A 2016-12-21 2016-12-21 A kind of Time Domain Electromagnetic computational methods and device Pending CN108228938A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201611192392.1A CN108228938A (en) 2016-12-21 2016-12-21 A kind of Time Domain Electromagnetic computational methods and device

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201611192392.1A CN108228938A (en) 2016-12-21 2016-12-21 A kind of Time Domain Electromagnetic computational methods and device

Publications (1)

Publication Number Publication Date
CN108228938A true CN108228938A (en) 2018-06-29

Family

ID=62650902

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201611192392.1A Pending CN108228938A (en) 2016-12-21 2016-12-21 A kind of Time Domain Electromagnetic computational methods and device

Country Status (1)

Country Link
CN (1) CN108228938A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112327374A (en) * 2020-10-15 2021-02-05 广州市市政工程设计研究总院有限公司 DGTD forward modeling method for GPU ground penetrating radar complex medium

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1301812B1 (en) * 2000-06-29 2005-10-12 Object Reservoir, Inc. Method and system for modeling geological structures using an unstructured four-dimensional mesh
CN102332055A (en) * 2011-09-26 2012-01-25 南京航空航天大学 Simulative calculation method for extremely-low-frequency electromagnetic waves
CN105022850A (en) * 2014-04-25 2015-11-04 南京理工大学 Surface acoustic wave device modeling method
CN105374064A (en) * 2015-11-17 2016-03-02 中国矿业大学(北京) Three-dimensional streamline visualization method for groundwater flow field
CN105893678A (en) * 2016-04-01 2016-08-24 吉林大学 FDTD (Finite-Difference Time-Domain)-based three-dimensional induction-polarization double-field numerical simulation method

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1301812B1 (en) * 2000-06-29 2005-10-12 Object Reservoir, Inc. Method and system for modeling geological structures using an unstructured four-dimensional mesh
CN102332055A (en) * 2011-09-26 2012-01-25 南京航空航天大学 Simulative calculation method for extremely-low-frequency electromagnetic waves
CN105022850A (en) * 2014-04-25 2015-11-04 南京理工大学 Surface acoustic wave device modeling method
CN105374064A (en) * 2015-11-17 2016-03-02 中国矿业大学(北京) Three-dimensional streamline visualization method for groundwater flow field
CN105893678A (en) * 2016-04-01 2016-08-24 吉林大学 FDTD (Finite-Difference Time-Domain)-based three-dimensional induction-polarization double-field numerical simulation method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
CLÉMENT DUROCHAT ET AL: "High order non-conforming multi-element discontinuous Galerkin method for time domain electromagnetics", 《APPLIED MATHEMATICS AND COMPUTATION》 *
YAO-JIANG ZHANG; ET AL: "An Efficient Hybrid Finite-Element Analysis of Multiple Vias Sharing the Same Anti-Pad in an Arbitrarily Shaped Parallel-Plate Pair", 《IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES》 *
张双文: "时域有限元法及其截断边界条件的研究", 《中国博士学位论文全文数据库电子期刊 基础科学辑》 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112327374A (en) * 2020-10-15 2021-02-05 广州市市政工程设计研究总院有限公司 DGTD forward modeling method for GPU ground penetrating radar complex medium

Similar Documents

Publication Publication Date Title
Chen et al. Discontinuous Galerkin time-domain methods for multiscale electromagnetic simulations: A review
Wagner et al. Efficient computation of persistent homology for cubical data
CN111898330B (en) Integrated circuit electromagnetic response calculation method and device based on multilevel parallel strategy
JP5255714B2 (en) Three-dimensional fluid simulation method
Chen et al. ParAFEMCap: A parallel adaptive finite-element method for 3-D VLSI interconnect capacitance extraction
Chai et al. Fast ${\cal H} $-Matrix-Based Direct Integral Equation Solver With Reduced Computational Cost for Large-Scale Interconnect Extraction
Dault et al. The generalized method of moments for electromagnetic boundary integral equations
Yang et al. Development of 3D PUFEM with linear tetrahedral elements for the simulation of acoustic waves in enclosed cavities
Persova et al. Improving the computational efficiency of solving multisource 3-D airborne electromagnetic problems in complex geological media
Chen et al. A memory-efficient implementation of perfectly matched layer with smoothly varying coefficients in discontinuous Galerkin time-domain method
Mousel A massively parallel adaptive sharp interface solver with application to mechanical heart valve simulations
Zhong et al. Fast calculation of scattering by 3-D inhomogeneities in uniaxial anisotropic multilayers
Xie et al. Parallel adaptive finite element algorithms for solving the coupled electro-diffusion equations
CN108228938A (en) A kind of Time Domain Electromagnetic computational methods and device
Sarakorn 2-D magnetotelluric modeling using finite element method incorporating unstructured quadrilateral elements
Marek et al. A parallel boundary element method for the electromagnetic analysis of large structures with lossy conductors
Coyle et al. Evidence of exponential convergence in the computation of Maxwell eigenvalues
CN111339688A (en) Method for solving rocket simulation model time domain equation based on big data parallel algorithm
Liu et al. Layered ${\cal H} $-Matrix Based Inverse and LU Algorithms for Fast Direct Finite-Element-Based Computation of Electromagnetic Problems
Rautio et al. The unified-FFT algorithm for fast electromagnetic analysis of planar integrated circuits printed on layered media inside a rectangular enclosure
IT202100015602A1 (en) PROCEDURE FOR CALCULATING PHYSICAL QUANTITIES OF A CONDUCTIVE BODY, CORRESPONDING PROCESSING SYSTEM AND COMPUTER PRODUCT
CN108345704A (en) A kind of explicit time iteration Time Domain Electromagnetic computational methods and device
Feng et al. Choking loops on surfaces
JP2005044331A (en) Apparatus and program for analyzing distributed constant in transmission line
Kosmanis et al. A systematic and topologically stable conformal finite-difference time-domain algorithm for modeling curved dielectric interfaces in three dimensions

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
WD01 Invention patent application deemed withdrawn after publication

Application publication date: 20180629

WD01 Invention patent application deemed withdrawn after publication