CN109684740A - A kind of electromagnetism multiscale simulation method based on hybrid grid and time step - Google Patents
A kind of electromagnetism multiscale simulation method based on hybrid grid and time step Download PDFInfo
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Abstract
The invention belongs to time-domain calculation electromagnetism fields, are related to a kind of electromagnetism multiscale simulation method based on hybrid grid and time step.The present invention is by being macro-scale and micro-scale two parts by multiple dimensioned time domain electromagnetic PROBLEM DECOMPOSITION, realize Scale separation, the solution scale of former problem is effectively reduced, and discrete using being suitble to the hybrid grid of its feature to carry out in microscopic units, further reduced it and solve freedom degree.In terms of time iteration, independent time step is used for different microscopic units and carries out time discrete, effectively prevents the too small disadvantage for causing time iteration number excessive of localized micro size of mesh opening.After going out microscopic information by microcosmic problem solving, the coupling between Macro Problems and microcosmic problem is realized, substituted into Macro Problems and solution is iterated using macroscopic time step-length, be finally reached the technical effect of the multiple dimensioned time domain electromagnetic problem of Efficient Solution.
Description
Technical field
The invention belongs to time-domain calculation electromagnetism fields, and it is more to be related to a kind of electromagnetism based on hybrid grid and time step
Dimension calculation method.
Background technique
Modernization battlefield on, military aircraft, naval vessels, battlebus etc. arms equipment all carry a large amount of electronic weaponry, this
A little weapon some can detecte local military situation, and what is had can carry out electronic countermeasure operation with directional transmissions high power electronic pulse.Cause
This, there is the complicated electromagnet phenomenons such as extremely complex electromagnetic interference and high-frequency impulse in certain battlefield space.Information
Chemical weapons installing is standby be for complex electromagnetic environment it is very sensitive, in order to guarantee that these equipment can be in complicated battlefield electromagnetism
Its effectiveness still is played under environment, needs the multiple dimensioned electromagnetic environment of complexity of the energy sufficiently Synthetic Theatre of War in design, such ability
The analysis and design for equiping with arms equipment for electromagnetism provide sufficient theory support.
In addition, the structure of large scale integrated circuit and modern antennas is more and more multiple with the progress of electronic fabrication processes
It is miscellaneous, and there is complicated Multi-scale model Electricity Functional to meet material appearance, such as photonic crystal, super magnetic material, thermo electric material and light
Material etc. is manipulated, its difficulty for carrying out electromagnetical analogies is risen with it.For fine simulation these complicated circuits, novel day
The electronic system of line and material with complex composition, needs the influence to its all microstructure all to take in, because its structure is multiple
Miscellaneous, size differs greatly, and carries out research association to it and faces bigger difficulty.
Traditional numerical method encounters bigger difficulty, such as above-mentioned complex electromagnetic environment when handling Issues On Multi-scales
Under electromagnetic interference, novel nano structure electromagnetic material performance evaluation etc..These electromagnetic problems have typical Analysis On Multi-scale Features,
The electric fine structure that there is some details to be much smaller than wavelength, and some has the TV university structure much larger than wavelength.For this several
What very big problem of scale span, it is discrete according to traditional method progress grid, domain is solved in order to enable grid to accurately calculate
Geometry, material characteristics, satisfied precision can just be obtained by needing to divide grid fine enough.But it will lead to grid in this way
Number is very huge, fairly large unknown quantity, especially PSTD method can be generated in modeling process, with size of mesh opening
Reduction, the time iteration number for needing to carry out is consequently increased, this will lead to the cost of flood tide computing resource, sometimes even
Will lead to can not calculate.Therefore, how by numerical method to solve the problems, such as that extensive multiple dimensioned time domain electromagnetic is current to calculate electricity
The a big difficulty of magnetics research.
Summary of the invention
For above-mentioned there are problem or deficiency, to solve the problems, such as existing Numerical Methods Solve multiple dimensioned time domain electromagnetic on a large scale
When the huge problem of calculation amount, the electromagnetism Multi-Scale Calculation based on hybrid grid and time step that the present invention provides a kind of
Method.
A kind of electromagnetism multiscale simulation method based on hybrid grid and time step, comprising the following steps:
Step 1 establishes computation model according to actual electromagnetic problem；
Step 2, computation model built for step 1 ignore all micro details according to the needs of actual electromagnetic problem
Part carries out mesh generation on a macroscopic scale, and the solution domain of entire computation model is divided into the K macroscopic views not overlapped
Unit.The size of macro is greater than the minimum feature size solved in domain.
Step 3 considers all microstructures and microscopic information, according to needing using hybrid grid pair for actual electromagnetic problem
Macro carries out second of mesh generation, obtains microcosmic refined net.
The subdivision of microscopic units carries out on the discrete-base of macro, and the size of microscopic units is not more than macro
The characteristic dimension of internal microstructure.There is no the part of microstructure for macro inside, two dimension uses quadrilateral mesh
Subdivision, three-dimensional use hexahedral mesh；For the internal part with microstructure, two dimension uses triangular mesh subdivision, three
Wesy's quadrilateral grid.
Step 4 carries out linearly by the hybridization weak form of the golden method construct maxwell equation group of gal the Liao Dynasty, and to electromagnetic field
It decomposes.
Step 4-1, the electromagnetic problem for solving domain is established.
If solution domain is Ω ∈ R3,To solve domain boundary, wherein ΓPECFor desired electrical wall boundary, ΓABCFor ABSORPTION EDGE
Boundary, the then electromagnetic problem solved in domain are written as:
Step 4-2, the hybridization weak form of maxwell equation group is established by the golden method of gal the Liao Dynasty.
Solving domain Ω and carrying out macroscopical discrete rear region of grid is TH, unit K ∈ T after discrete in regionH.It is assumed that Pm(K)
It is not less than the polynomial space of m for dimension in unit, it is discrete come representation space with V, then there is V:={ v ∈ L2(Ω):v|K∈[Pm
(K)]3for_all(K∈TH), the golden weak form of gal the Liao Dynasty of maxwell equation group can indicate are as follows:
All macro boundary face set after discrete are denoted as εH, at element sides interfaceThere are tangential components
Function space Λ can be expressed asIntroduced cross variable λ ∈ Λ, and by formula (2)
Become hybrid versions:
Step 4-3, it needs to carry out linear decomposition to electromagnetic field according to Macro Problems and microcosmic problem
Electric field and magnetic field are subjected to linear decomposition, are decomposed into two parts:
Wherein,WithComponent only hybridizes variable λ with the moment and macroscopic boundary condition is related, with the electricity inside unit
Magnetic field and the function of currentIt is unrelated, andWith HfComponent and internal electromagnetic field and the function of currentIt is related, and hybridize variable
λ and macroscopic boundary condition are unrelated.The purpose for carrying out linear decomposition to electromagnetic field is by the effect of macro-scale boundary condition and list
The effect of first built-in field separates, to be able to construct global Macro Problems and microcosmic local problem, and is easy to implement macro
Coupling between sight problem and microcosmic problem.
Step 5 introduces multiple dimensioned basic function, and it is discrete to carry out basic function, is analyzed, is constructed macro in macro-scale later
It sees " global issue ".
Step 5-1, multiple dimensioned basic function is introduced, and it is discrete to carry out basic function.
Macro Problems are established on the interface of macro, and enabling ψ first is the basic function on macroscopical coarse grid face, and
Enable dim (ΛH) indicate the total freedom degree dimension of macro interface.Because amount relevant to macroscopical grid mainly have λ,
AndSo on a macroscopic scale to hybridization variable λ and electromagnetic fieldIt may be expressed as: after discrete
Wherein αiFor the undetermined coefficient of macro-scale, need to solve to obtain by Macro Problems, and
For multiple dimensioned basic function, its concrete form can just be obtained by needing to be solved in microscopic units by numerical method.
Step 5-2, it is analyzed by macro-scale, constructs macroscopical " global issue ".
The essential purpose of Macro Problems is to establish the entire connectivity for solving domain, allows each macro coupling each other
It closes, if there are following forms for global issue there is no energy loss (as there was only the boundary PEC) in region:
If macro-regions there are absorbing boundary and excitation, need to introduce boundary information global issue, ABSORPTION EDGE is introduced
Global issue behind boundary and excitation are as follows:
After macro-scale progress basic function is discrete, global issue is following form:
Step 6 carries out independent time and spatial spreading in microscopic units, obtains the basic function of microscopic units and micro-
Local time stepping is seen, and combines actual grid search-engine, integrates microscopic units matrix, is constructed microcosmic " local problem ", to
The solution of multiple dimensioned basic function.
Step 6-1, independent time and spatial spreading are carried out on localized micro unit.
By each macro K ∈ THAs independent Finite Element Space carry out it is discrete, it is discrete after region be denoted asOften
The zone of dispersion of one microscopic units is denoted as k, then hasφ is enabled to indicate the basic function on microcosmic thin unit,It is macro
Total freedom degree of localized micro grid in unit K is seen, then multiple dimensioned basic function is discrete in micro-scale are as follows:
In terms of time discrete, macroscopic time interval △ t:=[t of the selection based on macroscopical grid firstn-1,tn], because
Requirement of the micro grid of each local unit to time step is different, it is therefore desirable to need to be arranged according to microscopic units
Meet the local time interval of its requirement, local time interval is obtained by macroscopic time interval is further discrete.Enable τKFor macroscopic view
Local time stepping in unit K subdomain is divided into s interval for macroscopic time interval, then has tn-1+sτK=tn。
Step 6-2, microcosmic " local problem " is constructed.
Microcosmic " local problem " is constructed using time-discontinuous Galerkin method DGTD, it is micro- in secondary discrete rear macro K
Elemental area set is seen to be denoted asIt enablesIndicate the face of microscopic units.For the face on the face boundary not comprising macro K
Set is denoted asConvolution (3) can be obtained with interruption Galerkin method:
By linear decomposition, formula (10) is decomposed, available local problem:
Wherein { e } and { h } indicates numerical flux, because constructed by DGTD method in microcosmic question essence,
Numerical flux can be used central flux, windward flux or penalize a flux.Microscopic units and macro intersection { e } with
The value of { h } is the value e and h of actual electromagnetic field.And [| φ |]=nk×φk+nk'×φk', wherein k' is indicated adjacent with k
Microscopic units number.
Step 6-3, each microscopic units are accordingly solved, integrates each microscopic units matrix.
Step 7 carries out local problem's solution using the independent microcosmic time step of their own in each microscopic units
Obtained multiple dimensioned basic function is substituted into macroscopical global issue after the completion of the iterative solution of all local problems by time iteration,
The solution of global issue is carried out with macroscopic time step-length.
Step 8 updates electric and magnetic fields, and continues through time iteration and obtain the solution of required Time Domain Electromagnetic.
Further, macroscopic time step-length is consistent with the maximum microscopic units time step of grid in the step 7, so that
The time iteration effect for obtaining entirely solution domain is best.
In conclusion the present invention is by being macro-scale and micro-scale two by multiple dimensioned time domain electromagnetic PROBLEM DECOMPOSITION
Point, Scale separation is realized, effectively reduces the solution scale of former problem, and use in microscopic units and be suitble to its feature
Hybrid grid progress is discrete, further reduced its and solves freedom degree.In terms of time iteration, for different microscopic units
Time discrete is carried out using independent time step, effectively prevents that localized micro size of mesh opening is too small to lead to time iteration
The excessive disadvantage of number.After going out microscopic information by microcosmic problem solving, the coupling between Macro Problems and microcosmic problem is realized
It closes, substituted into Macro Problems and solution is iterated using macroscopic time step-length.It is finally reached the multiple dimensioned time domain of Efficient Solution
The technical effect of electromagnetic problem.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Fig. 2 is macroscopical mesh generation schematic diagram of embodiment.
Fig. 3 is the localized micro element subdivision figure of embodiment.
Fig. 4 is that the isoparametric coordinate of embodiment converts schematic diagram.
Fig. 5 is the plane wave field distribution result of embodiment.
Fig. 6 is that the point of observation A code calculated result of embodiment and theoretical value compare.
Fig. 7 is the L2 norm error of embodiment.
Specific embodiment
Implementation of the invention is described further with reference to the accompanying drawing.
Refering to fig. 1, the present invention provides a kind of time-domain electromagnetics based on hybrid grid and incorporation time step-length is multiple dimensioned
Calculation method, detailed process are as follows:
In step 1, the present embodiment, the square area with side length for 0.5m is propagated example and is analyzed, according to what is solved
The type of actual electromagnetic field selects computation model to be calculated.
Step 2, computation model built for step 1 ignore all micro details according to the needs of actual electromagnetic problem
Part carries out mesh generation on a macroscopic scale, will entirely solve domain (computation model) and be divided into what K=64 was not overlapped
Macro, macroscopical grid dividing of use as shown in Fig. 2, and each macro side be further divided into two sections.It is macroscopical single
The size of member is greater than the minimum feature size solved in domain.
Step 3 considers all microstructures and microscopic information, according to needing using hybrid grid to macro for problem
Second of mesh generation is carried out, microcosmic refined net is obtained.
The subdivision of microscopic units carries out on macro discrete-base, and the size of microscopic units is no more than in macro
The characteristic dimension of portion's microstructure.In secondary subdivision, hybrid grid is used, needs to select according to the actual situation suitable
Microcosmic refined net carries out subdivision, is had using quadrilateral mesh subdivision for inside for the part of internal not microstructure
There is the part of microstructure using triangular mesh subdivision.The micro grid finally used divides as shown in Figure 3.
Step 4 carries out linearly by the hybridization weak form of the golden method construct maxwell equation group of gal the Liao Dynasty, and to electromagnetic field
It decomposes.
Step 4-1, the electromagnetic problem for solving domain is established.
If solution domain is Ω ∈ R3,To solve domain boundary, wherein ΓPECFor desired electrical wall boundary, ΓABCFor ABSORPTION EDGE
Boundary then solves the electromagnetic problem such as formula (1) in domain.
Step 4-2, the hybridization weak form of maxwell equation group is established by the golden method of gal the Liao Dynasty.
Solving domain Ω and carrying out macroscopical discrete rear region of grid is TH, unit K ∈ T after discrete in regionH.It is assumed that Pm(K)
It is not less than the polynomial space of m for dimension in unit, it is discrete come representation space with V, then there is V:={ v ∈ L2(Ω):v|K∈[Pm
(K)]3for_all(K∈TH), the golden weak form of gal the Liao Dynasty of maxwell equation group can be expressed as formula (2).
All macro boundary face set after discrete are denoted as εH, at element sides interfaceThere are tangential components
Function space Λ can be expressed asIntroduced cross variable λ ∈ Λ, and formula (2) are become
For hybrid versions (3).
Step 4-3, it needs to carry out linear decomposition to electromagnetic field according to Macro Problems and microcosmic problem；
Electric field and magnetic field are subjected to linear decomposition, two parts are decomposed into, as shown in formula (4).
Step 5 introduces multiple dimensioned basic function, and it is discrete to carry out basic function, is analyzed, is constructed macro in macro-scale later
It sees " global issue ".
Step 5-1, multiple dimensioned basic function is introduced, and it is discrete to carry out basic function.
Macro Problems primarily rest on macro interface, and enabling ψ first is the basic function on macroscopical coarse grid face, and
And enable dim (ΛH) indicate the total freedom degree dimension of macro interface.Because amount relevant to macroscopical grid mainly hasAndSo on a macroscopic scale to hybridization variable λ and electromagnetic fieldFormula (5) are represented by after discrete.
Step 5-2, it is analyzed by macro-scale, constructs macroscopical " global issue ".
The essential purpose of Macro Problems is to establish the entire connectivity for solving domain, allows each local unit coupling each other
Close, therefore, inside local unit the flux of boundary should be with the flux of entire macroscopical part, because the domain is only
There are absorbing boundaries and plane wave excitation, it is therefore desirable to which absorbing boundary and excitation introduce global issue, introduce absorbing boundary and swash
It encourages shown in rear global issue such as formula (7), after macro-scale progress basic function is discrete, global issue can be write as with formula (8) institute
Show form.
Step 6 carries out independent time and spatial spreading in microscopic units, obtains the basic function of microscopic units and micro-
Local time stepping is seen, and combines actual grid search-engine, integrates microscopic units matrix, is constructed microcosmic " local problem ", to
The solution of multiple dimensioned basic function.
Step 6-1, independent time and spatial spreading are carried out on localized micro unit.
By each unit K ∈ THCarried out as independent Finite Element Space it is discrete, it is discrete after region be denoted asIt is each
A small zone of dispersion is denoted as k, then hasIt enables φ indicate the basic function on microcosmic thin unit, and enablesIt is macroscopical single
Total freedom degree of localized micro grid in first K, then multiple dimensioned basic function can be discrete as shown in formula (9) in micro-scale.
In terms of time discrete, the time interval of macroscopic time interval and rectangle micro grid unit area is kept one
It causes, the time interval of triangle micro grid unit area is chosen for the 1/3 of rectangle part.
Step 6-2, microcosmic " local problem " is constructed using time-discontinuous Galerkin method DGTD, secondary discrete rear macro
Microscopic units face set in K is denoted asIt enablesIndicate the face of microscopic units.For not including the face side of macro K
The face set on boundary is denoted asConvolution (3) and interruption Galerkin method can obtain formula (10).
By linear decomposition, formula (10) is decomposed, the available local problem as shown in formula (11) (12):
Wherein { e } and { h } indicates numerical flux, because being to be constructed in microcosmic question essence by DGTD method, implements
Numerical flux is using flux windward in example.The value of { e } and { h } is the value e and h of actual electromagnetic field at elementary boundary.And
[| φ |]=nk×φk+nk'×φk', wherein k' indicates the microscopic units number adjacent with k.
Step 6-3, localized micro cell matrix is integrated；
In the present embodiment, microscopic units grid is made of triangular mesh and quadrilateral mesh, for triangular mesh,
Its mass matrixWith stiffness matrixThere are analytic solutions, therefore we are available:
Wherein, SkFor the area of unit, δ (i, j) is a function, and when i=j duration is 1, otherwise value is 0.Size three
Triangle interior is directed toward in the length of polygonal limit, direction.
It for quadrilateral mesh, needs to use isoparametric conversion and is solved, isoparametric conversion is as shown in figure 4, be firstly introduced into ginseng
Number coordinate (ξ, η), the coordinate transformation relation with rectangular co-ordinate (x, y) are as follows:
Wherein,(ξ1,η1)=(- 1, -1), (ξ2,η2)=(1, -1), (ξ1,η1)
=(1,1), (ξ1,η1)=(- 1,1).
Therefore the mass matrix of quadrilateral meshIt can be write as parameter coordinate form:
Wherein [J] is Jacobian matrix, under two-dimensional case are as follows:
For quadrilateral mesh stiffness matrixAccording to partial differential theory, have:
Therefore, stiffness matrixIt can be written as:
Herein, mass matrixWith stiffness matrixAll without analytic solutions, it is therefore desirable to be carried out by numerical integration
It solves.
For sediment flux ratio matrix Fh(only coefficient does not include vector portion) is a line integral under two-dimensional case,
Line integral basic function can be indicated are as follows:
Wherein ξ is the relative position on the online segment unit of coordinate points, and therefore, sediment flux ratio matrix F can indicate are as follows:
Coefficient m and n indicate element number, if m=n, integrate for same elemental area, if m ≠ n, for adjacent cells.
It is solved later by analytic method or numerical integration method.The sediment flux ratio matrix of triangular element and rectangular element
It can be obtained by this method.
In addition, there are one matrixes relevant to hybridization variable in local problemThis matrix is in two-dimentional feelings
Under condition be line integral, be a macro line segment basic function ψ and microscopic units line segment basic function φ integral because this two
The scale of a basic function is different, therefore also needs numerical integration and calculated.
It may finally obtain, microcosmic local problem (11) and the final matrix form of (12) are as follows:
Wherein k indicates that computing unit, k' indicate that adjacent cells, l indicate the set of place unit and adjacent cells.
Step 7 carries out local problem's solution using the independent microcosmic time step of their own in each microscopic units
Obtained multiple dimensioned basic function is substituted into macroscopical global issue after the completion of the iterative solution of all local problems by time iteration,
The solution of global issue is carried out with macroscopic time step-length.
Step 7-1, local problem is carried out using oneself independent microcosmic time step in each localized micro region to ask
The time iteration of solution.
When carrying out time iteration, time iteration is carried out to local problem first, subscript n is used for each local unit K
It indicates n-th of macroscopic time step, indicates s-th of local time's spacer step with subscript s.For rectangle microscopic units region, s=1；It is right
In triangular mesh region, s=3, time iteration form is as follows:
In actually calculating, formula (24) only needs to be calculated in first macroscopic time step, changes in the time later
It is only needed calculating formula (25) in generation, after the completion of local time's iteration, needs to solve obtained multiple dimensioned basic function numerical value
Solve eλ,ef,hλ,hfMacro Problems are substituted into be solved.
Step 7-2, the solution of global issue is carried out with macroscopic time step-length.
When solving Macro Problems, it is necessary first to macro matrix is formed by microscopic units matrix, by local minor matrix
Mh、ShIt is combined into global big matrix form MH={ Mh}、SH={ Sh, and the result that local problem is solvedAlso group
Dress is global formAnd the unit corresponding to macroscopic phase boundary finds out absorbing boundary and excitation institute
The big matrix S of corresponding overall situation coefficientA={ sa(the global big matrix of absorbing boundary coefficient) Sinc={ sinc(drive factor is global big
Matrix) and excitation Ginc={ ginc, convolution (8) can obtain the matrix form of macroscopical global issue:
Solution obtains macrovariableAfterwards, can carry out the electric field at new moment with
The update in magnetic field.
Step 8 updates electric and magnetic fields, and continues through time iteration and obtain the solution of required Time Domain Electromagnetic.
After completing the primary entire time iteration for solving domain, need to combine macrovariable and microcosmic multiple dimensioned basic function pair
Electric field and magnetic field carry out reduction update, the update method of new moment electric field and magnetic field are as follows:
Wherein, snIndicate the final moment of each local time's iteration,WithOnly need in first macroscopic time
It is calculated in step.
After having updated all electric field and magnetic field, need to carry out the calculating of subsequent time, to obtain each moment
The value of Time Domain Electromagnetic.
Field distribution result is calculated as shown in figure 5, the electric field theory value of point of observation A and code calculated value in computational domain
Comparison is as shown in fig. 6, shown in L2 error norm Error Graph 7.As can be seen that the distribution for the electric field being calculated meets practical put down
Surface wave electric field distribution law, theoretical value and code calculated value are also stable fine, and L2 norm error is stablized one when stablizing
The value of a very little, as a result correctly.
To sum up, the algorithm that the present invention uses is feasible, although the embodiment is relatively simple, it was realized
Journey covers all steps of the invention, which can be used for the calculating of increasingly complex electromagnetism problem, is finally reached efficiently
Solve the technical effect of multiple dimensioned time domain electromagnetic problem.
Claims (2)
1. a kind of electromagnetism multiscale simulation method based on hybrid grid and time step, comprising the following steps:
Step 1 establishes computation model according to actual electromagnetic problem；
Step 2, computation model built for step 1 ignore all micro details portions according to the needs of actual electromagnetic problem
Point, mesh generation is carried out on a macroscopic scale, and it is single that the solution domain of entire computation model is divided into the macroscopic view that K do not overlap
Member；The size of macro is greater than the minimum feature size solved in domain；
Step 3 considers all microstructures and microscopic information, according to needing using hybrid grid to macroscopic view for actual electromagnetic problem
Unit carries out second of mesh generation, obtains microcosmic refined net；
The subdivision of microscopic units carries out on the discrete-base of macro, and the size of microscopic units is no more than inside macro
The characteristic dimension of microstructure；There is no a part of microstructure for macro inside, two dimension using quadrilateral mesh subdivision,
Three-dimensional uses hexahedral mesh；For the internal part with microstructure, two dimension uses triangular mesh subdivision, three Wesys four
Side volume mesh；
Step 4, by the hybridization weak form of the golden method construct maxwell equation group of gal the Liao Dynasty, and electromagnetic field is linearly divided
Solution；
Step 4-1, the electromagnetic problem for solving domain is established；
If solution domain is Ω ∈ R3,To solve domain boundary, wherein ΓPECFor desired electrical wall boundary, ΓABCFor absorbing boundary, then
The electromagnetic problem solved in domain is written as:
Step 4-2, the hybridization weak form of maxwell equation group is established by the golden method of gal the Liao Dynasty；
Solving domain Ω and carrying out macroscopical discrete rear region of grid is TH, unit K ∈ T after discrete in regionHIf PmIt (K) is unit
Interior dimension is not less than the polynomial space of m, discrete come representation space with V, then has V:={ v ∈ L2(Ω):v|K∈[Pm(K)]3for_all(K∈TH), the golden weak form of gal the Liao Dynasty of maxwell equation group can indicate are as follows:
All macro boundary face set after discrete are denoted as εH, at element sides interfaceThere are tangential component functions
Space Λ can be expressed asIntroduced cross variable λ ∈ Λ, and formula (2) is become miscellaneous
Friendship form:
Step 4-3, it needs to carry out linear decomposition to electromagnetic field according to Macro Problems and microcosmic problem；
Electric field and magnetic field are subjected to linear decomposition, are decomposed into two parts:
Wherein,WithComponent only hybridizes variable λ with the moment and macroscopic boundary condition is related, with the electromagnetic field inside unit
And the function of currentIt is unrelated, andWith HfComponent and internal electromagnetic field and the function of currentIt is related, and hybridize variable λ and macro
It is unrelated to see boundary condition；
Step 5 introduces multiple dimensioned basic function, carries out analysis in macro-scale and constructs macroscopical global issue, on macroscopical coarse grid
It carries out discrete；
Step 5-1, multiple dimensioned basic function is introduced, and it is discrete to carry out basic function；
Macro Problems are established on the interface of macro, and enabling ψ first is the basic function on macroscopical coarse grid face, and is enabled
dim(ΛH) indicate the total freedom degree dimension of macro interface；On a macroscopic scale to hybridization variable λ and electromagnetic field
It may be expressed as: after discrete
Wherein αiFor the undetermined coefficient of macro-scale, need to solve to obtain by Macro Problems, andef、hfIt is multiple dimensioned
Basic function is solved to obtain its concrete form in microscopic units by numerical method；
Step 5-2, it is analyzed by macro-scale, it is preliminary to construct macroscopical global issue；
If energy loss is not present in region, there are following forms for global issue:
If there are absorbing boundary and excitations for macro-regions, boundary information is introduced into global issue, introduces absorbing boundary and excitation
Global issue afterwards are as follows:
After macro-scale progress basic function is discrete, global issue is following form:
Step 6 carries out independent time and spatial spreading in microscopic units, obtain microscopic units basic function and microcosmic office
Portion's time step, and actual grid search-engine is combined, microscopic units matrix is integrated, microcosmic local problem is constructed, to multiple dimensioned
The solution of basic function；
Step 6-1, independent time and spatial spreading are carried out on localized micro unit；
By each macro K ∈ THAs independent Finite Element Space carry out it is discrete, it is discrete after region be denoted asEach
The zone of dispersion of microscopic units is denoted as k, then hasφ is enabled to indicate the basic function on microcosmic thin unit,For macro K
Total freedom degree of interior localized micro grid, then multiple dimensioned basic function is discrete in micro-scale are as follows:
In terms of time discrete, macroscopic time interval Δ t:=[t of the selection based on macroscopical grid firstn-1,tn], according to microcosmic list
The local time interval for meeting its requirement is arranged in first needs, and local time interval is obtained by macroscopic time interval is further discrete
It arrives；Enable τKFor the local time stepping in macro K subdomain, it is divided into s interval for macroscopic time interval, then has tn-1+sτK=
tn；
Step 6-2, microcosmic local problem is constructed；
Microcosmic local problem is constructed using time-discontinuous Galerkin method DGTD, the microscopic units in secondary discrete rear macro K
Face set is denoted asIt enablesIndicate the face of microscopic units；The face set on the face boundary not comprising macro K is denoted asConvolution (3) can be obtained with interruption Galerkin method:
By linear decomposition, formula (10) is decomposed, available local problem:
Wherein { e } and { h } indicate numerical flux, and numerical flux flux or penalizes a flux using central flux, windward；In element sides
The value of { e } and { h } is the value e and h of actual electromagnetic field at boundary；[| φ |]=nk×φk+nk'×φk', wherein k' indicate and k
Adjacent microscopic units number；
Step 6-3, each microscopic units are accordingly solved, integrates each microscopic units matrix；
Step 7, the time for carrying out local problem's solution using the independent microcosmic time step of their own in each microscopic units
Obtained multiple dimensioned basic function is substituted into macroscopical global issue, with macroscopic view after the completion of the iterative solution of all local problems by iteration
The solution of time step progress global issue；
Step 8 updates electric and magnetic fields, and continues through time iteration and obtain the solution of required Time Domain Electromagnetic.
2. the electromagnetism multiscale simulation method based on hybrid grid and time step as described in claim 1, it is characterised in that:
Macroscopic time step-length is consistent with the maximum microscopic units time step of grid in the step 7.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111079357A (en) * | 2019-10-22 | 2020-04-28 | 重庆邮电大学 | Electromagnetic interference time domain analysis method of microstrip line on PCB under action of electromagnetic wave |
| CN111090958A (en) * | 2019-12-30 | 2020-05-01 | 西北工业大学 | Electromagnetic wave time domain efficient numerical mixing algorithm based on sub-grid technology |
| CN111931457A (en) * | 2020-09-27 | 2020-11-13 | 北京智芯仿真科技有限公司 | Multilayer integrated circuit electromagnetic field calculation method and device based on mixed order finite element |
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Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110251832A1 (en) * | 2010-04-13 | 2011-10-13 | CST-Computer Simulation Technology AG | Method, device and computer program product for determining an electromagnetic near-field of a field excitation source of an electrical system |
| CN104731996A (en) * | 2013-12-24 | 2015-06-24 | 南京理工大学 | Simulation method for rapidly extracting transient scattered signals of electric large-size metal cavity target |
| US20170315266A1 (en) * | 2016-04-29 | 2017-11-02 | Rodrick Myers | Method and system for forming and using a subsurface model in hydrocarbon operations |
| CN107908903A (en) * | 2017-12-11 | 2018-04-13 | 电子科技大学 | The matrix exponetial time decoupling method of index time integration method in complicated dispersive medium |
| CN107944141A (en) * | 2017-11-24 | 2018-04-20 | 电子科技大学 | Time-domain calculation electromagnetism numerical method based on hybridization time-discontinuous Galerkin method |
| CN107943755A (en) * | 2017-12-12 | 2018-04-20 | 电子科技大学 | The matrix exponetial dimension reduction method of the middle index time integration method of complicated dispersive medium |
| CN107992696A (en) * | 2017-12-13 | 2018-05-04 | 电子科技大学 | A kind of improved exponential time integration building method in complexity dispersive medium |
| CN108052738A (en) * | 2017-12-13 | 2018-05-18 | 电子科技大学 | The golden analysis method of high-order part unconditional stability time-discontinuous gal the Liao Dynasty of dispersive medium |
| CN108984914A (en) * | 2018-04-11 | 2018-12-11 | 电子科技大学 | A kind of quick multiscale simulation method solving complicated time domain electromagnetic problem |
| CN109190169A (en) * | 2018-08-02 | 2019-01-11 | 电子科技大学 | A kind of golden numerical method of Three-dimensional Time Domain electromagnetism hybridization time-discontinuous gal the Liao Dynasty |
| CN110502785A (en) * | 2019-07-15 | 2019-11-26 | 电子科技大学 | A kind of Three-dimensional Time Domain calculates the electromagnetism numerical method of waveguide S parameter |
-
2018
- 2018-12-27 CN CN201811606399.2A patent/CN109684740B/en active Active
Patent Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110251832A1 (en) * | 2010-04-13 | 2011-10-13 | CST-Computer Simulation Technology AG | Method, device and computer program product for determining an electromagnetic near-field of a field excitation source of an electrical system |
| CN104731996A (en) * | 2013-12-24 | 2015-06-24 | 南京理工大学 | Simulation method for rapidly extracting transient scattered signals of electric large-size metal cavity target |
| US20170315266A1 (en) * | 2016-04-29 | 2017-11-02 | Rodrick Myers | Method and system for forming and using a subsurface model in hydrocarbon operations |
| CN107944141A (en) * | 2017-11-24 | 2018-04-20 | 电子科技大学 | Time-domain calculation electromagnetism numerical method based on hybridization time-discontinuous Galerkin method |
| CN107908903A (en) * | 2017-12-11 | 2018-04-13 | 电子科技大学 | The matrix exponetial time decoupling method of index time integration method in complicated dispersive medium |
| CN107943755A (en) * | 2017-12-12 | 2018-04-20 | 电子科技大学 | The matrix exponetial dimension reduction method of the middle index time integration method of complicated dispersive medium |
| CN107992696A (en) * | 2017-12-13 | 2018-05-04 | 电子科技大学 | A kind of improved exponential time integration building method in complexity dispersive medium |
| CN108052738A (en) * | 2017-12-13 | 2018-05-18 | 电子科技大学 | The golden analysis method of high-order part unconditional stability time-discontinuous gal the Liao Dynasty of dispersive medium |
| CN108984914A (en) * | 2018-04-11 | 2018-12-11 | 电子科技大学 | A kind of quick multiscale simulation method solving complicated time domain electromagnetic problem |
| CN109190169A (en) * | 2018-08-02 | 2019-01-11 | 电子科技大学 | A kind of golden numerical method of Three-dimensional Time Domain electromagnetism hybridization time-discontinuous gal the Liao Dynasty |
| CN110502785A (en) * | 2019-07-15 | 2019-11-26 | 电子科技大学 | A kind of Three-dimensional Time Domain calculates the electromagnetism numerical method of waveguide S parameter |
Non-Patent Citations (2)
| Title |
|---|
| N.C.NGUYEN等: "Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell"s equations", 《JOURNAL OF COMPUTATIONAL PHYSICS》 * |
| 李星: "基于时域间断伽辽金方法的多尺度电磁问题研究", 《中国优秀博硕士学位论文全文数据库(博士)基础科学辑（月刊）》 * |
Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111079357A (en) * | 2019-10-22 | 2020-04-28 | 重庆邮电大学 | Electromagnetic interference time domain analysis method of microstrip line on PCB under action of electromagnetic wave |
| CN111090958A (en) * | 2019-12-30 | 2020-05-01 | 西北工业大学 | Electromagnetic wave time domain efficient numerical mixing algorithm based on sub-grid technology |
| CN111931457A (en) * | 2020-09-27 | 2020-11-13 | 北京智芯仿真科技有限公司 | Multilayer integrated circuit electromagnetic field calculation method and device based on mixed order finite element |
| CN111931457B (en) * | 2020-09-27 | 2021-01-15 | 北京智芯仿真科技有限公司 | Multilayer integrated circuit electromagnetic field calculation method and device based on mixed order finite element |
| CN113361138A (en) * | 2021-07-08 | 2021-09-07 | 电子科技大学 | Numerical solving method for nano surface plasmon non-local effect simulation |
| CN113361138B (en) * | 2021-07-08 | 2022-11-29 | 电子科技大学 | Numerical solving method for nano surface plasmon non-local effect simulation |
| CN113609816A (en) * | 2021-09-30 | 2021-11-05 | 北京智芯仿真科技有限公司 | Method and system for determining electromagnetic simulation failure frequency of multilayer large-scale integrated circuit |
| CN113609816B (en) * | 2021-09-30 | 2021-12-28 | 北京智芯仿真科技有限公司 | Method and system for determining electromagnetic simulation failure frequency of multilayer large-scale integrated circuit |
| CN116306036A (en) * | 2023-05-18 | 2023-06-23 | 南京理工大学 | Load balancing parallel method and medium of space-time mixed discrete DGTD |
| CN116306036B (en) * | 2023-05-18 | 2023-08-11 | 南京理工大学 | Load balancing parallel method and medium of space-time mixed discrete DGTD |
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