CN108984914A - A kind of quick multiscale simulation method solving complicated time domain electromagnetic problem - Google Patents
A kind of quick multiscale simulation method solving complicated time domain electromagnetic problem Download PDFInfo
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Abstract
The present invention provides a kind of quick multiscale simulation methods for solving complicated time domain electromagnetic problem, belong to Time Domain Electromagnetic and solve field.Complicated multiple dimensioned electromagnetic problem is separated into two parts: macro-scale and micro-scale by this method.It by being solved to obtain multiple dimensioned basic function in localized micro scale, and carries it into macro-scale and is solved, more accurately electromagnetic field can be obtained.Present invention efficiency when solving complicated time domain electromagnetic problem is higher, realizes Scale separation, can obtain more accurately solving on a macroscopic scale, it is easy to accomplish and it is parallel, it is a kind of multiple dimensioned electromagnetic problem numerical computation method with good stability.
Description
Technical field
The invention belongs to Time Domain Electromagnetics to solve field, in particular to a kind of to solve the quick of complicated time domain electromagnetic problem
Multiscale simulation method.
Background technique
With the continuous progress of science and technology, in Computational electromagnetics field face, fine structure is even received more and more
The problem of metrical scale.It the use of finite difference calculus is insoluble in these multiple dimensioned electromagnetic problems.And if using having
It limits first method to solve, in order to capture the variation of the physical characteristic generated on small scale, grid needs the enough essences divided
Carefully, to significantly increase calculation amount.In some special cases, because size of mesh opening variation is excessively violent, even if consumption
Many computing resources can not be solved accurately, and the problem of resulting even in can not solve.It can be seen that traditional is limited
First method often expends very big calculating time and computing resource when solving Issues On Multi-scales, and precision is not high, obtains not
Repay mistake.Therefore it needs one kind to catch the information of small scale on a macroscopic scale as far as possible in terms of Multi-Scale Calculation, while again can
Guarantee the numerical computation method of computational accuracy.
Since becoming research hotspot with Issues On Multi-scales, many different types of multiscale simulation methods are gradually mentioned
Out, including homogenization and averaging method (Homogenization Method, HM), heterogeneous multi-scale method
(Heterogeneous Multiscale Method, HMM), multi-level finite element modeling method (Multiscale Finite
Element Method, MsFEM), multi-scale finite volumetric method (Multiscale Finite Volume Method, MsFVM)
Etc..However these methods are difficult to be directly used in the solution of electromagnetism problem, and at present for the multiple dimensioned meter in terms of electromagnetism
The research of calculation method is also fewer.Although time-discontinuous Galerkin method (DGTD) can handle interruption type the problem of, have compared with
High flexibility has certain advantage in multiple dimensioned electromagnetism problem of the processing with fine structure, but it is micro- in solution
It still needs to divide independent refined net when seeing region, and is solved on single scale, it can not the change of Efficient Solution scale
Change very big problem.
Summary of the invention
To solve the above-mentioned problems, the present invention provides a kind of quick multiple dimensioned meters for solving complicated time domain electromagnetic problem
Complicated electromagnetic problem is decomposed into micro-scale and two parts of macro-scale by calculation method, by numerical method by microscopic information
It is efficiently equivalent in macro-scale, only needing to carry out problem solving in macro-scale later to can be obtained with microscopic information
High-precision result.This method not only increases the flexibility of multiple dimensioned electromagnetic problem grid dividing, and complicated more solving
Efficiency with higher when scale time domain electromagnetic problem.
A kind of quick multiscale simulation method solving complicated time domain electromagnetic problem, comprising the following steps:
Step 1, computation model is selected according to actual electromagnetic situation；
Step 2, grid dividing is carried out to solution domain, wherein be divided into macro and local microscopic units；
Step 3, the maxwell equation group for solving domain, and introduced cross variable are established, wheat is constructed by Galerkin's Procedure
The hybridization weak form of Ke Siwei equation group carries out linear decomposition to electromagnetic field；
Step 4, macro is analyzed, constructs basic function, the overall situation that macro-scale is established on macro is asked
Topic；
Step 5, pass through the time-discontinuous Galerkin method (LF2- based on second order leap-frog scheme on localized micro unit
DGTD method) time and spatial spreading are carried out, the Solve problems of localized micro unit are constructed, integrated localized micro unit is asked
Localized micro cell matrix needed for solution problem, and solved by GPU parallel method；
Step 6, obtained basic function will be solved and substitute into global issue update macrovariable, and be updated solution, obtained
Electric field magnetic field value；
Step 7, by time iteration, the solution of required Time Domain Electromagnetic is obtained.
Further, the step 2 includes following below scheme:
Step 21, domain will be solved and is divided into several macros not overlapped；
Step 22, each macro is divided into several localized micro units.
Further, the step 3 includes following below scheme:
Step 31, the maxwell equation group for solving domain is established；
Step 32, introduced cross variable, and pass through the hybridization weak form of the golden method construct maxwell equation group of gal the Liao Dynasty；
Step 33, electromagnetic field is linearly decomposed into electric and magnetic fields.
Further, the step 4 includes following below scheme:
Macro is analyzed, basic function is constructed, according to the boundary condition, macroscopic view is established on macro
The global issue of scale.
Further, the step 5 includes following below scheme:
Step 51, it is carried out using each macro as independent Finite Element Space discrete；
Step 52, according to DGTD method, the Solve problems of localized micro unit are constructed；
Step 53, it is solved by GPU parallel method.
Further, the step 6 includes following below scheme:
Obtained basic function will be solved and substitute into global issue update macrovariable, update obtains electric and magnetic fields value.
Further, the step 7 includes following below scheme:
The electric field for updating completion is substituted into the electromagnetic field update for carrying out next round again, finally obtains required time domain electricity
The solution in magnetic field.
Beneficial effects of the present invention: complicated multiple dimensioned electromagnetic problem is separated into two parts: macro-scale by this method
With micro-scale.By being solved to obtain multiple dimensioned basic function in localized micro scale, and carry it into macro-scale progress
It solves, more accurately electromagnetic field can be obtained.Present invention efficiency when solving complicated time domain electromagnetic problem is higher, realizes
Scale separation can obtain more accurately solving on a macroscopic scale, it is easy to accomplish and it is parallel, it is a kind of with good stability
Multiple dimensioned electromagnetic problem numerical computation method.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Fig. 2 is the flow chart of step 2 in Fig. 1.
Fig. 3 is the subdivision graph of macro.
Fig. 4 is the subdivision graph of localized micro unit.
Fig. 5 is the flow chart of step 3 in Fig. 1.
Fig. 6 is the flow chart of step 5 in Fig. 1
Specific embodiment
The embodiment of the present invention is described further with reference to the accompanying drawing.
Referring to Fig. 1, the present invention provides a kind of quick multiscale simulation method for solving complicated time domain electromagnetic problem,
Detailed process is as follows:
Step 1, computation model is selected according to actual electromagnetic situation.
In the present embodiment, according to the type for the actual electromagnetic field to be solved, computation model is selected to be calculated.
Step 2, grid dividing is carried out to solution domain, wherein be divided into macro and local microscopic units.
Referring to Fig. 2, step 2 is realized by following below scheme:
Step 21, domain will be solved and is divided into several macros not overlapped.
In the present embodiment, as needed, ignores electromagnetic problem details in need of consideration, carry out grid on a macroscopic scale
Subdivision.Domain will be solved, K macro is divided by coarse grid.The size of macroscopical grid only need with needed for Macro Problems
Solving precision it is related, medium, structure etc. inside unit can be non-uniform, macro subdivision such as Fig. 3 institute
Show.
Step 22, each macro is divided into several localized micro units.
In the present embodiment, after the completion of macroscopical subdivision, need further according to the characteristic dimension inside unit to each macroscopic view
Unit carries out secondary microcosmic subdivision, and the grid after subdivision belongs to micro-scale grid, localized micro unit is formed, to establish
Localized micro problem, it is as shown in Figure 4 to the secondary microcosmic subdivision of macro.
Step 3, the maxwell equation group for solving domain, and introduced cross variable are established, wheat is constructed by Galerkin's Procedure
The hybridization weak form of Ke Siwei equation group carries out linear decomposition to electromagnetic field.
Referring to Fig. 5, step 3 is realized by following below scheme:
Step 31, the maxwell equation group for solving domain is established.
In the present embodiment, maxwell equation group is introduced:
It is if solving domain For the boundary for solving domain, the region after domain Ω is discrete is TH, in region
Each unit K ∈ TH.Here, it is assumed that PpKIt (K) is unitUpper dimension is not less than pKIt is multinomial
Formula space, L2(Ω) is the square integrable space in the Ω of region, we, come the discrete of representation space, have with VThe golden weak form of gal the Liao Dynasty of maxwell equation group can indicate
Are as follows:
All element sides interfaces set after discrete is denoted as εH, at element sides interfaceThere are tangential component functions
Space Λ can be expressed as
Step 32, introduced cross variable, and pass through the hybridization weak form of the golden method construct maxwell equation group of gal the Liao Dynasty.
In the present embodiment, in zone of dispersion introduced cross variable λ, the maxwell equation group of above formula (2) weak form is become
For hybrid versions:
Step 33, electromagnetic field is linearly decomposed into electric and magnetic fields.
In the present embodiment, in order to which former PROBLEM DECOMPOSITION is preferably independent local problem and whole global issue,
Electric field and magnetic field are decomposed into two parts by the linear behavio(u)r that can use maxwell equation group:
Wherein,WithComponent only hybridizes that variable λ is related with the moment, unrelated with the function of current inside unit.AndWithComponent and internal electric currentThe electric field of effect and last moment are related with magnetic field, unrelated with boundary condition.
The purpose decomposed in this way is to separate the effect of boundary condition with the effect of unit built-in field, consequently facilitating construction
Coupling between Macro Problems and microcosmic problem.
Step 4, macro is analyzed, constructs basic function, the overall situation that macro-scale is established on macro is asked
Topic.
In the present embodiment, because hybridization variable λ is by electric field componentWith magnetic-field componentDetermination is calculated, therefore can
It is discrete with the basic function for carrying out macro-scale to three above component, enable dim (ΛH) indicate macro face total number, into
It may be expressed as: after row is discrete
Wherein αiFor the undetermined coefficient of macro-scale, ψiFor the face basic function on macroscopical coarse grid,WithIt is respectively electric
The basic function undetermined of field and magnetic field.When solving Maxwell equation, the processing of boundary condition is to solve for most important when equation
A part, temporarily first consider two class boundary conditions: desired electrical wall boundary Γp(PEC), absorbing boundary condition Γa(ABC):
It is the construction of macroscopical global issue later, the main function of global issue is to establish each local unit microcosmic
Connectivity of the part in global macro-scale.Therefore, flux of the microcosmic component of local unit at interface should be equal to whole macro
Part is seen in the flux on boundary.By taking electric field as an example, if zone boundary is the boundary PEC, there is no energy loss in boundary, then entirely
The golden form of gal the Liao Dynasty of office's problem are as follows:
If zone boundary is the boundary PEC, boundary part information should be added, the form of global issue are as follows:
Two parts are combined, and carry out the further discrete common version for obtaining global issue, specific representation
Are as follows:
At this point, total electric field and magnetic field can be written as following form:
Step 5, it is carried out time and spatial spreading on localized micro unit by LF2-DGTD method, construction part is micro-
The Solve problems of unit are seen, localized micro cell matrix needed for integrating the Solve problems of localized micro unit, and pass through GPU
Parallel method is solved.
Referring to Fig. 6, step 5 is realized by following below scheme:
Step 51, it is carried out using each macro as independent Finite Element Space discrete.
In the present embodiment, because there may be many information, such as interior media in local unit in Issues On Multi-scales
Unevenly, situations such as there are other microstructures, therefore variableWith variableIt needs with multiple dimensioned basic function table
Show, in order to accurately be solved to the two variables, needs discrete in locally progress second level and construct " local problem " to solve
These multiple dimensioned basic functions.
By each unit K ∈ THAs independent Finite Element Space carry out it is discrete, it is discrete after region be denoted asEach
Small zone of dispersion is denoted as k, then hasIntroduce the basic function on localized micro refined netWherein
For total freedom degree of the thin cell node of micro-scale in macro K, these basic functions indicate that macro K second level is discrete
The set of basic function on microcosmic thin unit afterwards, electric field can be discrete by multiple dimensioned basic function with magnetic field are as follows:
In addition, making to calculate more simple and effective, we are also an option that in step 3 to be further reduced calculation amount
Without the linear decomposition in magnetic field, only to electric field linear decomposition.It can be expressed as after magnetic field is discrete at this timeIn this way, updated magnetic can be directly obtained when solving microcosmic " local problem "
, it only needs to be updated electric field after solving Macro Problems.Solution procedure can be reduced by doing so, certain
Computational efficiency is further promoted in degree.
Step 52, according to DGTD method, the Solve problems of localized micro unit are constructed.
The set in the face of zone of dispersion is denoted asIndicate then have with γ in the face of each zonuleAnd it enablesIndicate the set for not including the face of zone boundary in region.It is discrete to partial region progress Finite Element Space, use Vh(K)
Indicate to local unit carry out microcosmic second level it is discrete after region.Have
Microcosmic " local problem ", construction complete are constructed by DGTD method, and in conjunction with the maxwell equation group of hybrid versions
Local problem's weak form are as follows:
The unit adjacent with k is indicated with k'.WithIndicate the outer normal vector on the face γ of k-th of unit,Indicate the
Outer normal vector on the face γ of k' unit, therefore have in above formula:
Local unit face after discrete is at local unit boundaryWhen,In addition, { vh}
Indicate the numerical flux in DGTD method, we are calculated using central flux herein.The representation of central flux is such as
Under:
Step 53, it is solved by GPU parallel method.
In the present embodiment, finally need to be solved by explicit time Iteration, we choose the second order frog herein
Tabbing formula is solved, and concrete form is as follows:
In addition, we are calculated using based on GPU paralleling tactic when calculating.Firstly, because LF2-DGTD method
It is a kind of explicit solution method, and it is independent of each other for solving between unit, therefore can be passed through when solving each local unit
GPU parallel method improves calculating speed.In addition, the local problem in each macro is mutually independent when solving, equally
Concurrency with height.Therefore for certain steps (for example solve by microcosmic Matrix Solving macro matrix when), herein I
Using second level GPU it is parallel, in a time step simultaneously to multiple macros carry out calculation processing, make calculating speed
Further promoted.
Step 6, obtained basic function will be solved and substitute into global issue update macrovariable, and be updated solution, obtained
Electric field magnetic field value.
In the present embodiment, after solution obtains multiple dimensioned basic function, Macro Problems can be directly substituted into further in macroscopical ruler
It is updated solution on degree, solves part in macroscopic view, it is most important that solve macro-scale component αi, from the foregoing, it can be understood that global
The form of problem is equivalent to solve one with macro seamed edge freedom degree to be total dimension as shown in (6) formula to the solution of the problem
Several systems of linear equations:
[A][αi]=[fi] (i=1~dim ΛH), (17)
Wherein,
Macroscopical componentAfter the completion of solution, that is, all electric field and magnetic field may be updated:
Step 7, by time iteration, the solution of required Time Domain Electromagnetic is obtained.
In the present embodiment, the electric field for updating completion is substituted into former problem to the electromagnetic field update for carrying out a new round again, this
A process moves in circles, and finally obtains the solution of required Time Domain Electromagnetic.
Those of ordinary skill in the art will understand that the embodiments described herein, which is to help reader, understands this
The principle of invention, it should be understood that protection scope of the present invention is not limited to such specific embodiments and embodiments.This field
Those of ordinary skill disclosed the technical disclosures can make according to the present invention and various not depart from the other of essence of the invention
Various specific variations and combinations, these variations and combinations are still within the scope of the present invention.
Claims (7)
1. a kind of quick multiscale simulation method for solving complicated time domain electromagnetic problem, which comprises the following steps:
Step 1, computation model is selected according to actual electromagnetic situation；
Step 2, grid dividing is carried out to solution domain, wherein be divided into macro and local microscopic units；
Step 3, the maxwell equation group for solving domain, and introduced cross variable are established, max is constructed by Galerkin's Procedure
The hybridization weak form of Wei equation group carries out linear decomposition to electromagnetic field；
Step 4, macro is analyzed, constructs basic function, the global issue of macro-scale is established on macro；
Step 5, pass through the time-discontinuous Galerkin method (side LF2-DGTD based on second order leap-frog scheme on localized micro unit
Method) time and spatial spreading are carried out, the Solve problems of localized micro unit are constructed, the Solve problems institute of localized micro unit is integrated
The localized micro cell matrix needed, and solved by GPU parallel method；
Step 6, obtained basic function will be solved and substitute into global issue update macrovariable, and be updated solution, obtain electric field
Magnetic field value；
Step 7, by time iteration, the solution of required Time Domain Electromagnetic is obtained.
2. the quick multiscale simulation method as described in claim 1 for solving complicated time domain electromagnetic problem, which is characterized in that institute
Stating step 2 includes following below scheme:
Step 21, domain will be solved and is divided into several macros not overlapped；
Step 22, each macro is divided into several localized micro units.
3. the quick multiscale simulation method as claimed in claim 2 for solving complicated time domain electromagnetic problem, which is characterized in that institute
Stating step 3 includes following below scheme:
Step 31, the maxwell equation group for solving domain is established；
Step 32, introduced cross variable, and pass through the hybridization weak form of the golden method construct maxwell equation group of gal the Liao Dynasty；
Step 33, electromagnetic field is linearly decomposed into electric and magnetic fields.
4. the quick multiscale simulation method as claimed in claim 3 for solving complicated time domain electromagnetic problem, which is characterized in that institute
Stating step 4 includes following below scheme:
Macro is analyzed, basic function is constructed according to the boundary condition and establishes macro-scale on macro
Global issue.
5. the quick multiscale simulation method as claimed in claim 4 for solving complicated time domain electromagnetic problem, which is characterized in that institute
Stating step 5 includes following below scheme:
Step 51, it is carried out using each macro as independent Finite Element Space discrete；
Step 52, according to DGTD method, the Solve problems of localized micro unit are constructed；
Step 53, it is solved by GPU parallel method.
6. the quick multiscale simulation method as claimed in claim 5 for solving complicated time domain electromagnetic problem, which is characterized in that institute
Stating step 6 includes following below scheme:
Obtained basic function will be solved and substitute into global issue update macrovariable, update obtains electric and magnetic fields value.
7. the quick multiscale simulation method as claimed in claim 6 for solving complicated time domain electromagnetic problem, which is characterized in that institute
Stating step 7 includes following below scheme:
The electric field for updating completion is substituted into the electromagnetic field update for carrying out next round again, finally obtains required Time Domain Electromagnetic
Solution.
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| CN109684740A (en) * | 2018-12-27 | 2019-04-26 | 电子科技大学 | A kind of electromagnetism multiscale simulation method based on hybrid grid and time step |
| 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 |
| CN113609796A (en) * | 2021-08-02 | 2021-11-05 | 中国船舶科学研究中心 | Multi-scale ship instability and capsizing evaluation method considering multi-liquid-tank sloshing |
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| CN113609796A (en) * | 2021-08-02 | 2021-11-05 | 中国船舶科学研究中心 | Multi-scale ship instability and capsizing evaluation method considering multi-liquid-tank sloshing |
| CN113609796B (en) * | 2021-08-02 | 2023-05-23 | 中国船舶科学研究中心 | Multi-scale ship body instability overturning assessment method considering multi-liquid tank sloshing |
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