CN107992696B - Improved exponential time integral construction method in complex dispersion medium - Google Patents

Improved exponential time integral construction method in complex dispersion medium Download PDF

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CN107992696B
CN107992696B CN201711324894.XA CN201711324894A CN107992696B CN 107992696 B CN107992696 B CN 107992696B CN 201711324894 A CN201711324894 A CN 201711324894A CN 107992696 B CN107992696 B CN 107992696B
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王浩
徐立
尹俊辉
杨中海
李斌
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University of Electronic Science and Technology of China
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Abstract

The invention discloses an improved exponential time integral construction method in a complex dispersion medium, which is applied to the field of three-dimensional electromagnetic analysis numerical values; the method comprises the steps of carrying out three-dimensional modeling on a multi-scale target to be analyzed and containing a complex dispersion medium, and establishing a corresponding geometric structure model; dividing the established geometric structure model by using a tetrahedral mesh; firstly, respectively integrating all local field components to respective corresponding global unknown quantities to construct a global semi-discrete format; then, the components of the electric field and the magnetic field are integrated into an unknown quantity to obtain an ordinary differential equation, namely an update equation of the electric field and the magnetic field; the updating of the electric field and the magnetic field only needs vector operation, and does not need to introduce a matrix index to realize updating like the traditional index time integration method, so that the dimension of the matrix index to be solved is obviously reduced, the calculation efficiency of the matrix index is effectively reduced, and the simulation efficiency of the time domain intermittent Galerkin method based on the index time integration method is improved.

Description

Improved exponential time integral construction method in complex dispersion medium
Technical Field
The invention belongs to the field of three-dimensional electromagnetic analysis, and particularly relates to a three-dimensional electromagnetic analysis numerical solving technology.
Background
With the development of stealth technology, internet of things electromagnetic compatibility, electromagnetic shielding and other technologies, various complex dispersion materials are more and more emphasized. Various stealth coating materials aiming at different application environments such as radar, infrared and even visible light in military stealth technology are widely adopted in the fields of anti-electromagnetic interference and electromagnetic shielding design of civil internet of things equipment, solar thin film batteries and the like. With the increasing complexity of electromagnetic environments, the demand for multi-spectral properties of these materials is increasing. Especially for a multi-scale target in a complex electromagnetic environment, the target itself has typical multi-scale characteristics in a geometric structure, and usually contains materials with dispersion or anisotropy properties, such as precious metals, transition metals or composite material coatings, and the coating materials not only inherit the multi-scale characteristics of the target itself in the geometric structure, but also have to face the multi-scale characteristics between different materials and between materials and metals (the precise simulation of the coating materials needs to perform grid encryption on material interfaces, thereby generating the so-called multi-scale characteristics on materials). These characteristics make a multi-scale target containing a complex dispersion medium to generate complex electromagnetic effects in a complex electromagnetic environment, and pose a serious challenge to the electromagnetic characteristics, stability and reliability of the target itself, and even to battlefield viability. Therefore, it is of great importance to accurately obtain the electromagnetic response characteristics of such a complex electromagnetic environment.
To truly and accurately simulate the electromagnetic response characteristics of a complex electromagnetic environment of such a multi-scale target, it is necessary to consider the dispersion and anisotropy characteristics of materials in simulation, and in addition, the materials have multi-spectral characteristics, and the accurate time-domain broadband electromagnetic simulation analysis of the materials is very challenging for the traditional computational electromagnetic method. The time domain discontinuous Galerkin method which is started in recent years is very flexible in terms of space dispersion and time dispersion, has high parallelism, and is particularly suitable for three-dimensional simulation analysis of such complex problems. However, the theory and the technology of the current time domain discontinuous Galerkin method have a great difference from the true realization of high-precision and high-performance electromagnetic simulation analysis of a multi-scale target containing complex dispersion media. For such large problems with typical multi-scale features, adaptive mesh encryption is one of the most important ways to guarantee computational accuracy and reduce computational overhead. However, the local mesh encryption makes the stability problem of the explicit time format more severe. If a global explicit time format is adopted, a normalized global time step will bring huge computational resource consumption, because the maximum time step must satisfy the stability condition of the minimum grid, resulting in a very small global time step and a large increase in the number of time iteration steps. This time step, determined by the minimum grid, is not necessary for large size grids. Therefore, in the local mesh encryption problem, the global time step will bring a lot of unnecessary computation overhead in the large-size mesh area. The fully implicit time format seems to solve this problem, and its unconditionally stable nature enables the time-domain discontinuous galois method to achieve the same accuracy of results with larger or even much larger time steps than the explicit time format. However, the cost is that a global linear equation set needs to be solved in each time iteration or a coefficient matrix of the global linear equation set needs to be inverted, and the huge computing resource consumption makes the full-implicit time-domain discontinuous Galerkin method difficult to be used for three-dimensional electromagnetic simulation analysis of actual large problems such as multi-scale complex electromagnetic environment problems. Therefore, there is an urgent need for a more efficient time format for time domain intermittent galileo analysis research of electromagnetic response characteristics of a complex electromagnetic environment for multi-scale targets.
In simulation analysis of a multi-scale target containing a complex dispersion medium, a traditional exponential time integration method starts from a local semi-discrete format derived by a time-domain discontinuous Galerkin method, and constructs a global semi-discrete format in the following form by respectively integrating all local field components into respective corresponding global unknown quantities
Figure BDA0001505460170000021
Wherein, the global diagonal block matrix is formed by the quality matrixes of grid cells; diagonal blocks of the global block matrix K correspond to the sum of the rigidity matrix and the self-acting flux matrix of each grid, and non-diagonal blocks correspond to the flux matrix on the interface;
Figure BDA0001505460170000022
and
Figure BDA0001505460170000023
respectively, electric field, magnetic field, and auxiliary polarization current (introduced by the dispersion model) unknowns;∞，ωdand gammadIs a dispersion model parameter, is a constant. Then the field is divided
Figure BDA0001505460170000024
And
Figure BDA0001505460170000025
integrated into an unknown vector u, the global semi-discrete format can be converted into the following ordinary differential equation form
Figure BDA0001505460170000026
Wherein
Figure BDA0001505460170000027
In the matrix index time integration method, it is necessary to solve a matrix index with respect to the coefficient matrix C. The calculation cost of the matrix index is almost exponentially increased along with the matrix dimension, and particularly for a multi-scale problem containing complex dispersion media, the matrix index dimension is huge, the solution cost is very large, and the performance improvement obtained by removing the stability limit of a fine grid in an index time integration format is obviously weakened.
Disclosure of Invention
In order to solve the problem that a traditional exponential time integration method is difficult to perform efficient and high-precision three-dimensional electromagnetic simulation analysis on a multi-scale target containing a complex dispersion medium, the invention provides an improved exponential time integration construction method in the complex dispersion medium.
The technical scheme adopted by the invention is as follows: a method of improved exponential time integral construction in a complex dispersive medium, comprising:
s1, carrying out three-dimensional modeling on a multi-scale target to be analyzed and containing a complex dispersion medium, and establishing a corresponding geometric structure model;
s2, subdividing the established geometric structure model by using tetrahedral meshes to obtain a plurality of tetrahedral meshes;
s3, constructing edge value problems, and deducing discontinuous Galerkin weak forms of local edge value problems in each tetrahedral mesh according to the Galerkin process;
s4, discretizing the discontinuous Galerkin weak form by adopting a basis function to obtain a discontinuous Galerkin semi-discrete format;
s5, integrating all field components into an unknown vector, and constructing a global semi-discrete format;
s6, integrating the electric field component and the magnetic field component into an unknown vector, and constructing an ordinary differential equation according to the global semi-discrete format obtained in the step S5;
s7, dividing the tetrahedral meshes obtained in the step S2 into fine meshes and coarse meshes according to the sizes of the meshes, and separating the unknown quantity of the ordinary differential equation according to the fine meshes and the coarse meshes;
s8, introducing a new exponential form unknown vector related by a fine grid to replace the unknown vector in the step S7, and obtaining a local unconditional stable exponential time integral format.
Further, the step S3 is to construct an edge value problem, specifically: according to a time domain Maxwell equation, by introducing a polarization current vector
Figure BDA0001505460170000031
Obtaining a mixed Maxwell-Drude equation; describing metal boundary conditions by adopting an ideal electric wall; intercepting the calculation area by using a Silver-Muller absorption boundary condition;
wherein the content of the first and second substances,
Figure BDA0001505460170000032
is an auxiliary potential shift vector, and t is a time variable.
Furthermore, the discontinuous galaojinweak form of the local edge value problem in each tetrahedral mesh specifically is:
Figure BDA0001505460170000041
wherein t is a time variable,∞is the relative dielectric constant at infinite frequency, omegadIs the plasma frequency, gammadAs the frequency of the impact is the frequency of the impact,
Figure BDA0001505460170000042
an outer normal unit vector on the given plane is given for the ith grid cell,
Figure BDA0001505460170000043
is the magnetic field vector inside the ith grid cell,
Figure BDA0001505460170000044
is the electric field vector inside the ith grid cell,
Figure BDA0001505460170000045
is the polarization current vector inside the ith grid cell,
Figure BDA0001505460170000046
an outer normal unit vector on the given plane for the jth grid cell,
Figure BDA0001505460170000047
is the electric field inside the jth grid cell, FhFor the set of all the faces, the number of faces,
Figure BDA0001505460170000048
for the basis function vector corresponding to the ith grid cell,0for the vacuum dielectric constant, μ is the permeability of the medium in the calculated area.
Further, in step S4, the discontinuous galaojin semi-discrete format specifically includes:
Figure BDA0001505460170000049
wherein the content of the first and second substances,
Figure BDA00015054601700000410
the unknown electric field vector inside the ith grid cell,
Figure BDA00015054601700000411
the unknown magnetic field vector inside the ith grid cell,
Figure BDA00015054601700000412
the unknown polarization current vector inside the ith grid cell,∞is the relative dielectric constant at infinite frequency, omegadIs the plasma frequency, gammadAs collision frequency, μ is the permeability of the medium in the calculation region,0is the dielectric constant in vacuum, t is the time variable, ViRepresenting a tetrahedron KiThe set of numbers for the mid-interface surface,
Figure BDA00015054601700000413
a matrix of electric field-dependent qualities is represented,
Figure BDA00015054601700000414
representing the magnetic field-dependent mass matrix, SiiPresentation interfaceijSelf-acting flux matrix of (S)ijRepresenting an interaction flux matrix of an ith grid cell and a jth grid cell, whereinijRepresenting the interface of the ith and jth grid cells.
Further, the ordinary differential equation expression in step S5 is:
Figure BDA00015054601700000415
wherein C is a coefficient matrix and t is a time variable.
The invention has the beneficial effects that: the improved index time integral construction method in the complex dispersion medium utilizes the time domain intermittent Galerkin method based on the index time integral method to improve the index time integral construction method for the sparse characteristic of the matrix index generated during the fine simulation analysis of the multi-scale problem containing the complex dispersion medium, obviously reduces the dimension of the matrix index to be solved, effectively reduces the calculation efficiency of the matrix index and further improves the simulation efficiency of the time domain intermittent Galerkin method based on the index time integral method.
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FIG. 1 is a flow chart of the scheme of the invention.
Detailed Description
In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to the accompanying drawings.
As shown in fig. 1, a scheme flow chart of the present invention is provided, and the technical scheme of the present invention is as follows: a method of improved exponential time integral construction in a complex dispersive medium, comprising:
and S1, carrying out three-dimensional modeling on the multi-scale target to be analyzed, which contains the complex dispersion medium, and establishing a corresponding geometric structure model. Multi-scale targets containing complex dispersive media to be analyzed, such as military vehicles, fighters and drones, are selected. And establishing a three-dimensional model according to the geometric characteristics and the material attributes of the target, and simultaneously adding a truncation absorption boundary condition to form a geometric structure model of the calculation region.
S2, subdividing the established geometric structure model by using tetrahedral meshes to obtain a plurality of tetrahedral meshes; specifically, the method comprises the following steps: a known procedure in the computational electromagnetics method is used for the geometric structure model created in the tetrahedral mesh partitioning step S1, and therefore this step will not be described in detail. The subdivided computing region is divided into a number of tetrahedral meshes, so that the continuous geometry space is converted into a discrete mesh space.
S3, constructing edge value problems, and deducing discontinuous Galerkin weak forms of local edge value problems in each tetrahedral mesh according to the Galerkin process;
the construction boundary value problem specifically includes: first, the following time domain Maxwell equation is used:
Figure BDA0001505460170000051
for complex dispersive media, embodiments of the present invention are described using the Drude dispersion model. In the dispersion model, the complex electric displacement can be expressed as
Figure BDA0001505460170000052
Wherein
Figure BDA0001505460170000061
Here, the∞Is the relative dielectric constant at infinite frequency, omegadIs the plasma frequency, gammadFor collision frequency, all three are Drude model parameters, which are directly related to material properties. Fourier transform is carried out on the formula (6) and the Fourier transform is brought into a Maxwell equation of the time domain to obtain the equation
Figure BDA0001505460170000062
The Fourier transform is obtained from the formula (7)
Figure BDA0001505460170000063
By introducing a polarization current vector
Figure BDA0001505460170000064
A mixed Maxwell-Drude equation is obtained:
Figure BDA0001505460170000065
wherein the content of the first and second substances,
Figure BDA0001505460170000066
is a vector of the electric field strength,
Figure BDA0001505460170000067
is the vector of the magnetic field strength, mu is the magnetic permeability of the medium in the calculation area,
Figure BDA0001505460170000068
an auxiliary potential shift vector is introduced for the Drude dispersion model, operator ^ represents rotation operation, and t is a time variable;
the embodiment of the invention adopts an ideal electric wall to describe the metal boundary condition:
Figure BDA0001505460170000069
wherein n is the out-of-boundary normal component,
Figure BDA00015054601700000610
is the unitization of n;
truncating the calculation region by using a Silver-Muller absorption boundary condition:
Figure BDA00015054601700000611
wherein the content of the first and second substances,
Figure BDA0001505460170000071
and
Figure BDA0001505460170000072
the incident excitation electric and magnetic fields, respectively, and the impedance Z and admittance Y, respectively, can be expressed as:
Figure BDA0001505460170000073
thus, equations (10), (11) and (12) together constitute the marginal problem of the present method.
Is provided with
Figure BDA0001505460170000074
Is a unit of tetrahedronKiAdjacent grid cells, i represents the ith grid cell, then K can be deduced according to the Galerkin processiInterrupted galaojin weak form of medium local boundary problem:
Figure BDA0001505460170000075
wherein the content of the first and second substances,∞is the relative dielectric constant at infinite frequency, omegadIs the plasma frequency, gammadAs the frequency of the impact is the frequency of the impact,
Figure BDA0001505460170000076
an outer normal unit vector on the given plane is given for the ith grid cell,
Figure BDA0001505460170000077
is the magnetic field vector inside the ith grid cell,
Figure BDA0001505460170000078
is the electric field vector inside the ith grid cell,
Figure BDA0001505460170000079
is the polarization current vector inside the ith grid cell,
Figure BDA00015054601700000710
an outer normal unit vector on the given plane for the jth grid cell,
Figure BDA00015054601700000711
is the electric field inside the jth grid cell, FhFor the set of all the faces, the number of faces,
Figure BDA00015054601700000712
for the basis function vector corresponding to the ith grid cell,0to calculate the relative vacuum permittivity of the medium in the region, μ is the permeability of the medium in the calculated region. The Galerkin process is a well-known process, is widely applied to a finite element method and a time-domain intermittent Galerkin method, and is not used any moreAnd (6) describing in detail.
S4, discretizing the discontinuous Galerkin weak form by adopting a basis function to obtain a discontinuous Galerkin semi-discrete format; the method specifically comprises the following steps: the discontinuous Galerkin method supports multiple types of basis functions, here high-order stacked vector basis functions are taken as an example. Local electromagnetic field inside tetrahedral mesh cells
Figure BDA00015054601700000713
Can be made of phiilThe linear combination of the basis functions is expressed as
Figure BDA00015054601700000714
Wherein d isiFor the number of local unknowns, determined by the order and type of the basis function, eilAnd hilAre the coefficients of the basis functions. Then, the discontinuous galaojin weak form obtained in step S4 is discretized according to the above formula to obtain tetrahedral mesh KiSemi-discrete format of local discontinuity Galerkin
Figure BDA0001505460170000081
Wherein, ViRepresenting a tetrahedron KiThe set of numbers for the mid-interface surface,
Figure BDA0001505460170000082
a matrix of electric field-dependent qualities is represented,
Figure BDA0001505460170000083
representing the magnetic field-dependent mass matrix, SiiPresentation interfaceijSelf-acting flux matrix of (S)ijRepresenting an interaction flux matrix of the ith grid cell and the jth grid cell; in addition, the method can be used for producing a composite material
Figure BDA0001505460170000084
Figure BDA0001505460170000085
Figure BDA0001505460170000086
Figure BDA0001505460170000087
Figure BDA0001505460170000088
Figure BDA0001505460170000089
ijRepresenting the interface of the ith and jth grid cells.
S5, integrating all field components into an unknown vector, and constructing a global semi-discrete format; the method specifically comprises the following steps: local unknowns
Figure BDA00015054601700000810
Respectively integrated into global unknowns
Figure BDA00015054601700000811
And
Figure BDA00015054601700000812
in the above-mentioned local semi-discrete format, the above-mentioned local semi-discrete format can be converted into the following global semi-discrete format
Figure BDA0001505460170000091
Wherein each diagonal block corresponds to a local quality matrix
Figure BDA0001505460170000092
(electric field dependent mass matrix) or
Figure BDA0001505460170000093
(magnetic field dependent mass matrix); the matrix K is a block matrix with diagonal blocks of
Figure BDA0001505460170000094
The non-diagonal block is
Figure BDA00015054601700000914
S6, dividing the field
Figure BDA0001505460170000095
Figure BDA0001505460170000096
Integration into an unknown vector
Figure BDA0001505460170000097
Obtaining the following ordinary differential equation form, namely the update equation of the electric field and the magnetic field
Figure BDA0001505460170000098
Wherein C is a coefficient matrix;
Figure BDA0001505460170000099
Figure BDA00015054601700000910
here, the polarization current-dependent auxiliary equation introduced by the Drude dispersion model in equation (16)
Figure BDA00015054601700000911
Only vector operation is needed, and updating is realized without introducing matrix indexes like a traditional exponential time integration method, so that the dimension of the matrix indexes to be required can be remarkably reduced.
S7, dividing the tetrahedral meshes obtained in the step S2 into fine meshes and coarse meshes according to the sizes of the meshes, and separating the unknown quantity of the ordinary differential equation according to the fine meshes and the coarse meshes; the method specifically comprises the following steps:
the meshes obtained in step S2 are classified into two types, fine meshes and coarse meshes, according to the mesh size. Then, based on this classification, the unknowns of the ordinary differential equations in step S6 can be separated into
Figure BDA00015054601700000912
Where the matrix P is a diagonal matrix with diagonal elements of 0 or 1, where 1 is used to mark the fine grid partial correlation unknowns and I is the identity matrix. The above ordinary differential equation (17) can be separated into
Figure BDA00015054601700000913
Wherein C isfCP and CcC (I-P) consists of fine and coarse grid related unknowns, respectively.
S8, introducing a new exponential form unknown vector related to the fine grid to replace the unknown vector in the step S7, removing the explicit dependence of the fine grid part on the ordinary differential equation time format, and obtaining a local unconditional stable exponential time integral format;
introducing new exponential form unknown vectors correlated by a fine grid
Figure BDA0001505460170000101
And carry-in (21) to replace the original unknown vector
Figure BDA0001505460170000102
Its left-end term can be converted into
Figure BDA0001505460170000103
And the right end item can also be converted into
Figure BDA0001505460170000104
After simplification, the exponential time integral format with stable local unconditional condition is obtained
Figure BDA0001505460170000105
To this end, the time format-to-fine grid partial correlation matrix C is removed by introducing a new variable (22)fExplicit dependence of, CfNo separate time iteration is required. And the number of the first and second electrodes,
Figure BDA0001505460170000106
and
Figure BDA0001505460170000107
the product of (a) is an identity matrix, so the matrix in equation (25)
Figure BDA0001505460170000108
Is a coarse grid partial correlation matrix CcHave the same characteristic spectrum. In other words, the fine mesh portion no longer affects the stability of equation (25). Then after further time dispersion of equation (25), the resulting time format is unconditionally stable for the fine grid part.
By comparing the formula (3) and the formula (18), it can be known that the dimension of the coefficient matrix C in the improved exponential time format is reduced by 33% compared with the dimension of the coefficient matrix C in the conventional exponential time format derived matrix, and the corresponding generation matrix index is obtained
Figure BDA0001505460170000109
Also reduced by 33%. The computational overhead of the matrix index increases almost exponentially with the matrix dimension, which is large especially for multi-scale problems involving complex dispersive media, becauseThe improved exponential time integration method can obviously improve the simulation analysis efficiency of the problems.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (2)

1. A method of improved exponential time integral construction in a complex dispersive medium, comprising:
s1, carrying out three-dimensional modeling on a multi-scale target to be analyzed and containing a complex dispersion medium, and establishing a corresponding geometric structure model;
s2, subdividing the established geometric structure model by using tetrahedral meshes to obtain a plurality of tetrahedral meshes;
s3, constructing edge value problems, and deducing discontinuous Galerkin weak forms of local edge value problems in each tetrahedral mesh according to the Galerkin process; the discontinuous Galerkin weak form of the local edge value problem in each tetrahedral mesh specifically comprises:
Figure FDA0002725936720000011
wherein, KiRepresenting tetrahedral units, t is a time variable,∞is the relative dielectric constant at infinite frequency, omegadIs the plasma frequency, gammadAs the frequency of the impact is the frequency of the impact,
Figure FDA0002725936720000012
an outer normal unit vector on the given plane is given for the ith grid cell,
Figure FDA0002725936720000013
is the magnetic field vector inside the ith grid cell,
Figure FDA0002725936720000014
the magnetic field vector inside the jth grid cell,
Figure FDA0002725936720000015
is the electric field vector inside the ith grid cell,
Figure FDA0002725936720000016
is the polarization current vector inside the ith grid cell,
Figure FDA0002725936720000017
an outer normal unit vector on the given plane for the jth grid cell,
Figure FDA0002725936720000018
is the electric field inside the jth grid cell, FhFor the set of all the faces, the number of faces,
Figure FDA0002725936720000019
for the basis function vector corresponding to the ith grid cell,0is the vacuum dielectric constant, μ is the permeability of the medium in the calculation region;
s4, discretizing the discontinuous Galerkin weak form by adopting a basis function to obtain a discontinuous Galerkin semi-discrete format; step S4, where the discontinuous galaojin semi-discrete format specifically includes:
Figure FDA00027259367200000110
wherein the content of the first and second substances,
Figure FDA00027259367200000111
the unknown electric field vector inside the ith grid cell,
Figure FDA00027259367200000112
the unknown magnetic field vector inside the ith grid cell,
Figure FDA00027259367200000113
the unknown magnetic field vector inside the jth grid cell,
Figure FDA00027259367200000114
unknown polarization current vector, ω, inside the ith grid celldFor the frequency of the plasma to be,0is the dielectric constant in vacuum, t is the time variable, ViRepresenting a tetrahedron KiThe set of numbers for the mid-interface surface,
Figure FDA0002725936720000021
a matrix of electric field-dependent qualities is represented,
Figure FDA0002725936720000022
representing the magnetic field-dependent mass matrix, SiiPresentation interfaceijThe self-action matrix of (a) is,ijrepresenting the interface of the ith and jth grid cells, SijRepresenting an interaction matrix of the ith grid unit and the jth grid unit, and mu is the magnetic permeability of the medium in the calculation area;
s5, integrating all field components into an unknown vector, and constructing a global semi-discrete format; global semi-discrete format
Figure FDA0002725936720000023
Wherein each diagonal block corresponds to an electric field related quality matrix
Figure FDA0002725936720000024
Or magnetic field dependent mass matrix
Figure FDA0002725936720000025
The matrix K is a block matrix with diagonal blocks of
Figure FDA0002725936720000026
The non-diagonal block is
Figure FDA0002725936720000027
S6, integrating the electric field component and the magnetic field component into an unknown vector
Figure FDA0002725936720000028
Constructing an ordinary differential equation according to the global semi-discrete format obtained in the step S5; the ordinary differential equation expression described in step S6 is:
Figure FDA0002725936720000029
wherein C is the corresponding coefficient matrix, t is the time variable,
Figure FDA00027259367200000210
s7, dividing the tetrahedral meshes obtained in the step S2 into fine meshes and coarse meshes according to the sizes of the meshes, and separating the unknown quantity of the ordinary differential equation according to the fine meshes and the coarse meshes; the ordinary differential equation is separated into
Figure FDA00027259367200000211
Wherein, CfCP and CcC (I-P) consists of fine and coarse grid related unknowns, respectively, P is a diagonal matrix with diagonal elements of 0 or 1;
s8, introducing a new exponential form unknown vector related to the fine grid to replace the unknown quantity in the step S7, and obtaining a local unconditional stable exponential time integral format; locally unconditionally stable exponential time integral format
Figure FDA00027259367200000212
2. The method according to claim 1, wherein the step S3 of constructing the boundary value problem is: according to a time domain Maxwell equation, by introducing a polarization current vector
Figure FDA0002725936720000031
Obtaining a mixed Maxwell-Drude equation; describing metal boundary conditions by adopting an ideal electric wall; intercepting the calculation area by using a Silver-Muller absorption boundary condition;
wherein the content of the first and second substances,
Figure FDA0002725936720000032
is an auxiliary potential shift vector, and t is a time variable.
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