High-efficiency time domain electromagnetic simulation method based on H matrix algorithm

Abstract

The invention discloses a high-efficiency time domain electromagnetic simulation method based on an H matrix algorithm, which can realize electromagnetic simulation on a large three-dimensional target. In the method, a time domain finite element method (TDFEM) is used as a background, a low-rank compression technique is used as a core, and a tree structure is used as a basis for carrying out logical unit (LU) decomposition on a sparse matrix generated by the TDFEM by a four arithmetic algorithm corresponding to the H matrix. The acquired upper and lower triangular factors have low-rank compressible characteristics, and the compressed matrix equation can realize quick solution of high-efficiency time domain electromagnetic simulation by the H matrix algorithm. The high-efficiency time domain electromagnetic simulation method has the advantages of fast computation speed, low memory consumption, controllable computation accuracy, good stability and the like, can reduce the complexity of computation to O(Nlog<2>N) and reduce the memory consumption to O(NlogN), can be widely applied to the solution of a large sparse linear system of equations during high-efficiency time domain electromagnetic simulation, and can provide important reference for analyzing the electromagnetic property of the large three-dimensional target.

Description

Technical field [0001] The present invention relates to an electromagnetic simulation technology, in particular to an electromagnetic simulation technology based on The matrix algorithm is an efficient time-domain electromagnetic simulation method, which can provide an important reference for the analysis of electromagnetic characteristics in the fields of communications, radar, microwave integrated circuits, etc. Background technique [0002] Electromagnetic simulation is a method to reproduce the essential process of actual electromagnetic phenomena on the computer. In the actual research process, when the researched system is expensive, the experiment is dangerous, or the experiment time is long, electromagnetic simulation is a particularly effective and convenient alternative research method. The core of electromagnetic simulation technology is the numerical calculation of electromagnetic field. The current numerical calculation methods for electromagnetic field are finite d...

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Problems solved by technology

The finite difference method and the finite difference time domain method can only use rectangular grids due to the limitation of the grid discretization method, so this method is difficult to simulate complex boundaries; although the finite element method can overcome the limitations of the finite difference method and the finite difference time domain method. However, in order to obtain the electromagnetic characteristics of broadband, cumbersome frequency sweeping operations are required, and these factors also greatly limit the electromagnetic simulation capabilities of the above methods; the time-domain finite element method has been proposed for less than 20 years. It can not only accurately simulate the complex geometric structure and medium composition characteristics of the target, but also obtain the broadband electromagnetic characteristics of the target very conveniently. It can not only effectively solve the modeling of complex research objects by the finite difference method and finite difference time domain method It can also give full play to the ability of the finite element method to model complex structures. It has the advantages of no numerical dispersion, low requirements for iteration stability, and easy parallelism.

The iterative solution is suitable for situations where the accuracy of the solution is not high. For sparse matrices, the computational complexity of the iterative solution is only O(N), where N represents the number of unknowns. Its main disadvantage is that when the structure of the simulation object is complex When , the coefficient matrix formed is poor, and the iterative convergence speed will be very slow or even non-convergent. Although the preconditioning technology can improve this situation, due to the limitations of the preconditioning technology, different problems need to correspond to different Therefore, it is difficult to find a general and efficient preconditioning technology, which causes difficulties in practical application; in addition, in solving the multi-right vector problem, that is, the coefficient matrix of the equation to be solved is constant and the right vector is constantly changing. time (the multi-time step problem in the time-domain finite element method belongs to this category), the matrix equation must be re-solved for each right vector, which is time-consuming and laborious

The direct solution method can overcome the above shortcomings of the iterative solution method, and has the characteristics of high solution accuracy and good stability. It also has great advantages in solving multi-right vector problems, but the disadvantages of the direct solution method are high computational complexity and large memory consumption.

Such as B.He, F.L.Teixeira, "Sparse and Explicit FETD via Approximate Inverse Hodge(Mass) Matrix," IEEE microwave and wireless components letters, vol.16, no.6, pp.348-350, June 2006. A direct solution based on sparse matrix inversion, which obtains the approximate inverse of the matrix instead of the exact inverse by controlling the matrix inversion parameters, which can reduce the computational complexity and memory requirements to a certain extent, but through the direct inversion method to solve a system of linear equations is not efficient

In addition, A.George, "Nested dissection of a regular finite element mesh," SIAM J. on Numerical Analysis, 10(2): 345-363, April 1973. Another direct solution method for solving sparse matrix equations is proposed in the literature , it can reduce the computational complexity to O(N 1.5 ), which is a method with good effect and wide application in the direct solution of existing sparse matrix equations, but O(N 1.5 ) is still a nonlinear complexity, which will cause the calculation time and memory consumption to increase sharply with the increase of the number of unknowns. When the simulation scale is large, it will cause the existing computer hardware configuration to be unbearable, so , time-domain finite element electromagnetic simulation urgently needs an effective direct solution technique to improve its simulation efficiency

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