Unconditional Stable and Conditionally Stable Hybrid Time-Domain Spectral Element Electromagnetic Analysis Method

Abstract

The invention discloses an unconditional stability and conditional stability mixed time domain spectral element electromagnetic analyzing method. In a traditional time domain spectral element method, for complex models, especially under the condition of containing multiscale problems, the sizes of meshes obtained through hexahedral subdivision are not uniform. In the subsequent time iteration, in order to ensure that an algorithm is stable and not diverging, the time step is set according to the size of the minimum subdivision mesh, and therefore the whole solution process wastes a large amount of time. The invention provides the self-adapting unconditional stability and conditional stability mixed time domain spectral element method. Small meshes and large meshes are automatically found out through the self-adapting method, an ordinary central difference format is used for the large mesh area, and a Newmark-beta difference format is used for the small mesh area, so that the unconditionally stable iteration format is obtained, the whole time step can be very large, and the solution time is greatly shortened.

Description

technical field [0001] The invention belongs to the mixed time-domain method of conditional stability and unconditional stability, in particular a rapid analysis technology for multi-scale electromagnetic problems. Background technique [0002] In 1864, on the basis of predecessors' research, Maxwell proposed a set of mathematical equations capable of summarizing the basic regressive path of the macroscopic electromagnetic field—the famous Maxwell's equations, which laid the foundation for the theoretical research of electromagnetism. The research of electromagnetic field theory has gradually penetrated into many technical science fields such as earth science, life science, medicine, material science and information science, greatly promoting the development of science and technology and the change of human life. [0003] For a long time in the early days, the research of electromagnetic field theory was dedicated to obtaining analytical solutions to some problems. However, ...

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Problems solved by technology

[0008] (1) The hexahedron and tetrahedron are mixed and divided, but the time-domain spectral element method is used for the hexahedron part, and the time-domain finite element method is used for the tetrahedron part. The mass matrix generated by the time-domain finite element method is sparse, and the inverse cost a lot The time plus the time step is set very small, so the solution speed is slow

[0009] (2) If different regions are divided into hexahedral grids, when using the time-domain spectral element method, in order to ensure the stability of the algorithm, the time step must be set according to the minimum grid size, so that the overall time iteration steps Will be a lot, resulting in slow solution time

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