Time Decomposition Method for the General Transient Simulation of Low-Frequency Electromagnetics

Abstract

Abstract-This paper describes a highly robust and efficient parallel computing method for the transient simulation of low-frequency electromagnetics with nonlinear materials and/or permanent magnets. In this method, time subdivisions are introduced to control the memory usage and nonlinear convergence. A direct block triangular matrix solver is applied to solve the formulated block matrix for each subdivision. This method has been implemented using the Message Passing Interface (MPI) for distributed memory parallel processing. Depending on the number of available MPI processes and physical memory, the entire nonlinear transient simulation can be divided into several subdivisions along the time-axis such that each MPI process handles only the computation for one time-step. Application examples are presented to demonstrate that this method can achieve excellent scalability of speedup.

Modeling of the Electromagnetic Field of a Rectangular Waveguide With Side Holes

“…For surface waves propagating in the impedance waveguide, in Eq. (12) it is necessary to make a replacement γ x → jγ x , then we getz 00 γ 2 ⊥ chγ x a − jkγ x shγ x a = 0, (13) where (12), (13) allow us to obtain a spectrum of both bulk and surface waves propagating in such a structure. As a result of the analysis, the frequency characteristics of the constant propagation of bulk and surface waves were obtained depending on various values of surface impedance and wavelengths.…”

“…Let us consider the propagation of magnetic waves in the current waveguide, provided that the surface impedance of a narrow wall is known, and it can be calculated from the relationships given in [12][13][14][15][16][17].…”

Calculation of the Electromagnetic Field of a Rectangular Waveguide With Chiral Medium

“…Normal waves of TE-type in the considered waveguide have the form [17][18][19][20][21][22][23][24][25][26][27][28]:…”

Electromagnetic sub-models for 3D edge-elements in transient non-linear simulation

“…This set ranges from two-dimensional approximations with nodal-based potentials (Weiss and Cendes, 1982) to more complex techniques allowing transient analysis of eddy currents in three-dimensional (3D) space (Biro and Preis, 1989). Many strategies with the objective of acceleration have been developed: time-harmonic approximations in which all field quantities are assumed to have sinusoidal variation with time (Paoli et al , 1998), multigrid strategies that change mesh density during the iteration process (Schinnerl et al , 1998) , surface-impedance boundary layers presuming an exponentially decreasing electromagnetic wave propagating normal to the relevant surfaces (Yi et al , 2013) or time decomposition methods allowing solving multiple time steps in parallel (He et al , 2017).…”