Unconditionally stable time stepping method for mixed finite element maxwell solvers

被引：0

作者：

Crawford, Zane D. ^{[1
,2
]}

Li, Jie ^{[1
]}

Christlieb, Andrew ^{[2
]}

Shanker, Balasubramaniam ^{[1
]}

机构：

[1] Department of Electrical and Computer Engineering, Michigan State University, East Lansing,MI, United States

[2] Department of Computational Science, Mathematics, and Engineering, Michigan State University, East Lansing,MI, United States

来源：

Progress In Electromagnetics Research C | 2020年 / 103卷

关键词：

Time domain finite element methods (TD-FEM) for computing electromagnetic fields are well studied. TD-FEM solution is typically effected using Newmark-Beta methods. One of the challenges of TD-FEM is the presence of a DC null-space that grows with time. This can be overcome by solving Maxwell equations directly. One approach; called time domain mixed finite element method (TDMFEM); discretizes Maxwell’s equations using appropriate spatial basis sets and leapfrog time stepping. Typically; the basis functions used to discretize field quantities have been low order. It is conditionally stable; and there is a strong link between time step size and mesh dependent eigenvalues; much like the Courant-Friedrichs-Lewy (CFL) condition. This implies that the time step sizes can be very small. To overcome this challenge; we use the Newmark-Beta approach. The principal contribution of this work is the development of; and rigorous proof of; unconditional stability for higher order TD-MFEM for different boundary conditions. Further; we analyze nullspaces of the resulting system; and demonstrate stability and convergence. All results are compared against the conditionally stable leapfrog approach. © 2020; Electromagnetics Academy. All rights reserved;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

引用

页码：17 / 30

共 50 条

[31] An Unconditionally Stable Single-Field Finite-Difference Time-Domain Method for the Solution of Maxwell Equations in Three Dimensions
Moradi, Mohammad
Nayyeri, Vahid
Ramahi, Omar M.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 2020, 68 (05) : 3859 - 3868
[32] UNCONDITIONALLY SUPERCLOSE ANALYSIS OF A NEW MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC EQUATIONS
Shi, Dongyang
Yan, Fengna
Wang, Junjun
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2019, 37 (01) : 1 - 17
[33] A hybrid finite-element/finite-difference method with an implicit-explicit time-stepping scheme for Maxwell's equations
Zhu, B.
Chen, J.
Zhong, W.
Liu, Q. H.
INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS, 2012, 25 (5-6) : 607 - 620
[34] Domain Decomposition Framework for Maxwell Finite Element Solvers and Application to PIC
Crawford, Zane D.
Ramachandran, O. H.
O'Connor, Scott
Dault, Daniel L.
Luginsland, J.
Shanker, B.
IEEE TRANSACTIONS ON PLASMA SCIENCE, 2024, 52 (01) : 168 - 179
[35] Unconditionally stable algorithms to solve the time-dependent Maxwell equations
Kole, JS
Figge, MT
De Raedt, H
PHYSICAL REVIEW E, 2001, 64 (06): : 66705/1 - 66705/14
[36] Solving the time-dependent Maxwell equations by unconditionally stable algorithms
Kole, JS
Figge, MT
De Raedt, H
COMPUTER SIMULATION STUDIES IN CONDENSED-MATTER PHYSICS XV, 2003, 90 : 205 - 210
[37] Correction of the Approximation Error in the Time-Stepping Finite Element Method
Kim, Byung-taek
Yu, Byoung-hun
Choi, Myoung-hyun
Kim, Ho-hyun
JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY, 2009, 4 (02) : 229 - 233
[38] Correction of the approximation error in the time-stepping finite element method
Dept. of Electrical Engineering, Kunsan National University, Korea, Republic of
J. Electr. Eng. Technol., 2009, 2 (229-233):
[39] An energy-stable finite element method for nonlinear Maxwell's equations
Li, Lingxiao
Lyu, Maohui
Zheng, Weiying
JOURNAL OF COMPUTATIONAL PHYSICS, 2023, 486
[40] A stable mixed finite element method on truncated exterior domains
Deuring, P
RAIRO-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1998, 32 (03): : 283 - 305

← 1 2 3 4 5 →