Convergence Enhancement for Embedded Domain Decomposition Method Through Spectral Radius Reduction

被引:0
作者
Lu, Jiaqing [1 ]
机构
[1] Ohio State Univ, Electro Sci Lab, Columbus, OH 43212 USA
关键词
Convergence; Mathematical models; Couplings; Surface impedance; Impedance; Finite element analysis; Conductors; Domain decomposition method (DDM); finite element method (FEM); Maxwell's equations; overlapping meshes; OPTIMIZED SCHWARZ METHODS; FINITE-ELEMENTS; ALGORITHMS;
D O I
10.1109/TMTT.2024.3386104
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
The embedded domain decomposition method (DDM) has emerged as an innovative DDM variant for electromagnetic simulations, offering enhanced flexibility in geometrical modeling and mesh generation. While previous studies have shown rapid convergence for this method, our recent applications have uncovered certain convergence challenges. Targeting these convergence issues, this work introduces a preconditioner by constructing an approximate inverse to the system matrix of embedded DDM. The preconditioner is built upon two major ingredients: randomized sampling and spectral radius reduction. Through randomized sampling of system equations, we efficiently extract essential information from the DDM matrix without the need for explicit entry evaluations. These samples are then progressively compressed in an adaptive manner combined with spectral radius estimations. Numerical experiments demonstrate the impact of spectral radius on system convergence and the effectiveness of numerical compression in optimizing system eigenspectrum. Subsequent validation through numerical examples showcases the preconditioner's capability in ensuring robust convergence and improving stability of embedded DDM.
引用
收藏
页码:5745 / 5758
页数:14
相关论文
共 35 条
[1]  
Anaren, B0110E50200AHF
[2]  
Cai XC, 1996, NUMER LINEAR ALGEBR, V3, P221, DOI 10.1002/(SICI)1099-1506(199605/06)3:3<221::AID-NLA80>3.3.CO
[3]  
2-Z
[4]  
Chan T. P., 1994, ACTA NUMER, V3, P61, DOI [10.1017/S0962492900002427, DOI 10.1017/S0962492900002427]
[5]   COMPOSITE OVERLAPPING MESHES FOR THE SOLUTION OF PARTIAL-DIFFERENTIAL EQUATIONS [J].
CHESSHIRE, G ;
HENSHAW, WD .
JOURNAL OF COMPUTATIONAL PHYSICS, 1990, 90 (01) :1-64
[6]   OPTIMIZED SCHWARZ METHODS FOR MAXWELL'S EQUATIONS [J].
Dolean, V. ;
Gander, M. J. ;
Gerardo-Giorda, L. .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2009, 31 (03) :2193-2213
[7]   VARIATIONAL ITERATIVE METHODS FOR NONSYMMETRIC SYSTEMS OF LINEAR-EQUATIONS [J].
EISENSTAT, SC ;
ELMAN, HC ;
SCHULTZ, MH .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (02) :345-357
[8]   A METHOD OF FINITE-ELEMENT TEARING AND INTERCONNECTING AND ITS PARALLEL SOLUTION ALGORITHM [J].
FARHAT, C ;
ROUX, FX .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1991, 32 (06) :1205-1227
[9]   Optimized Schwarz methods without overlap for the Helmholtz equation [J].
Gander, MJ ;
Magoulès, F ;
Nataf, F .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2002, 24 (01) :38-60
[10]   UPDATING THE INVERSE OF A MATRIX [J].
HAGER, WW .
SIAM REVIEW, 1989, 31 (02) :221-239