Paper Info
Title
The SCBiCG class of algorithms for complex symmetric linear systems with applications in several electromagnetic model problems.
Abstract
Frequency domain formulations of computational electromagnetic problems often require the solutions of complex-valued non-Hermitian systems of equations, which are still symmetric. For this kind of problems a whole class of sub-variant solver methods derived from the complex-valued Bi-Conjugate Gradient method is available. This class of methods contains established iterative methods as the Conjugate Orthogonal Conjugate Gradient (COCG) method, Bi-Conjugate Gradient Conjugate Residual (BiCGCR) method and Conjugate A-Orthogonal Conjugate Residual (COCR) method. The mathematical equivalence of the BiCGCR method and COCR method is shown and preconditioned variants of the various solvers are derived. An efficient kind of two-step preconditioning technique is also proposed. Numerical experiments involving e.g. electro-quasistatic frequency domain simulation are employed to show the difference in the convergence behaviors of these iterative methods and effectiveness of the two-step preconditioning techniques.
Year
DOI
Venue
2015
10.1016/j.cpc.2015.01.018
Computer Physics Communications
Keywords
Field
DocType
Conjugate gradient,BiCG method,Complex symmetric matrix,Krylov subspace method,Computational electromagnetics
Gradient method,Conjugate gradient method,Mathematical optimization,Biconjugate gradient stabilized method,Iterative method,Mathematical analysis,Algorithm,Nonlinear conjugate gradient method,Mathematics,Derivation of the conjugate gradient method,Biconjugate gradient method,Conjugate residual method
Journal
Volume
ISSN
Citations 
191
0010-4655
9
PageRank 
References 
Authors
0.57
7
4
Name
Order
Citations
PageRank
Xian-Ming Gu17912.52
Markus Clemens2123.17
Ting-Zhu Huang3851101.81
Liang Li4181.81