2021/10/01 by Owe Axelsson, Axelsson, Owe, Maeddeh Pourbagher +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #65F10 #65F50 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #cs.NA #math.NA #msc:65F10 #msc:65F50
paper · pdf · doi:10.48550/arxiv.2110.00537
13 pages, submitted
arxiv created 2021/10/01 · openalex publication_date 2021/10/01 · arxiv updated 2021/10/04 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with symmetric positive definite matrices can be solved readily by rewriting the complex matrix system in two-by-two block matrix form with real matrices which can be efficiently solved by iteration using the preconditioned square block (PRESB) preconditioning method and preferably accelerated by the Chebyshev method. The appearances of an indefinite matrix term causes however some difficulties. To handle this we propose different forms of matrix splitting methods, with or without any parameters involved. A matrix spectral analyses is presented followed by extensive numerical comparisons of various forms of the methods.