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Mathematics > Numerical Analysis

arXiv:2309.11023 (math)
[Submitted on 20 Sep 2023]

Title:Preconditioning for time-harmonic Maxwell's equations using the Laguerre transform

Authors:Andrew V. Terekhov
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Abstract:A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential equations. However, solving large systems of linear algebraic equations with indefinite ill-conditioned matrices is a challenge. The high order of the matrices limits the capabilities of the Gaussian method to solve such systems, since this requires large RAM and much calculation. To reduce these requirements, an iterative preconditioned algorithm based on integral Laguerre transform in time is used. This approach allows using multigrid algorithms and, as a result, needs less RAM compared to the direct methods of solving systems of linear algebraic equations.
Comments: 12 pages, 4 figures
Subjects: Numerical Analysis (math.NA)
MSC classes: 65
ACM classes: G.1.8
Cite as: arXiv:2309.11023 [math.NA]
  (or arXiv:2309.11023v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2309.11023

Submission history

From: Andrew Terekhov [view email]
[v1] Wed, 20 Sep 2023 02:59:47 UTC (2,824 KB)
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