OPTIMIZED SCHWARZ WAVEFORM RELAXATION METHODS FOR THE TELEGRAPHER EQUATION

Mohammad D. Al-Khaleel; Martin J. Gander; Pratik M. Kumbhar

doi:10.1137/24M1642962

OPTIMIZED SCHWARZ WAVEFORM RELAXATION METHODS FOR THE TELEGRAPHER EQUATION

Mohammad D. Al-Khaleel
, Martin J. Gander
, Pratik M. Kumbhar

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Schwarz waveform relaxation (SWR) methods are popular domain decomposition methods for solving time-dependent problems. Optimized SWR (OSWR) algorithms are a modern class of SWR algorithms using transmission conditions that exchange more information and involve parameters that can be used to optimize the convergence rate of OSWR. We present here an analysis of overlapping and nonoverlapping SWR and OSWR applied to the telegrapher equation. We derive explicit asymptotic expressions for the optimized parameters, and show their great impact on the convergence of OSWR. We also explain how closely the telegrapher equation is related to RLCG transmission line circuits, and construct new discretization schemes based on this relation, with stability and convergence analyses. We illustrate our theoretical results with numerical experiments.

Original language	British English
Pages (from-to)	A3528-A3551
Journal	SIAM Journal on Scientific Computing
Volume	46
Issue number	6
DOIs	https://doi.org/10.1137/24M1642962
State	Published - 2024

Keywords

domain decomposition methods
optimized transmission conditions
RLCG electric circuits
Schwarz waveform relaxation methods
telegrapher equation

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10.1137/24M1642962

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title = "OPTIMIZED SCHWARZ WAVEFORM RELAXATION METHODS FOR THE TELEGRAPHER EQUATION",

abstract = "Schwarz waveform relaxation (SWR) methods are popular domain decomposition methods for solving time-dependent problems. Optimized SWR (OSWR) algorithms are a modern class of SWR algorithms using transmission conditions that exchange more information and involve parameters that can be used to optimize the convergence rate of OSWR. We present here an analysis of overlapping and nonoverlapping SWR and OSWR applied to the telegrapher equation. We derive explicit asymptotic expressions for the optimized parameters, and show their great impact on the convergence of OSWR. We also explain how closely the telegrapher equation is related to RLCG transmission line circuits, and construct new discretization schemes based on this relation, with stability and convergence analyses. We illustrate our theoretical results with numerical experiments.",

keywords = "domain decomposition methods, optimized transmission conditions, RLCG electric circuits, Schwarz waveform relaxation methods, telegrapher equation",

author = "Al-Khaleel, \{Mohammad D.\} and Gander, \{Martin J.\} and Kumbhar, \{Pratik M.\}",

year = "2024",

doi = "10.1137/24M1642962",

language = "British English",

volume = "46",

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publisher = "Society for Industrial and Applied Mathematics Publications",

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T1 - OPTIMIZED SCHWARZ WAVEFORM RELAXATION METHODS FOR THE TELEGRAPHER EQUATION

AU - Al-Khaleel, Mohammad D.

AU - Gander, Martin J.

AU - Kumbhar, Pratik M.

PY - 2024

Y1 - 2024

N2 - Schwarz waveform relaxation (SWR) methods are popular domain decomposition methods for solving time-dependent problems. Optimized SWR (OSWR) algorithms are a modern class of SWR algorithms using transmission conditions that exchange more information and involve parameters that can be used to optimize the convergence rate of OSWR. We present here an analysis of overlapping and nonoverlapping SWR and OSWR applied to the telegrapher equation. We derive explicit asymptotic expressions for the optimized parameters, and show their great impact on the convergence of OSWR. We also explain how closely the telegrapher equation is related to RLCG transmission line circuits, and construct new discretization schemes based on this relation, with stability and convergence analyses. We illustrate our theoretical results with numerical experiments.

AB - Schwarz waveform relaxation (SWR) methods are popular domain decomposition methods for solving time-dependent problems. Optimized SWR (OSWR) algorithms are a modern class of SWR algorithms using transmission conditions that exchange more information and involve parameters that can be used to optimize the convergence rate of OSWR. We present here an analysis of overlapping and nonoverlapping SWR and OSWR applied to the telegrapher equation. We derive explicit asymptotic expressions for the optimized parameters, and show their great impact on the convergence of OSWR. We also explain how closely the telegrapher equation is related to RLCG transmission line circuits, and construct new discretization schemes based on this relation, with stability and convergence analyses. We illustrate our theoretical results with numerical experiments.

KW - domain decomposition methods

KW - optimized transmission conditions

KW - RLCG electric circuits

KW - Schwarz waveform relaxation methods

KW - telegrapher equation

UR - https://www.scopus.com/pages/publications/85210321908

U2 - 10.1137/24M1642962

DO - 10.1137/24M1642962

M3 - Article

AN - SCOPUS:85210321908

SN - 1064-8275

VL - 46

SP - A3528-A3551

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 6

ER -

OPTIMIZED SCHWARZ WAVEFORM RELAXATION METHODS FOR THE TELEGRAPHER EQUATION

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