On the stability and efficiency of high-order parallel algorithms for 3D wave problems

In this work, we investigate the stability conditions for four new high-order ADI type schemes proposed to solve 3D wave equations with a non-constant sound speed coefficient. This analysis is mainly based on the spectral method, therefore a basic benchmark problem is formulated with a constant soun...

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Veröffentlicht in:Mathematical modelling and analysis Jg. 30; H. 3; S. 553 - 570
Hauptverfasser: Čiegis, Raimondas, Amiranashvili, Shalva
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Vilnius Vilnius Gediminas Technical University 12.09.2025
Schlagworte:
3D wave problem
Accuracy
Acoustics
ADI discrete schemes
Algorithms
Analysis
Approximation
Boundary conditions
Efficiency
Energy methods
Linear algebra
parallel algorithms
Spectral methods
stability
Stability analysis
Velocity
Wave equations
parallel algorithms
ADI discrete schemes
stability
3D wave problem
ISSN:1392-6292, 1648-3510
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Abstract In this work, we investigate the stability conditions for four new high-order ADI type schemes proposed to solve 3D wave equations with a non-constant sound speed coefficient. This analysis is mainly based on the spectral method, therefore a basic benchmark problem is formulated with a constant sound speed coefficient. For a case of general non-constant coefficient the stability analysis is done by using the energy method. Our main conclusion states that the selected ADI type schemes use different factorization operators (mainly due to the need to approximate the artificial boundary conditions on the split time levels), but the general structure of the stability factors are similar for all schemes and thus the obtained CFL conditions are also very similar. The second goal is to compare the accuracy and efficiency of the selected ADI solvers. This analysis also includes parallel versions of these schemes. Two schemes are selected as the most effective and accurate.
AbstractList In this work, we investigate the stability conditions for four new high-order ADI type schemes proposed to solve 3D wave equations with a non-constant sound speed coefficient. This analysis is mainly based on the spectral method, therefore a basic benchmark problem is formulated with a constant sound speed coefficient. For a case of general non-constant coefficient the stability analysis is done by using the energy method. Our main conclusion states that the selected ADI type schemes use different factorization operators (mainly due to the need to approximate the artificial boundary conditions on the split time levels), but the general structure of the stability factors are similar for all schemes and thus the obtained CFL conditions are also very similar. The second goal is to compare the accuracy and efficiency of the selected ADI solvers. This analysis also includes parallel versions of these schemes. Two schemes are selected as the most effective and accurate. Keywords: ADI discrete schemes; 3D wave problem; stability; parallel algorithms. AMS Subject Classification: 65M06; 65M12.
In this work, we investigate the stability conditions for four new high-order ADI type schemes proposed to solve 3D wave equations with a non-constant sound speed coefficient. This analysis is mainly based on the spectral method, therefore a basic benchmark problem is formulated with a constant sound speed coefficient. For a case of general non-constant coefficient the stability analysis is done by using the energy method. Our main conclusion states that the selected ADI type schemes use different factorization operators (mainly due to the need to approximate the artificial boundary conditions on the split time levels), but the general structure of the stability factors are similar for all schemes and thus the obtained CFL conditions are also very similar. The second goal is to compare the accuracy and efficiency of the selected ADI solvers. This analysis also includes parallel versions of these schemes. Two schemes are selected as the most effective and accurate.
In this work, we investigate the stability conditions for four new high-order ADI type schemes proposed to solve 3D wave equations with a non-constant sound speed coefficient. This analysis is mainly based on the spectral method, therefore a basic benchmark problem is formulated with a constant sound speed coefficient. For a case of general non-constant coefficient the stability analysis is done by using the energy method. Our main conclusion states that the selected ADI type schemes use different factorization operators (mainly due to the need to approximate the artificial boundary conditions on the split time levels), but the general structure of the stability factors are similar for all schemes and thus the obtained CFL conditions are also very similar.The second goal is to compare the accuracy and efficiency of the selected ADI solvers. This analysis also includes parallel versions of these schemes. Two schemes are selected as the most effective and accurate.
Audience Academic
Author Amiranashvili, Shalva
Čiegis, Raimondas
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10.1016/j.cam.2019.04.013
10.1016/j.cam.2013.08.024
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StartPage 553
SubjectTerms 3D wave problem
Accuracy
Acoustics
ADI discrete schemes
Algorithms
Analysis
Approximation
Boundary conditions
Efficiency
Energy methods
Linear algebra
parallel algorithms
Spectral methods
stability
Stability analysis
Velocity
Wave equations
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Title On the stability and efficiency of high-order parallel algorithms for 3D wave problems
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