Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for heterogeneous sub-diffusion and diffusion-wave equations
This paper investigates the convergence behavior of the Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations. The algorithms are applied to regular domains in 1D and 2D for multiple subdomains, and the impact of different...
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| Vydané v: | Computers & mathematics with applications (1987) Ročník 150; s. 102 - 124 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Ltd
15.11.2023
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| ISSN: | 0898-1221, 1873-7668 |
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| Abstract | This paper investigates the convergence behavior of the Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations. The algorithms are applied to regular domains in 1D and 2D for multiple subdomains, and the impact of different constant values of the generalized diffusion coefficient on the algorithms' convergence is analyzed. The convergence rate of the algorithms is analyzed as the fractional order of the time derivative changes. The paper demonstrates that the algorithms exhibit slow superlinear convergence when the fractional order is close to zero, almost finite step convergence (exact finite step convergence for wave case) when the order approaches two, and faster superlinear convergence as the fractional order increases in between. The transitional nature of the algorithms' behavior is effectively captured through estimates with changes in the fractional order, and the results are verified by numerical experiments. |
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| AbstractList | This paper investigates the convergence behavior of the Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations. The algorithms are applied to regular domains in 1D and 2D for multiple subdomains, and the impact of different constant values of the generalized diffusion coefficient on the algorithms' convergence is analyzed. The convergence rate of the algorithms is analyzed as the fractional order of the time derivative changes. The paper demonstrates that the algorithms exhibit slow superlinear convergence when the fractional order is close to zero, almost finite step convergence (exact finite step convergence for wave case) when the order approaches two, and faster superlinear convergence as the fractional order increases in between. The transitional nature of the algorithms' behavior is effectively captured through estimates with changes in the fractional order, and the results are verified by numerical experiments. |
| Author | Sana, Soura Mandal, Bankim C. |
| Author_xml | – sequence: 1 givenname: Soura orcidid: 0000-0003-1892-9486 surname: Sana fullname: Sana, Soura email: ss87@iitbbs.ac.in – sequence: 2 givenname: Bankim C. surname: Mandal fullname: Mandal, Bankim C. email: bmandal@iitbbs.ac.in |
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| Cites_doi | 10.1016/j.aej.2021.02.056 10.1016/j.camwa.2023.04.004 10.1137/17M115311X 10.1111/j.1365-246X.1967.tb02303.x 10.1103/PhysRevE.51.R848 10.1103/PhysRevE.53.4191 10.3233/FI-2017-1489 10.1016/j.jcp.2007.05.012 10.1007/s11075-018-0557-4 10.1109/TCAD.1982.1270004 10.1002/mma.7369 10.1016/0893-9659(96)00089-4 10.1098/rspa.2001.0904 10.1016/j.jmaa.2008.10.018 10.1016/j.apnum.2005.03.003 10.1007/s11075-017-0364-3 10.3390/math8060884 10.1063/1.528578 10.1002/num.22112 10.1016/j.jcp.2009.02.007 10.1098/rsta.2019.0289 10.1137/S106482759732678X 10.1115/1.4000563 10.1016/j.jcp.2004.11.025 10.1137/S1064827596305337 10.1016/j.jcp.2014.11.034 10.1137/050642137 10.1007/s10543-020-00823-2 10.1002/(SICI)1097-0363(19970830)25:4<421::AID-FLD557>3.0.CO;2-J 10.1002/zamm.200310033 10.1007/s002110100345 10.4064/sm-18-2-191-198 10.1186/s13662-021-03468-9 10.1080/00207160.2019.1673892 10.1137/16M1082329 10.1137/16M1072620 |
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| Keywords | Sub-diffusion Neumann-Neumann Dirichlet-Neumann Waveform relaxation Diffusion-wave Domain decomposition |
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| Title | Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for heterogeneous sub-diffusion and diffusion-wave equations |
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