A parallel exponential integrator scheme for linear differential equations
New approximations of the matrix φ functions are developed. These approximations are rational functions of a specific form allowing simple and accurate schemes for linear systems. Furthermore, these approximations are fully parallelizable. Several tests show the efficiency of the method and its good...
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| Vydané v: | Applied numerical mathematics Ročník 208; s. 356 - 364 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.02.2025
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| ISSN: | 0168-9274 |
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| Abstract | New approximations of the matrix φ functions are developed. These approximations are rational functions of a specific form allowing simple and accurate schemes for linear systems. Furthermore, these approximations are fully parallelizable. Several tests show the efficiency of the method and its good parallelization properties. |
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| AbstractList | New approximations of the matrix φ functions are developed. These approximations are rational functions of a specific form allowing simple and accurate schemes for linear systems. Furthermore, these approximations are fully parallelizable. Several tests show the efficiency of the method and its good parallelization properties. |
| Author | Kaber, S.-M. Hecht, F. |
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| Cites_doi | 10.1137/0729014 10.1137/S1064827595295337 10.1137/140964655 10.1016/0021-9045(69)90030-6 10.1002/gamm.201310002 10.1016/j.cam.2003.08.006 10.1017/S0962492910000048 |
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| Keywords | Parallel computing Exponential integrators Matrix exponential |
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| References | Hecht, Kaber, Perrin, Plagne, Salomon (br0040) 2022 Lu (br0060) 2003; 161 Güttel (br0030) 2013; 36 Schmelzer, Trefethen (br0110) 2007; 29 Hochbruck, Lubich, Selhofer (br0050) 1998; 19 br0100 Minchev, Wright (br0080) Göckler, Grimm (br0020) 2014; 35 Saad (br0090) 1992; 29 Cody, Meinardus, Varga (br0010) 1969; 2 Hochbruck, Ostermann (br0070) 2010; 19 Minchev (10.1016/j.apnum.2024.10.018_br0080) Schmelzer (10.1016/j.apnum.2024.10.018_br0110) 2007; 29 Hecht (10.1016/j.apnum.2024.10.018_br0040) Güttel (10.1016/j.apnum.2024.10.018_br0030) 2013; 36 Göckler (10.1016/j.apnum.2024.10.018_br0020) 2014; 35 Hochbruck (10.1016/j.apnum.2024.10.018_br0050) 1998; 19 Hochbruck (10.1016/j.apnum.2024.10.018_br0070) 2010; 19 Saad (10.1016/j.apnum.2024.10.018_br0090) 1992; 29 Cody (10.1016/j.apnum.2024.10.018_br0010) 1969; 2 Lu (10.1016/j.apnum.2024.10.018_br0060) 2003; 161 |
| References_xml | – ident: br0080 article-title: A review of exponential integrators for first order semi-linear problems – volume: 161 year: 2003 ident: br0060 article-title: Computing a matrix function for exponential integrators publication-title: J. Comput. Appl. Math. – volume: 29 year: 1992 ident: br0090 article-title: Analysis of some Krylov subspace approximations to the matrix exponential operator publication-title: SIAM J. Numer. Anal. – volume: 2 year: 1969 ident: br0010 article-title: Chebyshev rational approximations to publication-title: J. Approx. Theory – volume: 29 year: 2007 ident: br0110 article-title: Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals publication-title: Electron. Trans. Numer. Anal. – ident: br0100 – volume: 36 year: 2013 ident: br0030 article-title: Rational Krylov approximation of matrix functions: numerical methods and optimal pole selection publication-title: GAMM-Mitt. – year: 2022 ident: br0040 article-title: Parallel approximation of the exponential of Hermitian matrices – volume: 19 year: 2010 ident: br0070 article-title: Exponential integrators publication-title: Acta Numer. – volume: 35 year: 2014 ident: br0020 article-title: Uniform approximation of publication-title: SIAM J. Matrix Anal. Appl. – volume: 19 year: 1998 ident: br0050 article-title: Exponential integrators for large systems of differential equations publication-title: SIAM J. Sci. Comput. – volume: 29 issue: 1 year: 1992 ident: 10.1016/j.apnum.2024.10.018_br0090 article-title: Analysis of some Krylov subspace approximations to the matrix exponential operator publication-title: SIAM J. Numer. Anal. doi: 10.1137/0729014 – volume: 29 year: 2007 ident: 10.1016/j.apnum.2024.10.018_br0110 article-title: Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals publication-title: Electron. Trans. Numer. Anal. – volume: 19 issue: 5 year: 1998 ident: 10.1016/j.apnum.2024.10.018_br0050 article-title: Exponential integrators for large systems of differential equations publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827595295337 – volume: 35 issue: 4 year: 2014 ident: 10.1016/j.apnum.2024.10.018_br0020 article-title: Uniform approximation of φ-functions in exponential integrators by a rational Krylov subspace method with simple poles publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/140964655 – ident: 10.1016/j.apnum.2024.10.018_br0040 – volume: 2 year: 1969 ident: 10.1016/j.apnum.2024.10.018_br0010 article-title: Chebyshev rational approximations to exp(−x) in [0,+∞) and applications to heat-conduction problems publication-title: J. Approx. Theory doi: 10.1016/0021-9045(69)90030-6 – volume: 36 issue: 1 year: 2013 ident: 10.1016/j.apnum.2024.10.018_br0030 article-title: Rational Krylov approximation of matrix functions: numerical methods and optimal pole selection publication-title: GAMM-Mitt. doi: 10.1002/gamm.201310002 – ident: 10.1016/j.apnum.2024.10.018_br0080 – volume: 161 year: 2003 ident: 10.1016/j.apnum.2024.10.018_br0060 article-title: Computing a matrix function for exponential integrators publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2003.08.006 – volume: 19 year: 2010 ident: 10.1016/j.apnum.2024.10.018_br0070 article-title: Exponential integrators publication-title: Acta Numer. doi: 10.1017/S0962492910000048 |
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| SubjectTerms | Exponential integrators Matrix exponential Parallel computing |
| Title | A parallel exponential integrator scheme for linear differential equations |
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