BAMPHI: Matrix-free and transpose-free action of linear combinations of φ-functions from exponential integrators
The time integration of stiff systems of Ordinary Differential Equations (ODEs), usually arising from the spatial discretization of Partial Differential Equations (PDEs), constitutes a hot topic in numerical analysis. In particular, exponential-type integrators have attracted much attention for thei...
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| Veröffentlicht in: | Journal of computational and applied mathematics Jg. 423; S. 114973 |
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| Sprache: | Englisch |
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15.05.2023
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | The time integration of stiff systems of Ordinary Differential Equations (ODEs), usually arising from the spatial discretization of Partial Differential Equations (PDEs), constitutes a hot topic in numerical analysis. In particular, exponential-type integrators have attracted much attention for their capacity to effectively handle the stiffness, allowing integration with large time steps. The efficiency of exponential-type integrators strongly relies on the fast computation of the action of the exponential of matrices which often change only slightly during the integration. The authors exploited this characteristic of exponential integrators to develop a backward stable algorithm, bamphi, which is designed to reuse the information gathered through the exponential integration steps, reaching unmatched levels of speed and accuracy on a variety of numerical experiments. |
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| AbstractList | The time integration of stiff systems of Ordinary Differential Equations (ODEs), usually arising from the spatial discretization of Partial Differential Equations (PDEs), constitutes a hot topic in numerical analysis. In particular, exponential-type integrators have attracted much attention for their capacity to effectively handle the stiffness, allowing integration with large time steps. The efficiency of exponential-type integrators strongly relies on the fast computation of the action of the exponential of matrices which often change only slightly during the integration. The authors exploited this characteristic of exponential integrators to develop a backward stable algorithm, bamphi, which is designed to reuse the information gathered through the exponential integration steps, reaching unmatched levels of speed and accuracy on a variety of numerical experiments. |
| ArticleNumber | 114973 |
| Author | Caliari, Marco Cassini, Fabio Zivcovich, Franco |
| Author_xml | – sequence: 1 givenname: Marco surname: Caliari fullname: Caliari, Marco email: marco.caliari@univr.it organization: Department of Computer Science, University of Verona, Italy – sequence: 2 givenname: Fabio surname: Cassini fullname: Cassini, Fabio email: fabio.cassini@unitn.it organization: Department of Mathematics, University of Trento, Italy – sequence: 3 givenname: Franco orcidid: 0000-0002-6604-7878 surname: Zivcovich fullname: Zivcovich, Franco email: franco.zivcovich@gmail.com organization: Laboratoire Jacques-Louis Lions, Sorbonne University, France |
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| Cites_doi | 10.1016/j.jcp.2022.110989 10.1016/j.jcp.2018.06.026 10.1007/s10208-017-9352-1 10.1016/j.jcp.2005.08.032 10.1137/17M1116672 10.1016/j.cam.2009.01.024 10.1137/S0036142902403875 10.1137/20M1371506 10.1137/S1064827502410633 10.1145/2168773.2168781 10.1016/j.jcp.2021.110289 10.1007/BF01601932 10.1016/j.parco.2019.01.005 10.1016/0024-3795(80)90169-X 10.1016/j.jcp.2003.12.010 10.1017/S0962492910000048 10.1007/s002110050202 10.1007/s10543-020-00834-z 10.1137/100788860 10.1093/imanum/drr059 10.1016/j.cam.2018.07.042 10.1137/0729014 10.1016/j.apnum.2008.03.021 10.1137/080717717 10.1016/j.jcp.2018.10.018 10.1137/15M1027620 10.1007/s10543-018-0718-9 10.1007/s10543-020-00809-0 10.1016/j.parco.2014.03.008 |
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| Keywords | Backward error analysis Linear combinations of φ-functions Stiff ODEs Exponential integrators Matrix exponential |
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| References | Gaudreault, Rainwater, Tokman (b9) 2018; 372 Caliari, Cassini, Zivcovich (b15) 2020; 60 Al-Mohy, Higham (b14) 2011; 33 Islas, Schober (b26) 2004; 197 Tokman (b5) 2006; 213 Saad (b13) 1980; 34 Ostermann, Einkemmer (b8) 2018; 23 Manteuffel, Starke (b22) 1996; 73 Martínez, Bergamaschi, Caliari, Vianello (b31) 2009; 231 Lord, Tambue (b28) 2013; 33 Caliari, Zivcovich (b20) 2019; 346 Deuflhard (b27) 1979; 30 Caliari, Cassini, Einkemmer, Ostermann, Zivcovich (b29) 2022; 455 Martone (b32) 2014; 40 Caliari, Cassini, Zivcovich (b30) 2022 Hochbruck, Lubich (b4) 2003; 41 Rousset, Schratz (b6) 2021; 59 Crouzeix, Palencia (b21) 2017; 38 Hochbruck, Ostermann, Schweitzer (b3) 2009; 47 Hairer, Lubich, Wanner (b7) 2006 Caliari, Kandolf, Ostermann, Rainer (b16) 2016; 38 Schreiber, Schaeffer, Loft (b33) 2019; 85 Caliari, Ostermann (b23) 2009; 59 Caliari, Einkemmer, Moriggl, Ostermann (b34) 2021; 437 Saad (b19) 1992; 29 Caliari, Kandolf, Zivcovich (b17) 2018; 58 Hochbruck, Ostermann (b1) 2010; 19 Luan, Pudykiewicz, Reynolds (b10) 2019; 376 Ostermann, Schratz (b25) 2018; 18 Luan (b2) 2021; 61 Kassam, Trefethen (b24) 2005; 26 Niesen, Wright (b11) 2012; 38 Saad (b12) 2003 Zivcovich (b18) 2019; 12 Caliari (10.1016/j.cam.2022.114973_b30) 2022 Caliari (10.1016/j.cam.2022.114973_b29) 2022; 455 Lord (10.1016/j.cam.2022.114973_b28) 2013; 33 Deuflhard (10.1016/j.cam.2022.114973_b27) 1979; 30 Caliari (10.1016/j.cam.2022.114973_b17) 2018; 58 Islas (10.1016/j.cam.2022.114973_b26) 2004; 197 Caliari (10.1016/j.cam.2022.114973_b15) 2020; 60 Gaudreault (10.1016/j.cam.2022.114973_b9) 2018; 372 Luan (10.1016/j.cam.2022.114973_b10) 2019; 376 Caliari (10.1016/j.cam.2022.114973_b23) 2009; 59 Crouzeix (10.1016/j.cam.2022.114973_b21) 2017; 38 Schreiber (10.1016/j.cam.2022.114973_b33) 2019; 85 Caliari (10.1016/j.cam.2022.114973_b34) 2021; 437 Caliari (10.1016/j.cam.2022.114973_b16) 2016; 38 Niesen (10.1016/j.cam.2022.114973_b11) 2012; 38 Luan (10.1016/j.cam.2022.114973_b2) 2021; 61 Rousset (10.1016/j.cam.2022.114973_b6) 2021; 59 Martínez (10.1016/j.cam.2022.114973_b31) 2009; 231 Hairer (10.1016/j.cam.2022.114973_b7) 2006 Ostermann (10.1016/j.cam.2022.114973_b25) 2018; 18 Hochbruck (10.1016/j.cam.2022.114973_b1) 2010; 19 Hochbruck (10.1016/j.cam.2022.114973_b3) 2009; 47 Martone (10.1016/j.cam.2022.114973_b32) 2014; 40 Ostermann (10.1016/j.cam.2022.114973_b8) 2018; 23 Saad (10.1016/j.cam.2022.114973_b13) 1980; 34 Al-Mohy (10.1016/j.cam.2022.114973_b14) 2011; 33 Zivcovich (10.1016/j.cam.2022.114973_b18) 2019; 12 Manteuffel (10.1016/j.cam.2022.114973_b22) 1996; 73 Tokman (10.1016/j.cam.2022.114973_b5) 2006; 213 Saad (10.1016/j.cam.2022.114973_b12) 2003 Saad (10.1016/j.cam.2022.114973_b19) 1992; 29 Caliari (10.1016/j.cam.2022.114973_b20) 2019; 346 Kassam (10.1016/j.cam.2022.114973_b24) 2005; 26 Hochbruck (10.1016/j.cam.2022.114973_b4) 2003; 41 |
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| Snippet | The time integration of stiff systems of Ordinary Differential Equations (ODEs), usually arising from the spatial discretization of Partial Differential... |
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| SubjectTerms | Backward error analysis Exponential integrators Linear combinations of [formula omitted]-functions Matrix exponential Stiff ODEs |
| Title | BAMPHI: Matrix-free and transpose-free action of linear combinations of φ-functions from exponential integrators |
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