Abstract
In this paper, we propose a novel nonstandard local Fourier analysis (LFA) variant for accurately predicting the multigrid convergence of problems with random and jumping coefficients. This LFA method is based on a specific basis of the Fourier space rather than the commonly used Fourier modes. To show the utility of this analysis, we consider, as an example, a simple cell-centered multigrid method for solving a steady-state single phase flow problem in a random porous medium. We successfully demonstrate the predictive capability of the proposed LFA using a number of challenging benchmark problems. The information provided by this analysis could be used to estimate a priori the time needed for solving certain uncertainty quantification problems by means of a multigrid multilevel Monte Carlo method.
| Original language | English |
|---|---|
| Pages (from-to) | A1385-A1413 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 41 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2019 |
| Externally published | Yes |
Bibliographical note
Funding Information:∗Submitted to the journal’s Methods and Algorithms for Scientific Computing section March 5, 2018; accepted for publication (in revised form) March 19, 2019; published electronically May 2, 2019. http://www.siam.org/journals/sisc/41-3/M117376.html Funding: The work of the second author was supported by the Spanish project FEDER/MCYT MTM2016-75139-R and the Diputación General de Aragón (Grupo de referencia APEDIF, ref. E24 17R). The work of the third author was supported by the European Union’s Horizon 2020 research and innovation program under Marie Sklodowska-Curie grant agreement 705402, POROSOS. †CWI, Centrum Wiskunde and Informatica, Amsterdam, The Netherlands ([email protected], [email protected], http://www.unizar.es/pde/fjgaspar/). ‡IUMA and Applied Mathematics Department, University of Zaragoza, Zaragoza, Spain ([email protected]). §CWI, Centrum Wiskunde and Informatica, Amsterdam, The Netherlands, and DIAM, Delft University of Technology, The Netherlands ([email protected]).
Funding Information:
The work of the second author was supported by the Spanish project FEDER/MCYT MTM2016-75139-R and the Diputaci?n General de Arag?n (Grupo de referencia APEDIF, ref. E24 17R). The work of the third author was supported by the European Union?s Horizon 2020 research and innovation program under Marie Sklodowska-Curie grant agreement 705402, POROSOS.
Publisher Copyright:
c 2019 Society for Industrial and Applied Mathematics
Funding
∗Submitted to the journal’s Methods and Algorithms for Scientific Computing section March 5, 2018; accepted for publication (in revised form) March 19, 2019; published electronically May 2, 2019. http://www.siam.org/journals/sisc/41-3/M117376.html Funding: The work of the second author was supported by the Spanish project FEDER/MCYT MTM2016-75139-R and the Diputación General de Aragón (Grupo de referencia APEDIF, ref. E24 17R). The work of the third author was supported by the European Union’s Horizon 2020 research and innovation program under Marie Sklodowska-Curie grant agreement 705402, POROSOS. †CWI, Centrum Wiskunde and Informatica, Amsterdam, The Netherlands ([email protected], [email protected], http://www.unizar.es/pde/fjgaspar/). ‡IUMA and Applied Mathematics Department, University of Zaragoza, Zaragoza, Spain ([email protected]). §CWI, Centrum Wiskunde and Informatica, Amsterdam, The Netherlands, and DIAM, Delft University of Technology, The Netherlands ([email protected]). The work of the second author was supported by the Spanish project FEDER/MCYT MTM2016-75139-R and the Diputaci?n General de Arag?n (Grupo de referencia APEDIF, ref. E24 17R). The work of the third author was supported by the European Union?s Horizon 2020 research and innovation program under Marie Sklodowska-Curie grant agreement 705402, POROSOS.
Keywords
- Local Fourier analysis
- Multigrid
- Multilevel Monte Carlo
- PDEs
- Random coefficients
- Uncertainty quantification