Variational formulations of time-dependent PDEs in space and time yield (d + 1)-dimensional problems to be solved numerically. This increases the number of unknowns as well as the storage amount. On the other hand, this approach enables adaptivity in space and time as well as model reduction w.r.t. both type of variables. In this paper, we show that matrix oriented techniques can significantly reduce the computational timings for solving the arising linear systems outperforming both time-stepping schemes and other solvers.
Matrix Oriented Reduction of Space-Time Petrov-Galerkin Variational Problems / Henning J.; Palitta D.; Simoncini V.; Urban K.. - ELETTRONICO. - 139:(2021), pp. 1049-1057. (Intervento presentato al convegno European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 tenutosi a Egmond aan Zee, The Netherlands nel 30 September 2019 - 4 October 2019) [10.1007/978-3-030-55874-1_104].
Matrix Oriented Reduction of Space-Time Petrov-Galerkin Variational Problems
Palitta D.;Simoncini V.;
2021
Abstract
Variational formulations of time-dependent PDEs in space and time yield (d + 1)-dimensional problems to be solved numerically. This increases the number of unknowns as well as the storage amount. On the other hand, this approach enables adaptivity in space and time as well as model reduction w.r.t. both type of variables. In this paper, we show that matrix oriented techniques can significantly reduce the computational timings for solving the arising linear systems outperforming both time-stepping schemes and other solvers.| File | Dimensione | Formato | |
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