Efficient solvers for time-dependent problems: a review of IMEX, LATIN, PARAEXP and PARAREAL algorithms for heat-type problems with potential use of approximate exponential integrators and reduced-order models - Université de technologie de Compiègne Access content directly
Journal Articles Advanced Modeling and Simulation in Engineering Sciences Year : 2016

Efficient solvers for time-dependent problems: a review of IMEX, LATIN, PARAEXP and PARAREAL algorithms for heat-type problems with potential use of approximate exponential integrators and reduced-order models

Abstract

In this paper, we introduce and comment some recent efficient solvers for time dependent partial differential or ordinary differential problems, considering both linear and nonlinear cases. Here “efficient” may have different meanings, for instance a computational complexity which is better than standard time advance schemes as well as a strong parallel efficiency, especially parallel-in-time capability. More than a review, we will try to show the close links between the different approaches and set up a general framework that will allow us to combine the different approaches for more efficiency. As a complementary aspect, we will also discuss ways to include reduced-order models and fast approximate exponential integrators as fast global solvers. For developments and discussion, we will mainly focus on the heat equation, in both linear and nonlinear form.

Dates and versions

hal-01958896 , version 1 (18-12-2018)

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Cite

Florian de Vuyst. Efficient solvers for time-dependent problems: a review of IMEX, LATIN, PARAEXP and PARAREAL algorithms for heat-type problems with potential use of approximate exponential integrators and reduced-order models. Advanced Modeling and Simulation in Engineering Sciences, 2016, 3 (8), ⟨10.1186/s40323-016-0063-y⟩. ⟨hal-01958896⟩
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