An application of RASPEN to discontinuous Galerkin discretisation for Richards’ equation in porous media flow
Nonlinear algebraic systems of equations resulting from Discontinuous Galerkin (DG) discretisation of partial differential equations are typically solved by Newton’s method. In this study, we propose a nonlinear preconditioner for Newton’s method for solving the system of equations which is the modi...
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| Main Authors: | , |
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| Format: | Chapter/Article Conference Paper |
| Language: | English |
| Published: |
2021
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| In: |
Modeling, simulation and optimization of complex processes HPSC 2018
Year: 2021, Pages: 323-335 |
| DOI: | 10.1007/978-3-030-55240-4_15 |
| Online Access: | Resolving-System, lizenzpflichtig, Volltext: https://doi.org/10.1007/978-3-030-55240-4_15 Verlag, lizenzpflichtig, Volltext: https://link.springer.com/chapter/10.1007/978-3-030-55240-4_15 
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| Author Notes: | Peter Bastian and Chaiyod Kamthorncharoen |
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| 520 | |a Nonlinear algebraic systems of equations resulting from Discontinuous Galerkin (DG) discretisation of partial differential equations are typically solved by Newton’s method. In this study, we propose a nonlinear preconditioner for Newton’s method for solving the system of equations which is the modification of RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton). We employ inexact inner solves and different Partition of Unity (PU) operators. Basically, the idea of RASPEN is to use fixed-point iteration to produce a new (non-)linear system which has the same solution as the original system and solve it using Newton’s method. The restricted additive Schwarz method is used as a non-linear preconditioner and enables parallel computation by division into subdomain problems. We apply this method to p-Laplace and Richards’ equation in porous media flow. | ||
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