Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations
We analyse two practical aspects that arise in the numerical solution of HamiltonJacobi-Bellman (HJB) equations by a particular class of monotone approximation schemes known as semi-Lagrangian schemes. These schemes make use of a wide stencil to achieve convergence and result in discretization matri...
| المؤلفون الرئيسيون: | , |
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| التنسيق: | Journal article |
| منشور في: |
Springer
2017
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| _version_ | 1826286168695635968 |
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| author | Reisinger, C Arto, J |
| author_facet | Reisinger, C Arto, J |
| author_sort | Reisinger, C |
| collection | OXFORD |
| description | We analyse two practical aspects that arise in the numerical solution of HamiltonJacobi-Bellman (HJB) equations by a particular class of monotone approximation schemes known as semi-Lagrangian schemes. These schemes make use of a wide stencil to achieve convergence and result in discretization matrices that are less sparse and less local than those coming from standard finite difference schemes. This leads to computational difficulties not encountered there. In particular, we consider the overstepping of the domain boundary and analyse the accuracy and stability of stencil truncation. This truncation imposes a stricter CFL condition for explicit schemes in the vicinity of boundaries than in the interior, such that implicit schemes become attractive. We then study the use of geometric, algebraic and aggregation-based multigrid preconditioners to solve the resulting discretised systems from implicit time stepping schemes efficiently. Finally, we illustrate the performance of these techniques numerically for benchmark test cases from the literature. |
| first_indexed | 2024-03-07T01:39:46Z |
| format | Journal article |
| id | oxford-uuid:9674459e-91f5-41a2-b221-4fa868328e6e |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:39:46Z |
| publishDate | 2017 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:9674459e-91f5-41a2-b221-4fa868328e6e2022-03-26T23:53:01ZBoundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9674459e-91f5-41a2-b221-4fa868328e6eSymplectic Elements at OxfordSpringer2017Reisinger, CArto, JWe analyse two practical aspects that arise in the numerical solution of HamiltonJacobi-Bellman (HJB) equations by a particular class of monotone approximation schemes known as semi-Lagrangian schemes. These schemes make use of a wide stencil to achieve convergence and result in discretization matrices that are less sparse and less local than those coming from standard finite difference schemes. This leads to computational difficulties not encountered there. In particular, we consider the overstepping of the domain boundary and analyse the accuracy and stability of stencil truncation. This truncation imposes a stricter CFL condition for explicit schemes in the vicinity of boundaries than in the interior, such that implicit schemes become attractive. We then study the use of geometric, algebraic and aggregation-based multigrid preconditioners to solve the resulting discretised systems from implicit time stepping schemes efficiently. Finally, we illustrate the performance of these techniques numerically for benchmark test cases from the literature. |
| spellingShingle | Reisinger, C Arto, J Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations |
| title | Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations |
| title_full | Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations |
| title_fullStr | Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations |
| title_full_unstemmed | Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations |
| title_short | Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations |
| title_sort | boundary treatment and multigrid preconditioning for semi lagrangian schemes applied to hamilton jacobi bellman equations |
| work_keys_str_mv | AT reisingerc boundarytreatmentandmultigridpreconditioningforsemilagrangianschemesappliedtohamiltonjacobibellmanequations AT artoj boundarytreatmentandmultigridpreconditioningforsemilagrangianschemesappliedtohamiltonjacobibellmanequations |