We present a Boundary Local Fourier Analysis (BLFA) to optimize the relaxation parameters of boundary conditions in a multigrid framework. The method is implemented to solve elliptic equations on curved domains embedded in a uniform Cartesian mesh, although it is designed to be extended for general PDEs in curved domains, wherever a multigrid technique can be implemented. The boundary is implicitly defined by a level-set function and a ghost-point technique is employed to treat the boundary conditions. Existing strategies in literature adopt a constant relaxation parameter on the whole boundary. In this paper, the relaxation parameters are optimized in terms of the distance between ghost points and boundary, with the goal of smoothing the residual along the tangential direction. Theoretical results are confirmed by several numerical tests in 1D, 2D and 3D, showing that the convergence factor associated with the smoothing on internal equations is not degraded by boundary effects.

Coco, A., Mazza, M., Semplice, M. (2023). A ghost-point smoothing strategy for geometric multigrid on curved boundaries. JOURNAL OF COMPUTATIONAL PHYSICS, 478 [10.1016/j.jcp.2023.111982].

A ghost-point smoothing strategy for geometric multigrid on curved boundaries

Mazza M.;
2023-01-01

Abstract

We present a Boundary Local Fourier Analysis (BLFA) to optimize the relaxation parameters of boundary conditions in a multigrid framework. The method is implemented to solve elliptic equations on curved domains embedded in a uniform Cartesian mesh, although it is designed to be extended for general PDEs in curved domains, wherever a multigrid technique can be implemented. The boundary is implicitly defined by a level-set function and a ghost-point technique is employed to treat the boundary conditions. Existing strategies in literature adopt a constant relaxation parameter on the whole boundary. In this paper, the relaxation parameters are optimized in terms of the distance between ghost points and boundary, with the goal of smoothing the residual along the tangential direction. Theoretical results are confirmed by several numerical tests in 1D, 2D and 3D, showing that the convergence factor associated with the smoothing on internal equations is not degraded by boundary effects.
2023
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08
English
Ghost -point
Multigrid
Local Fourier analysis
Curved boundary
Elliptic problems
Immersed boundary method
Coco, A., Mazza, M., Semplice, M. (2023). A ghost-point smoothing strategy for geometric multigrid on curved boundaries. JOURNAL OF COMPUTATIONAL PHYSICS, 478 [10.1016/j.jcp.2023.111982].
Coco, A; Mazza, M; Semplice, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/344047
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