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arXiv · 2205.09411

Geometric multigrid method for solving Poisson's equation on octree grids with irregular boundaries

Jannis Teunissen·Francesca Schiavello
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Abstract

A method is presented to include irregular domain boundaries in a geometric multigrid solver. Dirichlet boundary conditions can be imposed on an irregular boundary defined by a level set function. Our implementation employs quadtree/octree grids with adaptive refinement, a cell-centered discretization and pointwise smoothing. Boundary locations are determined at a subgrid resolution by performing line searches. For grid blocks near the interface, custom operator stencils are stored that take the interface into account. For grid block away from boundaries, a standard second-order accurate discretization is used. The convergence properties, robustness and computational cost of the method are illustrated with several test cases.

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Jannis Teunissen, Francesca Schiavello. 2022-05-19. Geometric multigrid method for solving Poisson's equation on octree grids with irregular boundaries. https://doi.org/10.1016/j.cpc.2023.108665

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