Geometric multigrid method for solving Poisson's equation on octree grids with irregular boundaries
Numerical Analysis
2023-01-26 v4 Numerical Analysis
Computational Physics
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.
Cite
@article{arxiv.2205.09411,
title = {Geometric multigrid method for solving Poisson's equation on octree grids with irregular boundaries},
author = {Jannis Teunissen and Francesca Schiavello},
journal= {arXiv preprint arXiv:2205.09411},
year = {2023}
}