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

• DOI: 10.1016/j.cpc.2023.108665
• Publication Date: 2023-01-20T07:04:58Z
• Authors: Jannis Teunissen; Francesca Schiavello
• Keywords: Octree; Multigrid method; Poisson's equation; Isosurface; Solver; Robustness; Smoothing; Pointwise; Quadtree

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