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

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.

References in corpus (4)

• The physics of streamer discharge phenomena
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• Double-pulse streamer simulations for varying interpulse times in air
• 3D particle-in-cell simulations of negative and positive streamers in C4F7N-CO2 mixtures
• Towards a Machine-Learned Poisson Solver for Low-Temperature Plasma Simulations in Complex Geometries
• Data-driven reduced modeling of streamer discharges in air