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.

翻译：提出了一种方法,将非正常的域边界纳入一个几何多电网求解器中。可以在一个定级函数界定的非正常边界上强加drichlet边界条件。我们的实施采用有适应性改进、以细胞为中心的离散和点平滑的四树/树网格。边界点通过进行线搜索以亚格网分辨率确定。对于接口附近的格格区块,则储存将界面考虑在内的自定义操作器电线板。对于远离边界的格子阻塞,则使用标准的二阶准确离散。方法的趋同性、稳健性和计算成本用几个测试案例加以说明。