论文标题
用于求解具有不规则边界的OCTREE网格上的泊松方程的几何多机方法
Geometric multigrid method for solving Poisson's equation on octree grids with irregular boundaries
论文作者
论文摘要
提出了一种方法，以在几何多机求解器中包括不规则的域边界。 DIRICHLET边界条件可以施加在由级别设置函数定义的不规则边界上。我们的实现采用了具有自适应精致的Quadtree/Octree网格，以细胞为中心的离散化和侧重齐平滑。通过执行线路搜索，以子元素分辨率确定边界位置。对于接口附近的网格块，存储了自定义操作员模具，将接口考虑在内。对于远离边界的网格块，使用标准的二阶准确离散化。该方法的收敛属性，鲁棒性和计算成本用几个测试用例说明。
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.
