A Boundary Condition-Capturing Multigrid Approach to Irregular Boundary Problems

We propose a geometric multigrid method for solving linear systems arising from irregular boundary problems involving multiple interfaces in two and three dimensions. In this method, we adopt a matrix-free approach; i.e., we do not form the fine grid matrix explicitly and we never form nor store the coarse grid matrices, as many other robust multigrid methods do. The main idea is to construct an accurate interpolation which captures the correct boundary conditions at the interfaces via a level set function. Numerical results are given to compare our multigrid method with black box and algebraic multigrid methods.