An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods (Communications in Computational Physics, 2020)
An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources. The interface is represented by the zerolevel set of a Lipschitz function $ϕ(x,y)$. Our adaptive mesh refinement is done withina small tube of $|ϕ(x,y)|≤δ$ with finer Cartesian meshes. The discrete linear system ofequations is solved by a multigrid solver. The AMR methods could obtain solutionswith accuracy that is similar to those on a uniform fine grid by distributing the meshmore economically, therefore, reduce the size of the linear system of the equations.Numerical examples presented show the efficiency of the grid refinement strategy.