A matrix-free Chimera approach based on Dirichlet–Dirichlet coupling for domain composition purposes

Abstract

A novel approach using an algebraic-based Chimera type domain composition method in the context of the finite element method for non-matching overlapping unstructured grids is proposed in this work. The scheme is based on both the transfer of information across each grid interface via Dirichlet boundary conditions and a high-order interpolation algorithm to obtain one global solution of the system. The solution can be obtained iteratively, with a convergence rate that is similar to that obtained with an analogous conformal mesh, and the matrix–vector operator can be computed with completely decoupled operations on both meshes. Furthermore, the scheme can be set as a linear operator that can be fed to a matrix-free efficient iterative solver, such as the BiConjugate Gradient Stabilized method. Several numerical examples using non-matching unstructured grids that are partially and completely overlapped with different element sizes are presented, assessing the precision and convergence rate of the method.