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

STORTI, BRUNO; GARELLI, LUCIANO; STORTI, MARIO; D'ELIA, JORGE

COMPUTERS & MATHEMATICS WITH APPLICATIONS (1987)

PERGAMON-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2020 vol. 79 p. 3310 - 3330

0898-1221

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.