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

STORTI, BRUNO; GARELLI, LUCIANO; STORTI, MARIO; D?ELÍA, JORGE

COMPUTERS & MATHEMATICS WITH APPLICATIONS (1987)

PERGAMON-ELSEVIER SCIENCE LTD

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 thefinite element method for non-matching overlapping unstructured grids is proposed in this work. The schemeis based on both the transfer of information across each grid interface via Dirichlet boundary conditionsand a high-order interpolation algorithm to obtain one global solution of the system. The solution can beobtained iteratively, with a convergence rate that is similar to that obtained with an analogous conformalmesh, and the matrix-vector operator can be computed with completely decoupled operations on bothmeshes. Furthermore, the scheme can be set as a linear operator that can be fed to a matrix-free efficientiterative solver, such as the BiConjugate Gradient Stabilized method. Several numerical examples usingnon-matching unstructured grids that are partially and completely overlapped with different element sizesare presented, assessing the precision and convergence rate of the method.