Auth: R. Glowinski, J. He, A. Lozinski, M. Picasso, J. Rappaz, V. Rezzonico, and J. Wagner
Book Summary: This research paper introduces a novel numerical domain decomposition method designed to solve elliptic problems containing multi-scale data by utilizing overlapping, non-nested grids. It targets scenarios where high-precision solutions are critical within specific, localized regions of a larger domain.
The authors propose a relaxed iterative technique that computes successive corrections to a coarse mesh solution specifically within localized “patches” containing a much finer mesh. The paper provides a mathematical analysis of the iteration operator’s spectral properties, establishes how to determine the optimal relaxation parameters, and examines how patch size impacts overall convergence. The methodology acts as a highly flexible completely overlapping domain decomposition framework, closely resembling the Fast Adaptive Composite grid (FAC) method, validated through 2D and 3D numerical experiments.
