Analysis of an inexact Schwarz domain decomposition method in 3D

We consider an inexact version of the Schwarz domain decomposition method in $3$D to solve a Laplace problem in a domain that is the union of two overlapping spheres. We solve each subproblem approximately by projecting its boundary data $L^2$-orthogonally onto the space of spherical harmonics of degree at most $N$. The model problem arises from the ddCOSMO solver used for implicit solvation in computational chemistry. We analyze the Schwarz-spherical domain decomposition method by establishing a new variant of the maximum principle.

Source: arXiv:2610.13793v1 - http://arxiv.org/abs/2610.13793v1 PDF: https://arxiv.org/pdf/2610.13793v1 Original Link: http://arxiv.org/abs/2610.13793v1