Mathematical analysis demonstrates contraction bounds for an inexact Schwarz–Fourier method, indicating guaranteed convergence for computational chemistry solvers.
Key Points
To analyze the convergence properties of an inexact Schwarz–Fourier domain decomposition method used to solve the Laplace equation on overlapping circular domains.
Formulated an inexact Schwarz solver where subproblems on overlapping discs are approximated via projection onto a Fourier subspace of the L2 boundary space.
Applied analytical frameworks relying on maximum principle arguments to assess iteration error.
Derived a novel variant of the maximum principle adapted to the overlapping disc geometry.
Established contraction number bounds in the maximum norm, providing theoretical convergence guarantees relevant to ddCOSMO chemical solvers.