2022 journal article

Overlapping Domain Decomposition Preconditioner for Integral Equations

SIAM Journal on Scientific Computing, 44(6), A3617–A3644.

By: C. Chen*  & G. Biros *

TL;DR: This work introduces a new preconditioner based on a novel overlapping domain decomposition that can be combined efficiently with existing fast direct solvers and applies the recursive skeletonization to subproblems associated with every subdomain. (via Semantic Scholar)
Source: ORCID
Added: November 1, 2023

. The discretization of certain integral equations, e.g., the first-kind Fredholm equa- tion of Laplace’s equation, leads to symmetric positive-definite linear systems, where the coefficient matrix is dense and often ill-conditioned. We introduce a new preconditioner based on a novel overlapping domain decomposition that can be combined efficiently with existing fast direct solvers. Empirically, we observe that the condition number of the preconditioned system is O (1), independent of the problem size. Our domain decomposition is designed so that we can construct approximate factorizations of subproblems efficiently. In particular, we apply the recursive skeletonization algo- rithm to subproblems associated with every subdomain. We present numerical results on problem sizes up to 16384 2 in 2D and 256 3 in 3D, which were solved in less than 16 hours and three hours, respectively, on an Intel Xeon Platinum 8280M.