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arXiv · 2610.14447

Symmetric two-level preconditioning for the method of reflections

Jongho Park
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Abstract

We develop and analyze a symmetric two-level preconditioner for the method of reflections for Laplace problems in perforated domains. Using constant boundary modes, we define a coarse correction through a symmetric coercive dual formulation. Combining this coarse correction with parallel reflection corrections gives a symmetric positive definite preconditioner for solving the dual system by the conjugate gradient method. Under a geometric separation condition, we prove a condition number bound independent of the number and sizes of the holes and the diameter of the ambient domain. We also derive geometry-dependent convergence estimates for the one-level methods that explain the need for a coarse correction.

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Jongho Park. 2026-10-10. Symmetric two-level preconditioning for the method of reflections. https://arxiv.org/abs/2610.14447

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