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math.NA2026
Uniform Inf-Sup Norm Equivalence and Robust Operator Preconditioning for Stokes Flow in tight domains with Periodic Pillars
Qi Xin, Yan Xie, Chen-song Zhang +2
Many microfluidic and porous-media computations reduce to the same core task: solving a Stokes saddle-point system on a domain perforated by a dense periodic array of pillars, as i…
math.NA2026
Massively parallel Schwarz methods for the high frequency Helmholtz equation
Yan Xie, Shihua Gong, Ivan G. Graham +2
We investigate the parallel one-level overlapping Schwarz method for solving finite element discretization of high-frequency Helmholtz equations. The resulting linear systems are l…
math.NA2023★ 1 cited
MGCNN: a learnable multigrid solver for sparse linear systems from PDEs on structured grids
Yan Xie, Minrui Lv, Chensong Zhang
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches rel…