1 citations · 3 across the 5 of their papers we have counts for
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Sparse operator compression of higher-order elliptic operators with rough coefficients
Thomas Y. Hou, Pengchuan Zhang
We introduce the sparse operator compression to compress a self-adjoint higher-order elliptic operator with rough coefficients and various boundary conditions. The operator compres…
An adaptive fast solver for a general class of positive definite matrices via energy decomposition
Thomas Y. Hou, D. Huang, K. C. Lam +1
In this paper, we propose an adaptive fast solver for a general class of symmetric positive definite (SPD) matrices which include the well-known graph Laplacian. We achieve this by…
A sparse decomposition of low rank symmetric positive semi-definite matrices
Thomas Y. Hou, Qin Li, Pengchuan Zhang
Suppose that is symmetric positive semidefinite with rank . Our goal is to decompose into rank-one matrices $\sum_{k=1}^K g_k g_k^T…
Exploring the locally low dimensional structure in solving random elliptic PDEs
Thomas Y. Hou, Qin Li, Pengchuan Zhang
We propose a stochastic multiscale finite element method (StoMsFEM) to solve random elliptic partial differential equations with a high stochastic dimension. The key idea is to sim…