5 citations · 7 across the 11 of their papers we have counts for
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Algebraic multigrid methods for metric-perturbed coupled problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriora…
Parameter-free preconditioning for nearly-incompressible linear elasticity
James H Adler, Xiaozhe Hu, Yuwen Li +1
It is well known that via the augmented Lagrangian method, one can solve Stokes' system by solving the nearly incompressible linear elasticity equation. In this paper, we show that…
Rational approximation preconditioners for multiphysics problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the…
Solving Graph Laplacians via Multilevel Sparsifiers
Xiaozhe Hu, Junyuan Lin
We consider effective preconditioners for solving Laplacians of general weighted graphs. Theoretically, spectral sparsifiers (SSs) provide preconditioners of optimal computational…
A Deep Neural Network/Meshfree Method for Solving Dynamic Two-phase Interface Problems
Xingwen Zhu, Xiaozhe Hu, Pengtao Sun
In this paper, a meshfree method using the deep neural network (DNN) approach is developed for solving two kinds of dynamic two-phase interface problems governed by different dynam…
A Mesh-free Method Using Piecewise Deep Neural Network for Elliptic Interface Problems
Cuiyu He, Xiaozhe Hu, Lin Mu
In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks…