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math.NA2021★ 1 cited
Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough Coefficients
Xinliang Liu, Lei Zhang, Shengxin Zhu
In this paper, we demonstrate the construction of generalized Rough Polyhamronic Splines (GRPS) within the Bayesian framework, in particular, for multiscale PDEs with rough coeffic…
math.NA2021★ 2 cited
Iterated numerical homogenization for multi-scale elliptic equations with monotone nonlinearity
Xinliang Liu, Eric Chung, Lei Zhang
Nonlinear multi-scale problems are ubiquitous in materials science and biology. Complicated interactions between nonlinearities and (nonseparable) multiple scales pose a major chal…
math.NA2018
Fast eigenpairs computation with operator adapted wavelets and hierarchical subspace correction
Hehu Xie, Lei Zhang, Houman Owhadi
We present a method for the fast computation of the eigenpairs of a bijective positive symmetric linear operator . The method is based on a combination of operator ada…