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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…