460 citations · 1.9k across the 48 of their papers we have counts for
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A Simple and Efficient Preconditioning Scheme for Heaviside Enriched XFEM
Christapher Lang, David Makhija, Alireza Doostan +1
The eXtended Finite Element Method (XFEM) is an approach for solving problems with non-smooth solutions. In the XFEM, the approximate solution is locally enriched to capture discon…
Variational multiscale analysis: the fine-scale Green's function for stochastic partial differential equations
Jayanth Jagalur-Mohan, Onkar Sahni, Alireza Doostan +1
We present the variational multiscale (VMS) method for partial differential equations (PDEs) with stochastic coefficients and source terms. We use it as a method for generating acc…
A weighted L1-minimization approach for sparse polynomial chaos expansions
Ji Peng, Jerrad Hampton, Alireza Doostan
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard l1…