533 citations · 623 across the 21 of their papers we have counts for
5 papers · 1 filter
Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
Yixuan Wang
This thesis develops numerical and theoretical approaches for understanding and analyzing singularity formation in Partial Differential Equations (PDEs). The singularity formation…
Exponentially Convergent Multiscale Finite Element Method
Yifan Chen, Thomas Y. Hou, Yixuan Wang
We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale s…
Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations
Yifan Chen, Thomas Y. Hou, Yixuan Wang
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the waven…
Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions
Yifan Chen, Thomas Y. Hou, Yixuan Wang
In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main result…
Approximation to Singular Quadratic Collision Model in Fokker-Planck-Landau Equation
Ruo Li, Yanli Wang, Yixuan Wang
We propose a Hermite-Galerkin spectral method to numerically solve the spatially homogeneous Fokker-Planck-Landau equation with singular quadratic collision model. To compute the c…