A new way of devising numerical methods is introduced whose distinctive feature is the computation of a finite element approximation only in a polyhedral subdomain D of the origina...
In many problems, one wishes to solve the Helmholtz equation in cylindrical or spherical coordinates which introduces variable coefficients within the differentiated terms. Fourth ...
Spectral analysis approaches have been actively studied in machine learning and data mining areas, due to their generality, efficiency, and rich theoretical foundations. As a natur...
Dijun Luo, Heng Huang, Chris H. Q. Ding, Feiping N...
In this paper, we introduce a new nonlinear evolution partial differential equation for sparse deconvolution problems. The proposed PDE has the form of continuity equation that ar...
We propose a method for efficient solution of elliptic problems with multiscale features and randomly perturbed coefficients. We use the multiscale finite element method (MsFEM) as...