6 papers
Dual Variational Neural Network for the -Laplace Problem
Tianhao Hu, Guanglian Li, Fengru Wang +2
The reliable and accurate numerical approximation of the -Laplacian is particularly challenging in the extreme regimes and , where the operator becomes ei…
An Iterative Direct Sampling Method for Reconstructing Moving Inhomogeneities in Parabolic Problems
Bangti Jin, Fengru Wang, Jun Zou
We propose in this work a novel iterative direct sampling method for imaging moving inhomogeneities in parabolic problems using boundary measurements. It can efficiently identify t…
A Stable Iterative Direct Sampling Method for Elliptic Inverse Problems with Partial Cauchy Data
Bangti Jin, Fengru Wang, Jun Zou
We develop a novel iterative direct sampling method (IDSM) for solving linear or nonlinear elliptic inverse problems with partial Cauchy data. It integrates three innovations: a da…
Adaptive Approximations of Inclusions in a Semilinear Elliptic Problem Related to Cardiac Electrophysiology
Bangti Jin, Fengru Wang, Yifeng Xu
In this work, we investigate the numerical reconstruction of inclusions in a semilinear elliptic equation arising in the mathematical modeling of cardiac ischemia. We propose an ad…
Iterative Direct Sampling Method for Elliptic Inverse Problems with Limited Cauchy Data
Kazufumi Ito, Bangti Jin, Fengru Wang +1
In this work, we propose an innovative iterative direct sampling method to solve nonlinear elliptic inverse problems from a limited number of pairs of Cauchy data. It extends the o…
An Iterative Deep Ritz Method for Monotone Elliptic Problems
Tianhao Hu, Bangti Jin, Fengru Wang
In this work, we present a novel iterative deep Ritz method (IDRM) for solving a general class of elliptic problems. It is inspired by the iterative procedure for minimizing the lo…