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04/10/2023
Anisotropic analysis of VEM for time-harmonic Maxwell equations in inhomogeneous media with low regularity
It has been extensively studied in the literature that solving Maxwell e...
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12/14/2022
On the maximum angle conditions for polyhedra with virtual element methods
Finite element methods are well-known to admit robust optimal convergenc...
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09/29/2022
Transformer Meets Boundary Value Inverse Problems
A Transformer-based deep direct sampling method is proposed for solving ...
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05/27/2022
A family of immersed finite element spaces and applications to three dimensional 𝐇(curl) interface problems
Maxwell interface problems are of great importance in many electromagnet...
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02/21/2022
Immersed Virtual Element Methods for Maxwell Interface Problems in Three Dimensions
Finite element methods for Maxwell's equations are highly sensitive to t...
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08/02/2021
Immersed Virtual Element Methods for Elliptic Interface Problems
This article presents an immersed virtual element method for solving a c...
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04/15/2021
Learn an index operator by CNN for solving diffusive optical tomography: a deep direct sampling method
In this work, we investigate the diffusive optical tomography (DOT) prob...
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03/08/2021
A Virtual Finite Element Method for Two Dimensional Maxwell Interface Problems with a Background Unfitted Mesh
A virtual element method (VEM) with the first order optimal convergence ...
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11/24/2020
Solving Two Dimensional H(curl)-elliptic Interface Systems with Optimal Convergence On Unfitted Meshes
In this article, we develop and analyze a finite element method with the...
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09/17/2020
Construct Deep Neural Networks Based on Direct Sampling Methods for Solving Electrical Impedance Tomography
This work investigates the electrical impedance tomography (EIT) problem...
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06/19/2020
Error Analysis of Symmetric Linear/Bilinear Partially Penalized Immersed Finite Element Methods for Helmholtz Interface Problems
This article presents an error analysis of the symmetric linear/bilinear...
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04/30/2020
Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis
Immersed finite element (IFE) methods are a group of long-existing numer...
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04/28/2020
An Enriched Immersed Finite Element Method for Interface Problems with Nonhomogeneous Jump Conditions
This article presents and analyzes a p^th-degree immersed finite element...
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04/19/2020