A simple and efficient interface-fitted mesh generation algorithm which can produce a semi-
structured interface-fitted mesh in two and three dimensions quickly is developed in this …

This article presents an immersed finite element (IFE) method for solving the typical three-
dimensional second order elliptic interface problem with an interface-independent Cartesian …

In this paper, we propose a novel mesh-free numerical method for solving the elliptic
interface problems based on deep learning. We approximate the solution by the neural …

This article develops and analyzes ap th degree immersed finite element (IFE) method for
solving the elliptic interface problems with meshes independent of the coefficient …

We present a unified framework for developing and analyzing immersed finite-element (IFE)
spaces for solving typical elliptic interface problems with interface-independent meshes …

Abstract Generalized or Extended Finite Element Methods (GFEM/XFEM) of degree 1 for
interface problems have been reported in the literature; they (i) yield optimal order of …

Finite element methods for electromagnetic problems modeled by Maxwell-type equations
are highly sensitive to the conformity of approximation spaces, and non-conforming methods …

Motivated by the need to handle complex boundary conditions efficiently and accurately in
particle-in-cell (PIC) simulations, this paper presents a three-dimensional (3D) linear …

Immersed finite element (IFE) methods are a group of long-existing numerical methods for
solving interface problems on unfitted meshes. A core argument of the methods is to avoid a …

We define a new finite element method for a steady state elliptic problem with discontinuous
diffusion coefficients where the meshes are not aligned with the interface. We prove optimal …