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 …

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

We present a high order immersed finite element (IFE) method for solving the elliptic
interface problem with interface-independent meshes. The IFE functions developed here …

This article presents the first higher degree immersed finite element (IFE) method with
proven optimal convergence for elliptic interface problems with nonhomogeneous jump …

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 develo** 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 …

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 …

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