Related papers: Reconstruction of interfaces using CGO solutions f…
In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on…
Ray optics is an intuitive and computationally efficient model for wave propagation through nonuniform media. However, the underlying geometrical-optics (GO) approximation of ray optics breaks down at caustics, erroneously predicting the…
Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential…
As an approximate theory that is highly regarded for its computational efficiency, geometrical optics (GO) is widely used for modeling waves in various areas of physics. However, GO fails at caustics, which significantly limits its…
In this paper we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver…
This paper is devoted to the problem of recovering a potential $q$ in a domain in $\mathbb{R}^d$ for $d \geq 3$ from the Dirichlet to Neumann map. This problem is related to the inverse Calder\'on conductivity problem via the Liouville…
We present a simple numerical algorithm for solving elliptic equations where the diffusion coefficient, the source term, the solution and its flux are discontinuous across an irregular interface. The algorithm produces second-order accurate…
We propose a low-dimensional interface reduction method for elliptic interface problems based on conservative flux reconstruction. The approach combines a fitted $P_1$ finite element discretization with a flux recovery procedure following…
We consider the inverse problem of the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D with limited boundary observations of the electric field. The theoretical…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
We use Ikehata's enclosure method to reconstruct penetrable unknown inclusions in a plane elastic body in time-harmonic waves. Complex geometrical optics solutions with complex polynomial phases are adopted as the probing utility. In a…
In this paper, we present an accurate numerical method for the time-harmonic Maxwell's equations for bi-periodic multilayered media with quasi-periodic incident waves using the Method of Fundamental Solutions in conjunction with a…
In this article, we develop and analyze a finite element method with the first family N\'ed\'elec elements of the lowest degree for solving a Maxwell interface problem modeled by a $\mathbf{H}(\text{curl})$-elliptic equation on unfitted…
For research in the field of transformation optics and for the calculation of optically inhomogeneous lenses the method of geometrization of the Maxwell equations seems to be perspective. The basic idea is to transform the coefficients of…
We present a variational optimization approach for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and conductivity functions in time-dependent Maxwell's system using limited…
We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…
A novel interface reconstruction strategy for volume of fluid (VOF) methods is introduced that represents the liquid-gas interface as two planes that co-exist within a single computational cell. In comparison to the piecewise linear…
For the free boundary problem of the plasma-vacuum interface to three-dimensional ideal incompressible magnetohydrodynamics (MHD), the a priori estimates of smooth solutions are proved in Sobolev norms by adopting a geometrical point of…
We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…
With the goal of accurately extracting the optical field losses in a three-dimensional (3D), circularly coiled waveguide (e.g., bent optical fiber), this effort presents the numerical methodologies that are implemented for an envelope…