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We study Maxwell's equations in conducting media with perfectly conducting boundary conditions on Lipschitz domains, allowing rough material coefficients and $L^2$-data. Our first contribution is a direct proof of well-posedness of the…
The purpose of this article is to study extrapolation of solvability for boundary value problems of elliptic systems in divergence form on the upper half-space assuming De Giorgi type conditions. We develop a method allowing to treat each…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
Simulations involving free surfaces and fluid interfaces are important in many areas of engineering. There is, however, still a need for improved simulation methods. Recently, a new efficient geometric VOF method called isoAdvector for…
In this paper, we investigate topological modes of different physical systems defined on arbitrary two-dimensional curved surfaces. We consider the shallow water equations, inhomogeneous Maxwell's equations, Jackiw-Rebbi model and show how…
In the framework of a mixed finite element method, a structure-preserving formulation for incompressible magnetohydrodynamic (MHD) equations with general boundary conditions is proposed. A leapfrog-type temporal scheme fully decouples the…
Numerical solution of equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes for the time evolution. A predefined grid in the problem domain and a…
We study an inverse problem for the time-dependent Maxwell system in an inhomogeneous and anisotropic medium. The objective is to recover the initial electric field $\mathbf{E}_0$ in a bounded domain $\Omega \subset \mathbb{R}^3$, using…
We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric…
We establish up to the boundary regularity estimates in weighted $L^{p}$ spaces with Muckenhoupt weights $A_{p}$ for weak solutions to the Hodge systems \begin{align*} d^{\ast}\left(Ad\omega\right) +…
Discrete fracture models with reduced-dimensional treatment of conductive and blocking fractures are widely used to simulate fluid flow in fractured porous media. Among these, numerical methods based on interface models are intensively…
We review recent simulation studies of interfaces between immiscible homopolymer phases. Special emphasis is given to the presentation of efficient simulation techniques and powerful methods of data analysis, such as the analysis of…
The geometrical approximation of the extended Maxwell equation in curved spacetime incorporating interactions induced by the vacuum polarization effects is considered. Taking into account these QED interactions and employing the analogy…
This paper considers a general class of iterative optimization algorithms, referred to as linear-optimization-based convex programming (LCP) methods, for solving large-scale convex programming (CP) problems. The LCP methods, covering the…
We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is…
A novel reconstruction method is introduced for the severely ill-posed inverse problem of limited-angle tomography. It is well known that, depending on the available measurement, angles specify a subset of the wavefront set of the unknown…
Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified…
An inverse obstacle scattering problem for the electromagnetic wave governed by the Maxwell system over a finite time interval is considered. It is assumed that the wave satisfies the Leontovich boundary condition on the surface of an…
In this paper we present recent developments concerning a Cell-Centered Arbitrary Lagrangian Eulerian (CCALE) strategy using the Moment Of Fluid (MOF) interface reconstruction for the numerical simulation of multi-material compressible…
Surface normal integration is a fundamental problem in computer vision, dealing with the objective of reconstructing a surface from its corresponding normal map. Existing approaches require an iterative global optimization to jointly…