相关论文: A two-level domain-decomposition preconditioner fo…
A novel approach to computing time-harmonic solutions of Maxwell's equations by time-domain simulations is presented. The method, EM-WaveHoltz, results in a positive definite system of equations which makes it amenable to iterative solution…
In this paper, we review the construction of periodic fundamental solutions and periodic layer potentials for various differential operators. Specifically, we focus on the Laplace equation, the Helmholtz equation, the Lam\'e system, and the…
We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfect matched layer (PML). This method divides the domain of interest into thin layers and proposes a new transmission condition between the…
We prove that the time-harmonic solutions to Maxwell's equations in a 3D exterior domain converge to a certain static solution as the frequency tends to zero. We work in weighted Sobolev spaces and construct new compactly supported…
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…
The paper develops a second-order time-domain moment matching framework for the structure-preserving model reduction of second-order dynamical systems of high dimension, avoiding the first-order double-sized equivalent system. The moments…
A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are two keys in our algorithm, one is how to choose a suitable…
We propose a matrix-free parallel two-level-deflation preconditioner combined with the Complex Shifted Laplacian preconditioner(CSLP) for the two-dimensional Helmholtz problems. The Helmholtz equation is widely studied in seismic…
This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular…
We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…
This paper treats the time-harmonic electro-magnetic scattering or radiation problem governed by Maxwell's equations in an exterior weak Lipschitz domain divided into two disjoint weak Lipschitz parts We will present a solution theory using…
This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formulated with absorbing boundary layers based on complex coordinate stretching. The preconditioner problem is a Helmholtz problem where not…
We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a…
This paper considers the time-harmonic Maxwell equations with impedance boundary condition.We present $H^2$-norm bound and other high-order norm bounds for strong solutions. The $H^2$-estimate have been derived in [M. Dauge, M. Costabel and…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
The goal of this paper is to prove a stable determination of the coefficients for the time-harmonic Maxwell equations, in a Lipschitz domain, by boundary measurements.
We present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a $2$-dimensional triangulated surface $\Gamma$ in $\mathbb{R}^3$. We allow $\Gamma$ to…
Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…