相关论文: Two-level preconditioners for the Helmholtz equati…
This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…
We propose domain decomposition preconditioners for the solution of an integral equation formulation of forward and inverse acoustic scattering problems with point scatterers. We study both forward and inverse problems and propose…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
The goal of this paper is to propose preconditioners for the system of linear equations that arises from a discretization of fourth order elliptic problems using spectral element methods. These preconditioners are constructed using…
This paper is concerned with the numerical solution of porous-media flow and transport problems , i. e. heterogeneous, advection-diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time…
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…
We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert…
In this article, we present a new preconditioner, MatExPre, for the high-frequency Helmholtz equation by leveraging the properties of matrix exponentials. Our approach begins by reformulating the Helmholtz equation into a…
In the present paper we study the solvability of the Dirichlet problem for second order divergence form elliptic operators with bounded measurable coefficients which are small perturbations of given operators in rough domains beyond the…
This article investigates the numerical solution of the Diffusive Wave equation posed on domains containing a large number of polygonal perforations, motivated by urban flood modeling. Such geometries induce strong multiscale effects driven…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
We consider the Helmholtz equation with real analytic coefficients on a bounded domain $\Omega\subset\mathbb{R}^{d}$. We take $d+1$ prescribed boundary conditions $f^{i}$ and frequencies $\omega$ in a fixed interval $[a,b]$. We consider a…
We formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions when the normal derivative of {\psi} vanishes on an irregular closed…
We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by…
This paper discusses the theory and numerical method of two-scale analysis for the multiscale Landau-Lifshitz-Gilbert equation in composite ferromagnetic materials. The novelty of this work can be summarized in three aspects: Firstly, the…
Second-order automorphic forms are similar to the usual automorphic forms but have a weaker automorphy condition. We answer a question of Zagier and find the dimensions of spaces of holomorphic, even weight, second-order forms. We also…
This paper considers a class of noncoercive nonlinear elliptic problems with coefficients defined in Marcinkiewicz and Lorentz spaces. We prove the existence of a solution for the corresponding Dirichlet problem and investigate the higher…
In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…
For Kirchhoff plate bending problems on domains whose boundaries are curvilinear polygons a discretization method based on the consecutive solution of three second-order problems is presented. In Rafetseder and Zulehner (preprint,…
This paper is a short guideline to the decomposition of a compressible velocity into vortical and compressible structures using standard flow solvers. In particular, this is a fast solution to get an idea of the compressible fields inside…