5 citations · 10 across the 17 of their papers we have counts for
19 papers · 1 filter
Adaptive Iterative Numerical Homogenization for Quasilinear Nonmonotone Elliptic PDE
Maher Khrais, Barbara Verfürth
We propose and analyze an adaptive iterative numerical homogenization method to approximate the solution of a class of quasilinear nonmonotone elliptic problems that is of multisca…
Subspace decomposition with defect diffusion coefficient
Dilini Kolombage, Axel Målqvist, Barbara Verfürth
Elliptic diffusion problems with multiscale heterogeneous coefficients lead to poorly conditioned discrete systems and therefore require effective preconditioning strategies. While…
Linearized Localized Orthogonal Decomposition for Quasilinear Nonmonotone Elliptic PDE
Maher Khrais, Barbara Verfürth
In this paper, we propose and analyze a multiscale method for a class of quasilinear elliptic problems of nonmonotone type with spatially multiscale coefficient. The numerical appr…
Offline-online approximation of multiscale eigenvalue problems with random defects
Dilini Kolombage, Barbara Verfürth
In this paper, we consider an elliptic eigenvalue problem with multiscale, randomly perturbed coefficients. For an efficient and accurate approximation of the solutions for many di…
Wave propagation in high-contrast media: periodic and beyond
Élise Fressart, Barbara Verfürth
This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new…
Fully discrete Heterogeneous Multiscale Method for parabolic problems with multiple spatial and temporal scales
Daniel Eckhardt, Barbara Verfürth
The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual ce…
Higher-order finite element methods for the nonlinear Helmholtz equation
Barbara Verfürth
In this work, we analyze the finite element method with arbitrary but fixed polynomial degree for the nonlinear Helmholtz equation with impedance boundary conditions. We show well-…
An offline-online strategy for multiscale problems with random defects
Axel Målqvist, Barbara Verfürth
In this paper, we propose an offline-online strategy based on the Localized Orthogonal Decomposition (LOD) method for elliptic multiscale problems with randomly perturbed diffusion…
Multiscale Scattering in Nonlinear Kerr-Type Media
Roland Maier, Barbara Verfürth
We propose a multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient. The meth…
A multiscale method for heterogeneous bulk-surface coupling
Robert Altmann, Barbara Verfürth
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformu…
A generalized finite element method for problems with sign-changing coefficients
Théophile Chaumont-Frelet, Barbara Verfürth
Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite el…
Numerical homogenization for nonlinear strongly monotone problems
Barbara Verfürth
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted m…
Computational high frequency scattering from high contrast heterogeneous media
Daniel Peterseim, Barbara Verfürth
This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constitu…
From Domain Decomposition to Homogenization Theory
Daniel Peterseim, Dora Varga, Barbara Verfürth
This paper rediscovers a classical homogenization result for a prototypical linear elliptic boundary value problem with periodically oscillating diffusion coefficient. Unlike class…
Heterogeneous Multiscale Method for the Maxwell equations with high contrast
Barbara Verfürth
In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the (time-harmonic) Maxwell scattering problem with high contrast. The method is constructed for a setting…
Numerical homogenization for indefinite H(curl)-problems
Barbara Verfürth
In this paper, we present a numerical homogenization scheme for indefinite, time-harmonic Maxwell's equations involving potentially rough (rapidly oscillating) coefficients. The me…
Numerical homogenization of H(curl)-problems
Dietmar Gallistl, Patrick Henning, Barbara Verfürth
If an elliptic differential operator associated with an -problem involves rough (rapidly varying) coefficients, then solutions to the corresponding $\mat…
A new Heterogeneous Multiscale Method for the Helmholtz equation with high contrast
Mario Ohlberger, Barbara Verfürth
In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the Helmholtz equation with high contrast. The method is constructed for a setting as in Bouchitté and Fel…
A new Heterogeneous Multiscale Method for time-harmonic Maxwell's equations based on divergence-regularization
Patrick Henning, Mario Ohlberger, Barbara Verfürth
In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a diverg…