Barbara Verfürth

A New Heterogeneous Multiscale Method for Time-Harmonic Maxwell's Equations

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 divergence-regularization in one of the cell problems. This allows us to introduce fine-scale correctors that are not subject to a cumbersome divergence-free constraint and which can hence easily be implemented. To analyze the method, we first revisit classical homogenization theory for time-harmonic Maxwell equations and derive a new homogenization result that makes use of the divergence-regularization in the two-scale homogenized equation. We then show that the HMM is equivalent to a discretization of this equation. In particular, writing both problems in a fully coupled two-scale formulation is the crucial starting point for a corresponding numerical analysis of the method. With this approach we are able to prove rigorous a priori error estimates in the

Numerical Homogenization of H(curl)-Problems

\mathbf{H}(\mbox{curl})

A New Heterogeneous Multiscale Method for the Helmholtz Equation with High Contrast

- and the

Analysis of multiscale methods for the two-dimensional Helmholtz equation with highly heterogeneous coefficient. Part I. Homogenization and the Heterogeneous Multiscale Method

H^{-1}

A new Heterogeneous Multiscale Method for time-harmonic Maxwell's equations based on divergence-regularization

-norm and we derive reliable and efficient localized residual-based a posteriori error estimates.

Analysis of multiscale methods for the two-dimensional Helmholtz equation with highly heterogeneous coefficient. Part II. Two-scale Localized Orthogonal Decomposition

If an elliptic differential operator associated with an

Localized Orthogonal Decomposition for two-scale Helmholtz-typeproblems

{H}({curl})

Analysis of multiscale methods for time-harmonic Maxwell's equations

-problem involves rough (rapidly varying) coefficients, then solutions to the corresponding

Mathematical analysis of transmission properties of electromagnetic meta-materials

{H}({curl})

Numerical homogenization for indefinite H(curl)-problems

-problem admit typicall...