Achim Schädle

Fast Convolution for Nonreflecting Boundary Conditions

Nonreflecting boundary conditions for problems of wave propagation are nonlocal in space and time. While the nonlocality in space can be efficiently handled by Fourier or spherical expansions in special geometries, the arising temporal convolutions still form a computational bottleneck. In the present article, a new algorithm for the evaluation of these convolution integrals is proposed. To compute a temporal convolution over Nt successive time steps, the algorithm requires O(Nt log Nt) operations and O(log Nt) memory. In the numerical examples, this algorithm is used to discretize the Neumann-to-Dirichlet operators arising from the formulation of nonreflecting boundary conditions in rectangular geometries for Schrodinger and wave equations.

Optical Microscopy via Spectral Modifications of a Nanoantenna

The existing optical microscopes form an image by collecting photons emitted from an object. Here we report on the experimental realization of microscopy without the need for direct optical communication with the sample. To achieve this, we have scanned a single gold nanoparticle acting as a nanoantenna in the near field of a sample and have studied the modification of its intrinsic radiative properties by monitoring its plasmon spectrum.

Fast and Oblivious Convolution Quadrature

We give an algorithm to compute

Observation of magnetization waves in negative-index photonic metamaterials

N

Domain decomposition method for Maxwell’s equations: Scattering off periodic structures

steps of a convolution quadrature approximation to a continuous temporal convolution using only

Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory

O(N\, \log N)

Non-reflecting boundary conditions for the two-dimensional Schrödinger equation

multiplications and

Fast Runge-Kutta approximation of inhomogeneous parabolic equations

O(\log N)

Transparent Boundary Conditions for Time-Dependent Problems

active memory. The method does not require evaluations of the convolution kernel but instead uses

Adaptive FEM solver for the computation of electromagnetic eigenmodes in 3D photonic crystal structures

O(\log N)