Paper on Error-Driven Dynamical hp-Meshes for the Discontinuous Galerkin Method in Time-Domain

My paper on error-driven dynamical hp-meshes for DG in the time-domain was accepted for publication in the Journal of Computational and Applied Mathematics. The paper abstract reads:

An hp-adaptive Discontinuous Galerkin Method for electromagnetic wave propagation phenomena in the time-domain is proposed. The method is highly efficient and allows for the first time the adaptive full-wave simulation of large, time-dependent problems in three-dimensional space. Refinement is performed anisotropically in the approximation order p and the mesh step size h regardless of the resulting level of hanging nodes. For guiding the adaptation process a variant of the concept of reference solutions with largely reduced computational costs is proposed. The computational mesh is adapted such that a given error tolerance is respected throughout the entire time-domain simulation.

For examples of dynamical hp-meshes see this post or this one. Please find the paper here on the JCAM website.

Paper on the Numerical Modeling of Metallic Nano-Tips

Josip Mihaljevic, Jens Niegemann, Christian Hafner and I submitted a paper on the numerical modeling of metallic nano-tips to Quantum Matter. My contribution deals with the simulation of laser-induced electron emission from such tips. A visualization of the process is shown below.

Snapshots of electrons in an electrostatic field (not visible) after emission from a (simplified) metallic nanotip by an impinging femtosecond laser pulse impinging.

Snapshots of electrons in an electrostatic field (not visualized) after emission from a (simplified) metallic nano-tip induced by an impinging femtosecond laser pulse.

UPDATE (Nov 3, 2013):
The paper has been accepted for publication.

The paper is available online.

Paper on a Non-dissipative space-time hp-discontinuous Galerkin method for the time-dependent Maxwell Equations

Martin Lilienthal developed a space-time discontinuous Galerkin method. Unlike other works, this formulation is non-dissipative, which is achieved through non-coinciding choices of the trial and test spaces. Please find the preprint on arXiv.

Paper on a DG Trefftz Method in Time-Domain

Fritz Kretzschmar, Igor Tsukerman and started working on a novel DG method using a Trefftz-type basis in time-domain. The method is formulated in a space-time FE setting and provides high order approximations in both, space and time, where the high order accuracy in time comes at no extra costs in terms in degrees of freedom. We demonstrated spectral convergence over the full space-time domain.

You can get the preprint on arXiv.