Difference between revisions of "InfiniteElemente"

From Wiki
Jump to: navigation, search
Line 35: Line 35:
  
 
== Project Members ==
 
== Project Members ==
* [http://www.asc.tuwien.ac.at/~schoeberl/wiki/index.php/Gregor_Gantner  MSc. Gregor Gantner]
 
 
* [http://www.math.tuwien.ac.at/~melenk  Univ.Prof. PhD. Jens Markus Melenk]
 
* [http://www.math.tuwien.ac.at/~melenk  Univ.Prof. PhD. Jens Markus Melenk]
* [http://www.asc.tuwien.ac.at/~lnannen  Assistant Prof. Dr. Lothar Nannen] (Projektleiter)
+
* [http://www.asc.tuwien.ac.at/~lnannen  Assistant Prof. Dr. Lothar Nannen] (PI)
 
* [http://www.asc.tuwien.ac.at/~schoeberl  Univ.Prof. Dr. Joachim Schöberl]
 
* [http://www.asc.tuwien.ac.at/~schoeberl  Univ.Prof. Dr. Joachim Schöberl]
  
 
== Funding Period ==
 
== Funding Period ==
 
FWF grant P26252 from 08/2014 until 07/2017
 
FWF grant P26252 from 08/2014 until 07/2017

Revision as of 10:50, 5 September 2014


Infinite elements for exterior Maxwell problems

Address

Assistant Prof. Dr. Lothar Nannen<br\> Institute for Analysis and Scientific Computing (Inst. E 101)<br\> Vienna University of Technology<br\> Wiedner Hauptstraße 8-10<br\> 1040 Wien, Austria

Aims

In this project we develop and analyze highly accurate and fast solvers for electromagnetic scattering as well as resonance problems in open systems. Open systems means that some physical effects are non-local and physical quantities such as the electric or magnetic field exist on unbounded domains. Such problems occur for example in the modeling and the simulation of meta-materials, photonic cavities or plasmon resonances.

For computational purposes, these unbounded domains are truncated to bounded domains using transparent boundary conditions at the artificial boundaries. There exist several numerical realizations of transparent boundary conditions. In this project we study new infinite element methods based on a radiation condition called pole condition, which characterizes radiating solutions via the singularities of their (partial) Laplace transforms. In numerical experiments these methods show a fast exponential convergence with respect to the number of additional degrees of freedom per degree of freedom on the artificial boundary. However, only a few one-dimensional convergence results for scalar problems are available.

The project is subdivided into two parts: A numerical analysis part and an algorithmic part. In the analytic part of this project the convergence of the infinite element methods will be established for scattering as well as resonance problems.

In the algorithmic part new iterative solvers will be combined with the infinite element methods to provide fast, highly accurate solvers for exterior Maxwell problems. For bounded domains, these solvers are based on domain decomposition preconditioners for a mixed hybrid discontinuous Galerkin formulation with non-standard penalty terms. Preliminary studies show small iteration numbers even without any coarse grid correction. Therefore they are well-suited for large scale problems.

Software

ngs-waves: Add-on to the finite element package ngsolve for acoustic and electromagnetic scattering and resonance problems.

Project Members

Funding Period

FWF grant P26252 from 08/2014 until 07/2017