Martin-Luther-Universität Halle-Wittenberg


Manuela Bank-Zillmann

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Marlis Hochbruck: On the numerical solution of linear Maxwell's equations

Termin Donnerstag, 18. Januar 2018, 17.00 - 18.30 Uhr
Veranstaltungsart Kolloquium
Reihe Interdisziplinäres Kolloquíum
Einrichtung Naturwissenschaftliche Fakultät II
Veranstalter Naturwissenschaftliche Fakultät II
Veranstaltungsort Gustav-Mie-Hörsaal, Experimentalhörsaal Physik, Raum 1.04
Straße Theodor-Lieser-Straße 9
PLZ/Ort 06120 Halle (Saale)
Ansprechpartner Prof. Dr. Martin Arnold
Telefon +49 345-5524653


In this talk we present an overview on the numerical solution of time-dependent linear Maxwell's equations with an emphasis on the time integration. For the space discretization we consider discontinuos Galerkin methods which can handle complex geometries by using unstructured, possibly locally refined meshes. For the time integration we discuss different options, starting with standard explicit and implicit methods.

After a general introduction, our main interest is in problems where the spatial mesh contains only a small number of tiny mesh elements (i.e. elements with a very small diameter) while most of the mesh are coarse. Solving such problems with an explicit time integration scheme requires a constraint on the time step size related to the diameter of the smallest mesh element to ensure stability, the well-known CFL condition. This makes the simulation inefficient, in particular if the number of tiny mesh elements is small compared to the total number of elements. A natural way to overcome this restriction is using implicit time integrators but these come with the expense of having to solve a large linear system in each time step.

A more suitable approach consists in treating only the tiny mesh elements implicitly while retaining an explicit time integration for the remaining coarse elements. This results in so-called locally implicit methods. We will show how such methods can be constructed and implemented efficiently, present results of a rigorous error analysis, and close with numerical examples.

Joint work with Andreas Sturm, KIT, supported by DFG CRC 1173.



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