Seminars at the Faculty of Informatics

Variable time stepping for wave scattering problems

The Faculty of Informatics is pleased to announce a seminar given by Maria Lopez Fernandez

DATE: Wednesday, April 9 2014
PLACE: USI Lugano Campus, room SI-015, Informatics building (Via G. Buffi 13)
TIME: 13.30

We address the time integration of convolution-evolution equations by using variable time steps. Our main application is the efficient approximation of retarded potentials arising in wave scattering problems or "hyperbolic time-domain integral equations". In this context theá main difficulty from the computational point of view comes from space-dependent delays in time which appear in the resulting integral equations. Our ultimate goal is to minimize both the computational cost and the memory requirements by developing adaptive methods in space and time and fast and memory reducing algorithms for their implementation.
In the last years the application of Lubich's Convolution Quadrature to approximate retarded potentials has become very popular. The Convolution Quadrature method approximates the integral equations in the Laplace domain, where the temporal and the spatial variables decouple, and is very stable. Furthermore it provides an approximation which inherits the convolution structure at discrete level and allows for fast implementations based on Fourier techniques. Unfortunately the original Convolution Quadrature is conceptually limited to uniform time stepping.
Working always in the Laplace domain, I will present a generalization of Lubich's Convolution Quadrature which allows for variable time steps. The design and analysis of the new method relies on the contour integral representation of the numerical solution in the complex plane. For the practical implementation we derive a special quadrature and a highly parallellizable algorithm. Numerical experiments are provided to show the potential of our approach.
I will briefly mention results for other types of nonlocal evolution equations at the end of my talk.

Maria Lopez-Fernandez is a Lecturer of Numerical Analysis at the Institute of Mathematics of the University of Zurich, where she works since 2010.
She studied at the University of Valladolid (Spain), getting a bachelor degree in Mathematics in 2000 and a PhD in 2005. In between 2007 and 2010 she was a postdoctoral researcher at the University Autonoma of Madrid (Spain), an assistant professor at the University Carlos III of Madrid and a postdoctoral researcher at the Institute of Mathematical Sciences of the Spanish National Research Council (ICMAT-CSIC).

HOST: Prof. Rolf Krause