Numerical simulation of highly oscillatory problems with applications.

The research project aspires a new approach for the numerical simulation of physical processes and models that exhibit wave characteristics. The emphasis lies on the development of new methods for acoustic and electromagnetic scattering problems at high frequencies, with applications in diverse areas. Specifically, the results may contribute to the numerical simulation of certain cancer therapies and to the research into causes of human deafness, in collaboration with international partners. The accurate numerical simulation of highly oscillatory problems is often intractable using classical approaches: the representation of highly oscillatory functions requires a large number of discretization points, which leads to excessive computing times and memory usage. In addition, the implementation of known numerical methods often requires the costly evaluation of large numbers of highly oscillatory integrals. A fundamental solution is proposed in this project for both limitations. Recent methods that achieve this goal were initially developed by the promotors and will be analysed, extended and implemented for more complex applications.

Keywords:Numerical integration, Helmholtz equation, Scientific computing, High frequency, Wave propagation

Disciplines:Applied mathematics in specific fields, Computer architecture and networks, Distributed computing, Information sciences, Information systems, Programming languages, Scientific computing, Theoretical computer science, Visual computing, Other information and computing sciences