High Performance Algorithms for Time Dependent Wave Scattering from a Bounded Obstacle
Maria Cristina Recchioni
Istituto di Matematica e Statistica
Università di Ancona
Piazza Martelli 8, 60121 Ancona, Italy
e-mail : recchioni@posta.econ.unian.it
Francesco Zirilli
Dipartimento di Matematica "G. Castelnuovo"
Università di Roma "La Sapienza"
00185 Roma, Italy
e-mail : f.zirilli@caspur.it
We present a numerical method to compute the solution of a time dependent three dimensional scattering problem for the wave equation. That is given a bounded simply connected obstacle having a known constant acoustic impedance find the scattered wave generated by an incoming wave packet that hits the obstacle. The scattered wave is obtained as the solution of an exterior problem for the wave equation, and is computed as a superposition of time harmonic waves. Each time harmonic wave is computed using the operator expansion method. The method we present is highly parallelizable both with respect to the time and the space variables. In fact the computation of the time harmonic waves can be carried out in parallel and a high level of parallelism can be used in the computation of each time harmonic wave via the operator expansion method. Numerical results on test problems obtained with a parallel implementation of the numerical method proposed here are shown. A discussion of the results both from the numerical and from the physical point of view is given. Some animations of the numerical results obtained are shown.
