Wednesday,
March 21, 2:00 p.m. GWC 604
Miguel Sanchez
Dept. Math. & Stats
Study on the Accuracy and Competitiveness of the Mapped Chebyshev Method
Abstract
Many real applications of partial differential equations involve
acoustic waves through heterogeneous media. This introduces
discontinuous coefficients in the problem. In [ SIAM J. Sci. Comput.,
26(2004), pp. 259-271], Bertil Gustafsson and Eva Mossberg state the
importance of high order methods to solve these kinds of problems and
formulate a fourth order finite difference method to solve an acoustic
problem with discontinuous coefficients. This report investigates
using spectral methods for the same problem. We show that the
solution maintains first order accuracy with no dispersion errors.
Specifically, we apply the parameter-dependent mapped Chebyshev method
as introduced by Dan Kosloff and Hillel Tal-Ezer, [J. Comput. Phys.,
104(1993), pp. 457-469]. We study possible choices of parameters and
apply them to constant coefficient problems before applying our
findings to the heterogeneous media problem. We find a parameter
dependent on the number of grid points that, with some minor loss in
accuracy, maintains stability and allows larger time steps. We
compare our results to those obtained by using the standard Chebyshev
method and the fourth-order compact method introduced in [ SIAM J.
Sci. Comput., 26(2004), pp. 272-293], and discuss the advantages in
using the mapped Chebyshev method.
For further information please contact:
mittelmann@asu.edu