Absorbing boundary conditions of the second order
for the pseudospectral Chebyshev methods for wave propagation
Abstract
We describe the implementation
of one-way wave equations of the second order in conjuction
with pseudospectral
methods for wave propagation in two space dimensions.
These equations are first reformulated as hyperbolic
systems of the first order and absorbing boundaries
are implementad by appropriate modification of the matrix
of this system. The resulting matrix
corresponding to one-way wave equation based on Pad\'e
approximation has all
eigenvalues in the complex negative half
plane which allow the stable integration of the underlying
system by any ODE solver in the sense of ``eigenvalue
stability''. The obtained numerical scheme
is much more accurate than the schemes
obtained before which utilized absorbing boundary conditions
of the first order and is also capable of integrating
the wave propagation problems on much larger time
intervals than it was possible before.
It is also demonstrated that implementation of wide-angle
one-way wave equations leads to unstable numerical
schemes (joint work with A. Gelb and B. Welfert).
