Abstract by Dane Grundvig
Deferred-Corrections fourth and sixth order schemes for acoustic waves with Farfield Expansion ABCs
Numerical methods to obtain numerical solutions with high order convergence to the exact solution of the scattering of acoustic waves are derived. The derivation is based on a high order local Farfield Expansion absorbing boundary condition developed by Dr. Villamizar. The property of the Farfield Expansion ABC to couple with any interior high order method and produce a new method with an overall order of convergence equal to the method employed in the interior is exploited. For the interior scheme, a deferred-corrections technique is used which obtains numerical solutions approximating the exact solution which exhibit sixth and fourth order convergence, while employing the same 5-point stencil of the standard centered second order method. Numerical experiments for both Dirichlet and Neumann problems are performed and their results in terms of complexity, computational cost, and convergence are analyzed.