SC 99-46 Frank Schmidt, Tilmann Friese, David Yevick: Transparent Boundary Conditions for Split-Step Pad\`e
Approximations of the One-Way Helmholtz Equation (in
preparation)
Abstract: We present nonlocal discrete transparent boundary
conditions for arbitrary
split-step Padapproximations of the two-dimensional
one-way Helmholtz
equation. Our approach generalizes previous methods to
factorizations of
arbitrary order. The boundary conditions are computed in
a recursive manner
without the use of special series or functions. The
proposed algorithm
results in an unconditionally stable propagation method.
Keywords: Helmholtz equation,
Wide-angle approximation,
Pad/e split step approximation,
Transparent boundary conditions,
Finite-element method
MSC: 65M60, 65M55