SC 99-45 Tilman Friese, Frank Schmidt, David Yevick: Transparent Boundary Conditions for a Wide-Angle
Approximation of the One-Way Helmholtz Equation (in
preparation)
Abstract: We present nonlocal discrete transparent boundary
conditions for a
fourth-order wide-angle approximation of the
two-dimensional Helmholtz
equation. The boundary conditions are exact in the sense
that they supply
the same discrete solution on a bounded interior domain
as would be
obtained by considering the problem on the entire
unbounded domain with zero
boundary conditions at infinity. The proposed algorithm
results in an unconditionally stable propagation method.
Numerical
examples from optics illustrate the efficiency of our
approach.
Keywords: Helmholtz equation,
Wide-angle approximation,
Transparent boundary conditions,
Finite-element method
MSC: 65M60, 65M55