Journal of Computational Physics
Matrix computations (3rd ed.)
Absorbing PML boundary layers for wave-like equations
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Preconditioning Sparse Nonsymmetric Linear Systems with the Sherman--Morrison Formula
SIAM Journal on Scientific Computing
The Use of Wavelets in the Operator Expansion Method for Time-Dependent Acoustic Obstacle Scattering
SIAM Journal on Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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We consider a direct scattering problem for an impenetrable obstacle. This problem is solved numerically with the operator expansion method, that can be seen as a perturbative method with respect to the boundary of the considered obstacle. This method requires the solution of various linear systems having the same coefficient matrix. The main result of this paper is the efficient solution of such linear systems with a numerical linear algebra algorithm based on the well-known Sherman-Morrison formula.