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We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all frequencies....
We present an integral equation method for solving boundary value
problems of the Helmholtz equation in unbounded domains. The
method relies on the factorisation of one of the
Calderón projectors by an operator approximating the exterior
admittance (Dirichlet to Neumann) operator of the scattering
obstacle. We show how the pseudo-differential calculus allows us
to construct such approximations and that this yields integral
equations without internal resonances and being well-conditioned
at all...
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