A spin integral equation for electromagnetic and acoustic scattering
This work provides a robust numerical method for scattering problems, eliminating a known bottleneck (spurious resonances) for computational electromagnetics and acoustics.
The authors present a new integral equation for electromagnetic and acoustic scattering that avoids breakdown at interior spurious resonances and uses unconstrained function spaces. The operator is bounded and analytic in the wave number, enabling parallel solution of sound-soft and sound-hard Helmholtz problems in 3D.
We present a new integral equation for solving the Maxwell scattering problem against a perfect conductor. The very same algorithm also applies to sound-soft as well as sound-hard Helmholtz scattering, and in fact the latter two can be solved in parallel in three dimensions. Our integral equation does not break down at interior spurious resonances, and uses spaces of functions without any algebraic or differential constraints. The operator to invert at the boundary involves a singular integral operator closely related to the three dimensional Cauchy singular integral, and is bounded on natural function spaces and depend analytically on the wave number. Our operators act on functions with pairs of complex two by two matrices as values, using a spin representation of the fields.