Fast high-order algorithms and well-conditioned integral equations for high-frequency sound-hard scattering problems

This text introduces 1) New Regularized Combined Field Integral Equations (CFIE-R) for the solution of frequency-domain sound-hard scattering problems, and, 2) Fast, high-order algorithms for the numerical solution of the CFIE-R and related integral equations. Like the classical Combined Field Integral Equation (CFIE), the CFIE-R are unikely-solvable integral equations based on use of single and double layer potentials. Unlike the CFIE, however, the CFIE-R utilize a composition of the double-layer potential with a regularizing operator that gives rise to highly-favorable spectral properties—thus making it possible to produce accurate solutions by means of iterative solvers in small numbers of iterations. The CFIE-R-based fast high-order integral algorithms introduced in this text enable highly accurate solution of challenging sound-hard scattering problems, including hundred-wavelength cases, in single-processor runs on present-day desktop computers. A variety of numerical results demonstrate the qualities of the numerical solvers as well as the advantages that arise from the new integral equation formulation.