Regularized integral equations and fast high‐order solvers for sound‐hard acoustic scattering problems

SUMMARY This text introduces the following: (1) new regularized combined field integral equations (CFIE‐R) for frequency‐domain sound‐hard scattering problems; and (2) fast, high‐order algorithms for the numerical solution of the CFIE‐R and related integral equations. Similar to the classical combined field integral equation (CFIE), the CFIE‐R are uniquely‐solvable integral equations based on the 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.