A fourth-order Cartesian grid method for multiple acoustic scattering on closely packed obstacles

In this paper, we present a fourth-order Cartesian grid-based boundary integral method (BIM) for multiple acoustic scattering problem on closely packed obstacles. We reformulate the exterior Helmholtz value problems (BVPs) as Fredholm equation (BIE) of second kind some unknown density function. Unlike traditional method, distinctive feature our scheme is that do not require quadratures and direct evaluations nearly singular, singular or hyper-singular integrals in solution BIEs. Instead, reinterpret solutions to equivalent simple interface an extended rectangle domain, which can be solved efficiently by finite difference coupled with numerical corrections, FFT based interpolations. Extensive experiments show formally high-order accurate, fast convergent particular insensitive complexity scatterers.