An efficient high-order Nystrom scheme for acoustic scattering by inhomogeneous penetrable media withdiscontinuous material interface

作者：Anand Akash^*; Pandey Ambuj; Kumar B V Rathish; Paul Jagabandhu

来源：Journal of Computational Physics, 2016, 311: 258-274.

DOI：10.1016/j.jcp.2016.01.028

• Acoustic scattering
• Lippmann-Schwinger integral equation
• High-order methods
• Integral equation methods

This text proposes a fast, rapidly convergent Nystrom method for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by inhomogeneous obstacles, while allowing the material properties to jump across the interface. The method works with overlapping coordinate charts as a description of the given scatterer. In particular, it employs "partitions of unity" to simplify the implementation of high-order quadratures along with suitable changes of parametric variables to analytically resolve the singularities present in the integral operator to achieve desired accuracies in approximations. To deal with the discontinuous material interface in a high-order manner, a specialized quadrature is used in the boundary region. The approach further utilizes an FFT based strategy that uses equivalent source approximations to accelerate the evaluation of large number of interactions that arise in the approximation of the volumetric integral operator and thus achieves a reduced computational complexity of O(NlogN) for an N-point discretization. A detailed discussion on the solution methodology along with a variety of numerical experiments to exemplify its performance are presented in this paper.

• 出版日期2016-4-15