IFGF-accelerated integral equation solvers for acoustic scattering

12/12/2021
by   Edwin Jimenez, et al.
0

We present an accelerated and hardware parallelized integral-equation solver for the problem of acoustic scattering by a two-dimensional surface in three-dimensional space. The approach is based, in part, on the novel Interpolated Factored Green Function acceleration method (IFGF) that, without recourse to the Fast Fourier Transform (FFT), evaluates the action of Green function-based integral operators for an N-point surface discretization at a complexity of (Nlog N) operations instead of the (N^2) cost associated with nonaccelerated methods. The IFGF algorithm exploits the slow variations of factored Green functions to enable the fast evaluation of fields generated by groups of sources on the basis of a recursive interpolation scheme. In the proposed approach, the IFGF method is used to account for the vast majority of the computations, while, for the relatively few singular, nearly-singular and neighboring non-singular integral operator evaluations, a high-order rectangular-polar quadrature approach is employed instead. Since the overall approach does not rely on the FFT, it is amenable to efficient shared- and distributed-memory parallelization; this paper demonstrates such a capability by means of an OpenMP parallel implementation of the method. A variety of numerical examples presented in this paper demonstrate that the proposed methods enable the efficient solution of large problems over complex geometries on small parallel hardware infrastructures. Numerical examples include acoustic scattering by a sphere of up to 128 wavelengths, an 80-wavelength submarine, and a turbofan nacelle that is more than 80 wavelengths in size, requiring, on a 28-core computer, computing times of the order of a few minutes per iteration and a few tens of iterations of the GMRES iterative solver.

READ FULL TEXT

page 9

page 12

page 14

page 15

page 16

page 17

page 18

page 19

research
10/06/2020

"Interpolated Factored Green Function" Method for accelerated solution of Scattering Problems

This paper presents a novel "Interpolated Factored Green Function" metho...
research
04/08/2021

A fast solver for elastic scattering from axisymmetric objects by boundary integral equations

Fast and high-order accurate algorithms for three dimensional elastic sc...
research
11/02/2022

A highly accurate perfectly-matched-layer boundary integral equation solver for acoustic layered-medium problems

Based on the perfectly matched layer (PML) technique, this paper develop...
research
09/27/2019

Regularized integral equation methods for elastic scattering problems in three dimensions

This paper presents novel methodologies for the numerical simulation of ...
research
04/02/2020

VoxCap: FFT-Accelerated and Tucker-Enhanced Capacitance Extraction Simulator for Voxelized Structures

VoxCap, a fast Fourier transform (FFT)-accelerated and Tucker-enhanced i...
research
09/01/2020

AIMx: An Extended Adaptive Integral Method for the Fast Electromagnetic Modeling of Complex Structures

Surface integral equation (SIE) methods are of great interest for the ef...
research
07/21/2020

DecoSurf: Recursive Geodesic Patterns on Triangle Meshes

In this paper, we show that many complex patterns, which characterize th...

Please sign up or login with your details

Forgot password? Click here to reset