Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2412.11162

An FFT-accelerated PML-BIE Solver for Three-Dimensional Acoustic Wave Scattering in Layered Media

Hangya Wang·Wangtao Lu
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper is concerned with three-dimensional acoustic wave scattering in two-layer media, where the two homogeneous layers are separated by a locally perturbed plane featuring an axially symmetric perturbation. A fast novel boundary integral equation (BIE) method is proposed to solve the scattering problem within a cylindrical perfectly matched layer (PML) truncation. We use PML-transformed Green's functions to derive BIEs in terms of single- and double-layer potentials for the wave field and its normal derivative on the boundary of each truncated homogeneous region. These BIEs, combined with interface and PML boundary conditions, form a complete system that accurately approximates the scattering problem. An FFT-based approach is introduced to efficiently and accurately discretize the surface integral operators in the BIEs, where a new kernel splitting technique is developed to resolve instabilities arising from the complex arguments in Green's functions. Numerical experiments demonstrate the efficiency and accuracy of the proposed method, as well as the exponential decay of truncation errors introduced by the PML.

Explore related subjects

math.NAcs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hangya Wang, Wangtao Lu. 2024-12-15. An FFT-accelerated PML-BIE Solver for Three-Dimensional Acoustic Wave Scattering in Layered Media. https://arxiv.org/abs/2412.11162

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fully spectral scheme for the linear BGK equation on the whole space

In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $Φ$, even if the method could be applied to different collision operators. It is based upon the projection on Hermite polynomials in velocity and orthonormal polynomials with respect to the weight $e^{-$Φ$}$ in space. The potential $Φ$ is assumed to be a polynomial. It is, to the author's knowledge, the first scheme which preserves hypocoercive behavior in addition to the conservation laws. These different properties are illustrated numerically on both quadratic and double well potential.

math.NA↗
arXiv2026

Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds

This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in $\mathbb{R}^d$ and compact Riemannian manifolds. While inverse inequalities are well-studied for polynomial spaces, their extension to kernel-based trial spaces poses significant challenges. For bounded Lipschitz domains, we extend prior Bernstein inequalities, which only apply to a limited range of Sobolev orders, to the full range of lower and upper orders, and derive Nikolskii inequalities that bound $L_\infty$ norms by $L_2$ norms. For compact Riemannian manifolds, we focus on restricted kernels, which are defined as the restriction of positive definite kernels from the ambient Euclidean space to the manifold, and prove their counterparts.

math.NA↗
arXiv2026

Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks

This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables that reformulates the system into n independent initial-boundary value problems. The asymptotic expansions are then constructed and rigorously justified by deriving an error estimate based on the energy method.

math.NA↗