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We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…

Numerical Analysis · Mathematics 2018-05-15 Lise-Marie Imbert-Gerard , Felipe Vico , Leslie Greengard , Miguel Ferrando

This paper considers the scattering of a time-harmonic acoustic plane wave by an elastic body with an unbounded periodic surface. The original problem can be confined to the analysis of the fields in one periodic cell. With the help of the…

Numerical Analysis · Mathematics 2026-02-11 Sijia Li , Lei Lin , Junliang Lv

The multipole expansion can be formulated in spherical and Cartesian coordinates. By constructing an explicit map linking both formulations in isotropic media, we discover a lack of equivalence between them in anisotropic media. In…

Simulation of the acoustic wave equation plays an important role in various applications, including audio engineering, medical imaging, and fluid dynamics. However, the complexity of the propagation medium can pose challenges, such as the…

Numerical Analysis · Mathematics 2024-11-20 Tao Yu , Tailong Jin , Yanfeng Shen , Lei Zhang

In anisotropic media, the standard perfectly matched layer (PML) technique suffers irrevocable instability in terminating the unbounded problem domains. It remains an open question whether a stable PML-like absorbing boundary condition…

Numerical Analysis · Mathematics 2021-11-23 Yong Gao , Wangtao Lu

In clinical imaging, magnetic resonance (MR) image volumes are often acquired as stacks of 2D slices with decreased scan times, improved signal-to-noise ratio, and image contrasts unique to 2D MR pulse sequences. While this is sufficient…

Computer Vision and Pattern Recognition · Computer Science 2026-03-09 Samuel W. Remedios , Shuwen Wei , Shuo Han , Jinwei Zhang , Aaron Carass , Kurt G. Schilling , Dzung L. Pham , Jerry L. Prince , Blake E. Dewey

Perfectly Matched Layer (PML) is a widely adopted non-reflecting boundary treatment for wave simulations. Reducing numerical reflections from a discretized PML has been a long lasting challenge. This paper presents a new discrete PML for…

Numerical Analysis · Mathematics 2019-03-12 Albert Chern

For the study of complex synthetic and biological molecular systems by computer simulations one is still restricted to simple model systems or to by far too small time scales. To overcome this problem multiscale techniques are being…

Statistical Mechanics · Physics 2007-05-23 Matej Praprotnik , Kurt Kremer , Luigi Delle Site

We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…

Numerical Analysis · Mathematics 2025-07-09 Yulei Liao , Pingbing Ming

In this paper, we design a truly exact and optimal perfect absorbing layer (PAL) for domain truncation of the two-dimensional Helmholtz equation in an unbounded domain with bounded scatterers. This technique is based on a complex…

Numerical Analysis · Mathematics 2019-10-22 Zhiguo Yang , Li-Lian Wang , Yang Gao

We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the…

Numerical Analysis · Mathematics 2016-08-16 Jérôme Droniou , Robert Eymard

We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic…

Computational Physics · Physics 2007-05-23 S. Rahman , H. P. Langtangen , C. H. W. Barnes

A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave equation in the whole real axis and numerical discretization is designed for solving the reduced PML problem on a bounded domain. The nonlocal PML poses challenges…

Numerical Analysis · Mathematics 2022-02-22 Yu Du , Jiwei Zhang

The conventional Perfectly Matched Layer (PML) is unstable for certain kinds of anisotropic media. This instability is intrinsic and independent of PML formulation or implementation. The Multi-axial PML (MPML) removes such instability using…

Geophysics · Physics 2016-12-22 Kai Gao , Lianjie Huang

Linear acoustic wave-splitting is an often used tool in describing sound-wave propagation through earth's subsurface. Earth's subsurface is in general anisotropic due to the presence of water-filled porous rocks. Due to the complexity and…

Mathematical Physics · Physics 2019-03-07 B. L. G. Jonsson , M. Norgren

Perfectly Matched Layers (PML) has become a very common method for the numerical approximation of wave and wave-like equations on unbounded domains. This technique allows one to obtain accurate solutions while working on a finite…

Analysis of PDEs · Mathematics 2025-03-11 Kurt Bryan , Michael S. Vogelius

This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of…

Mathematical Physics · Physics 2016-11-02 Howard W. Levinson , Vadim A. Markel

In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in…

Computational Physics · Physics 2014-08-08 Amit K. Patra , S. Gopalakrishnan , Ranjan Ganguli

This work presents a variational physics-informed deep learning framework for phase-field modelling of brittle crack propagation in anisotropic media. Previous Deep Ritz Method (DRM) approaches have focused on second-order, isotropic…

Computational Physics · Physics 2026-04-15 N. Plungė , P. Brommer , R. S. Edwards , E. G. Kakouris

Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for…

Numerical Analysis · Mathematics 2016-12-21 Hisham Assi , Richard S. C. Cobbold