Related papers: Adapting free-space fast multipole method for laye…
A robust algorithm is proposed to reconstruct the spatial support and the Lam\'e parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of…
We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
Layered media have been studied extensively both for their importance in imaging technologies and as an example of a hyperbolic PDE with discontinuous coefficients. From the perspective of acoustic imaging, the time limited impulse response…
In the graph-based semi-supervised learning, the Green-function method is a classical method that works by computing the Green's function in the graph space. However, when applied to large graphs, especially those sparse ones, this method…
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space of the forcing terms to the space of the solutions with the…
We introduce the Fast Free Memory method (FFM), a new fast method for the numerical evaluation of convolution products. Inheriting from the Fast Multipole Method, the FFM is a descent-only and kernel-independent algorithm. We give the…
In micromagnetic simulations, the demagnetization field is by far the computationally most expensive field component and often a limiting factor in large multilayer systems. We present an exact method to calculate the demagnetization field…
Heat diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate…
The present work develops a rigorous framework for collective dipole oscillations in dense dielectric media by extending the Lorentz oscillator model to include both quadratic (second order) and cubic (third order) nonlinear restoring…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…
We introduce an $O(M)$ algorithm for evaluating the azimuthal Fourier modes $G_{k,m}$, $m = 0, 1, ..., M$, of the three-dimensional Helmholtz Green's function with real wavenumber $k$, together with all their first- and second-order…
In this paper, a fast multipole method (FMM) is proposed for 3-D Laplace equation in layered media. The potential due to charges embedded in layered media is decomposed into a free space component and four types of reaction field…
In this work, a numerical modal decomposition approach is applied to model the optical field of laser light after propagating through a highly multi-mode fiber. The algorithm for the decomposition is based on the reconstruction of measured…
An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels…
In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…
This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…