Related papers: An accelerated direct solver for scalar wave scatt…
In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…
This paper presents a novel framework to accelerate score-based diffusion models. It first converts the standard stable diffusion model into the Fokker-Planck formulation which results in solving large linear systems for each image. For…
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…
In this paper we consider the classic problems of scattering of waves from perfectly conducting cylinders with piecewise smooth boundaries. The scattering problems are formulated as integral equations and solved using a Nystr\"om scheme…
The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric…
We study the systematic numerical approximation of Maxwell's equations in dispersive media. Two discretization strategies are considered, one based on a traditional leapfrog time integration method and the other based on convolution…
Efficient numerical solution of the acoustic Helmholtz equation in heterogeneous media remains challenging, particularly for large-scale problems with spatially-varying density - a limitation that restricts applications in biomedical…
This study builds on a recent paper by Lai et al [Appl. Comput. Harmon. Anal., 2018] in which a novel boundary integral formulation is presented for scalar wave scattering analysis in two-dimensional layered and half-spaces. The seminal…
A discretization scheme for variable coefficient Helmholtz problems on two-dimensional domains is presented. The scheme is based on high-order spectral approximations and is designed for problems with smooth solutions. The resulting system…
Building upon recent results obtained in [7,8,9], we describe an efficient second order, A-stable scheme for solving the wave equation, based on the method of lines transpose (MOL$^T$), and the resulting semi-discrete (i.e. continuous in…
A fast method is proposed for solving the high frequency Helmholtz equation. The building block of the new fast method is an overlapping source transfer domain decomposition method for layered medium, which is an extension of the source…
We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules.…
In this paper we study the application of a simplified method to solve the dynamic radiative transfer problem in expanding envelopes. The method, which requires a computational effort similar to that of the diffusion approximation, is based…
In this work, we introduce a dispersive N(=2n)-wave interaction problem involving n velocities in two spatial dimensions and one temporal dimension. Exact solutions of the problem are exhibited. This is a generalization of the N-wave…
The Schr\"{o}dinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
In this study, we investigate atom--dimer scattering within the framework of the hyperspherical method. The coupled channel Schr\"odinger equation is solved using the R-matrix propagation technique combined with the smooth variable…
The paper is concerned with the three-dimensional electromagnetic scattering from a large open rectangular cavity that is embedded in a perfectly electrically conducting infinite ground plane. By introducing a transparent boundary…
The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the…
A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and…