相关论文: The method of polarized traces for the 2D Helmholt…
We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media, with online parallel complexity that scales empirically as $\mathcal{O}(\frac{N}{P})$, where $N$ is the number of volume…
We present a fast solver for the 3D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media. The solver is based on the method of polarized traces, coupled with distributed linear algebra libraries and…
We present a variant of the solver in Zepeda-N\'u\~nez and Demanet (2014), for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media. By changing the domain decomposition from a layered to a grid-like partition, this…
In this paper, a fast multipole method (FMM) is proposed to compute long-range interactions of wave sources embedded in 3-D layered media. The layered media Green's function for the Helmholtz equation, which satisfies the transmission…
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…
We develop efficient and high-order accurate solvers for the Helmholtz equation on complex geometry. The schemes are based on the WaveHoltz algorithm which computes solutions of the Helmholtz equation by time-filtering solutions of the wave…
We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by…
In this paper, we will introduce a new heterogeneous fast multipole method (H-FMM) for 2-D Helmholtz equation in layered media. To illustrate the main algorithm ideas, we focus on the case of two and three layers in this work. The key…
We present the first fast solver for the high-frequency Helmholtz equation that scales optimally in parallel, for a single right-hand side. The L-sweeps approach achieves this scalability by departing from the usual propagation pattern, 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 investigate the parallel one-level overlapping Schwarz method for solving finite element discretization of high-frequency Helmholtz equations. The resulting linear systems are large, indefinite, ill-conditioned, and complex-valued. We…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
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…
In this paper, we present a fast boundary integral method accelerated by the fast multipole method (FMM) for acoustic wave scattering governed by the scalar Helmholtz equation in multi-layered two-dimensional media. Multiple scatterers are…
This paper presents a fast iterative solver for Lippmann-Schwinger equation for high-frequency waves scattered by a smooth medium with a compactly supported inhomogeneity. The solver is based on the sparsifying preconditioner and a domain…
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our…
The Helmholtz equation arises in the study of electromagnetic radiation, optics, acoustics, etc. In spherical coordinates, its general solution can be written as a spherical harmonic series which satisfies the radiation condition at…
We introduce a novel multi-resolution Localized Orthogonal Decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The method merges the concepts of LOD and operator-adapted wavelets…
Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be used online during treatments to predict…
In this paper, we present a Localized Orthogonal Decomposition (LOD) in Petrov-Galerkin formulation for a two-scale Helmholtz-type problem. The two-scale problem is, for instance, motivated from the homogenization of the Helmholtz equation…