41 citations · 125 across the 15 of their papers we have counts for
10 papers · 1 filter
High-frequency limit of the inverse scattering problem: asymptotic convergence from inverse Helmholtz to inverse Liouville
Shi Chen, Zhiyan Ding, Qin Li +1
We investigate the asymptotic relation between the inverse problems relying on the Helmholtz equation and the radiative transfer equation (RTE) as physical models, in the high-freq…
L-Sweeps: A scalable, parallel preconditioner for the high-frequency Helmholtz equation
Matthias Taus, Leonardo Zepeda-Núñez, Russell J Hewett +1
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 scal…
A multiscale neural network based on hierarchical nested bases
Yuwei Fan, Jordi Feliu-Faba, Lin Lin +2
In recent years, deep learning has led to impressive results in many fields. In this paper, we introduce a multi-scale artificial neural network for high-dimensional non-linear map…
A multiscale neural network based on hierarchical matrices
Yuwei Fan, Lin Lin, Lexing Ying +1
In this work we introduce a new multiscale artificial neural network based on the structure of -matrices. This network generalizes the latter to the nonlinear case by…
The method of polarized traces for the 3D Helmholtz equation
Leonardo Zepeda-Núñez, Adrien Scheuer, Russell J. Hewett +1
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, cou…
A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media
Jun Fang, Jianliang Qian, Leonardo Zepeda-Núñez +1
We propose a hybrid approach to solve the high-frequency Helmholtz equation with point source terms in smooth heterogeneous media. The method is based on the ray-based finite eleme…
Learning Dominant Wave Directions For Plane Wave Methods For High-Frequency Helmholtz Equations
Jun Fang, Jianliang Qian, Leonardo Zepeda-Núñez +1
We present a ray-based finite element method (ray-FEM) by learning basis adaptive to the underlying high-frequency Helmholtz equation in smooth media. Based on the geometric optics…
Fast alternating bi-directional preconditioner for the 2D high-frequency Lippmann-Schwinger equation
Leonardo Zepeda-Núñez, Hongkai Zhao
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 solv…
Nested domain decomposition with polarized traces for the 2D Helmholtz equation
Leonardo Zepeda-Núñez, Laurent Demanet
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 $\ma…
The method of polarized traces for the 2D Helmholtz equation
Leonardo Zepeda-Núñez, Laurent Demanet
We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as $\mathcal{O}(\frac{N}{L})…