11 citations · 56 across the 26 of their papers we have counts for
4 papers · 1 filter
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…
Modified Virtual Grid Difference for Discretizing the Laplace-Beltrami Operator on Point Clouds
Meng Wang, Shingyu Leung, Hongkai Zhao
We propose a new and simple discretization, named the Modified Virtual Grid Difference (MVGD), for numerical approximation of the Laplace-Beltrami (LB) operator on manifolds sample…
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…
Variational Hamiltonian Monte Carlo via Score Matching
Cheng Zhang, Babak Shahbaba, Hongkai Zhao
Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, ho…