18 citations · 30 across the 18 of their papers we have counts for
21 papers
Sparsity for parametric PDEs with log-gamma random inputs and applications
Dinh Dũng, Van Kien Nguyen, Viet Ha Hoang
We propose a novel method for establishing the sparsity of the coefficients of the Laguerre generalized polynomial chaos expansion of solutions to parametric elliptic PDEs with log…
Robust space-time multiscale upscaling via multicontinuum homogenization for evolving perforated media
Wei Xie, Viet Ha Hoang, Yin Yang +1
Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous m…
A hierarchical approach for multicontinuum homogenization in high contrast media
Wei Xie, Viet Ha Hoang, Yin Yang +1
A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. T…
Bayesian inversion for Electrical Impedance Tomography by sparse interpolation
Quang Huy Pham, Viet Ha Hoang
We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. T…
Multilevel Markov Chain Monte Carlo for Bayesian Elliptic Inverse Problems with Besov Random Tree Priors
Andreas Stein, Viet Ha Hoang
We propose a multilevel Monte Carlo-FEM algorithm to solve elliptic Bayesian inverse problems with "Besov random tree prior". These priors are given by a wavelet series with stocha…
Optimal finite elements for ergodic stochastic two-scale elliptic equations
Viet Ha Hoang, Chen Hui Pang, Wee Chin Tan
We develop an essentially optimal finite element approach for solving ergodic stochastic two-scale elliptic equations whose two-scale coefficient may depend also on the slow variab…
Bayesian Inversion of Log-normal Eikonal Equations
Zhan Fei Yeo, Viet Ha Hoang
We study the Bayesian inverse problem for inferring the log-normal slowness function of the eikonal equation given noisy observation data on its solution at a set of spatial points…
Homogenization of a multiscale multi-continuum system
Jun Sur Richard Park, Viet Ha Hoang
We study homogenization of a locally periodic two-scale dual-continuum system where each continuum interacts with the other. Equations for each continuum are written separately wit…
Multiscale simulations for upscaled multi-continuum flows
Jun Sur Richard Park, Siu Wun Cheung, Tina Mai +1
We consider in this paper a challenging problem of simulating fluid flows, in complex multiscale media possessing multi-continuum background. As an effort to handle this obstacle,…
Hierarchical multiscale finite element method for multi-continuum media
Jun Sur Richard Park, Viet Ha Hoang
Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of mo…
Bayesian inverse problems for recovering coefficients of two scale elliptic equations
Viet Ha Hoang, Jia Hao Quek
We consider the Bayesian inverse homogenization problem of recovering the locally periodic two scale coefficient of a two scale elliptic equation, given limited noisy information o…
High dimensional finite elements for multiscale Maxwell wave equations
Van Tiep Chu, Viet Ha Hoang
We develop an essentially optimal numerical method for solving multiscale Maxwell wave equations in a domain . The problems depend on scales: one macro…
Reconciling Bayesian and perimeter regularization for binary inversion
Oliver R. A. Dunbar, Matthew M. Dunlop, Charles M. Elliott +2
A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On…
Homogenization of multiscale Maxwell wave equations
Van Tiep Chu, Viet Ha Hoang
We study homogenization of multiscale Maxwell wave equation that depends on separable microscopic scales in a domain on a finite time interval .…
Bayesian Multiscale Finite Element Methods. Modeling missing subgrid information probabilistically
Y. Efendiev, W. T. Leung, S. W. Cheung +3
In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational mode…
Homogenization error for two scale Maxwell equations
Van Tiep Chu, Viet Ha Hoang
For two scale elliptic equations in a domain , standard homogenization errors are deduced with the assumption that the solution of the homogenized equation belongs to $H^2…
Polynomial approximations of a class of stochastic multiscale elasticity problems
Viet Ha Hoang, Thanh Chung Nguyen, Bingxing Xia
We consider a class of elasticity equations in whose elastic moduli depend on separated microscopic scales, are random and expressed as a linear expansion of a…
Determining White Noise Forcing From Eulerian Observations in the Navier Stokes Equation
Viet Ha Hoang, Kody J. H. Law, Andrew M. Stuart
The Bayesian approach to inverse problems is of paramount importance in quantifying uncertainty about the input to and the state of a system of interest given noisy observations. H…
Complexity Analysis of Accelerated MCMC Methods for Bayesian Inversion
Viet Ha Hoang, Christoph Schwab, Andrew M. Stuart
We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the e…
Bayesian inverse problems for Burgers and Hamilton-Jacobi equations with white-noise forcing
Viet Ha Hoang
The paper formulates Bayesian inverse problems for inference in a topological measure space given noisy observations. Conditions for the validity of the Bayes formula and the well-…
Homogenization for advection-diffusion in a perforated domain
P. H. Haynes, V. H. Hoang, J. R. Norris +1
The volume of a Wiener sausage constructed from a diffusion process with periodic, mean-zero, divergence-free velocity field, in dimension 3 or more, is shown to have a non-random…