209 citations · 549 across the 39 of their papers we have counts for
10 papers · 2 filters
An improved discrete least-squares/reduced-basis method for parameterized elliptic PDEs
Max Gunzburger, Michael Schneier, Clayton Webster +1
It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basi…
Convergence of finite element solutions of stochastic partial integro-differential equations driven by white noise
Max Gunzburger, Buyang Li, Jilu Wang
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, wit…
A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows
Max Gunzburger, Traian Iliescu, Michael Schneier
Partial differential equations (PDEs) are often dependent on input quantities which are inherently uncertain. To quantify this uncertainty, these PDEs must be solved over a large e…
A Coupling Approach for Linear Elasticity Problems with Spatially Noncoincident Interfaces
Pavel Bochev, James Cheung, Max Gunzburger +1
We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we de…
Optimally accurate higher-order finite element methods on polytopial approximations of domains with smooth boundaries
James Cheung, Mauro Perego, Pavel Bochev +1
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the dom…
A higher-order ensemble/proper orthogonal decomposition method for the nonstationary Navier-Stokes equations
Max Gunzburger, Nan Jiang, Michael Schneier
Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as oc…
Fast Spherical Centroidal Voronoi Mesh Generation: A Lloyd-preconditioned LBFGS Method in Parallel
Huanhuan Yang, Max Gunzburger, Lili Ju
Centroidal Voronoi tessellation (CVT)-based mesh generation is a very effective technique for creating high-quality Voronoi meshes and their dual Delaunay triangulations that often…
A second-order time-stepping scheme for simulating ensembles of parameterized flow problems
Max Gunzburger, Nan Jiang, Zhu Wang
We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or…
An efficient algorithm for simulating ensembles of parameterized flow problems
Max Gunzburger, Nan Jiang, Zhu Wang
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to effi…
Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise
Max Gunzburger, Buyang Li, Jilu Wang
The stochastic time-fractional equation with space-time white noise is discretized in time by a backward-Euler convolution q…