12 Result(s)
within
Max Gunzburger
Computational Mathematics and Numerical Analysis
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Chapter and Conference Paper
Discretization of Cost and Sensitivities in Shape Optimization
We consider a problem in aircraft engine testing [1], [6]. Of special concern is the influence of the aircraft forebody on the flow that reaches the engine intake. Modern aircraft are too large to place in a w...
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Chapter
Sensitivities in Computational Methods for Optimal Flow Control
Flow optimization and control problems have the typical structure of all such problems. Their description involves
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Article
Error analysis of finite element approximations of the stochastic Stokes equations
Numerical solutions of the stochastic Stokes equations driven by white noise perturbed forcing terms using finite element methods are considered. The discretization of the white noise and finite element approx...
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Article
Analysis of Nonlinear Spectral Eddy-Viscosity Models of Turbulence
Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. ...
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Chapter
Voronoi Tessellations and Their Application to Climate and Global Modeling
We review the use of Voronoi tessellations for grid generation, especially on the whole sphere or in regions on the sphere. Voronoi tessellations and the corresponding Delaunay tessellations in regions and sur...
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Chapter and Conference Paper
An Adaptive Wavelet Stochastic Collocation Method for Irregular Solutions of Partial Differential Equations with Random Input Data
A novel multi-dimensional multi-resolution adaptive wavelet stochastic collocation method (AWSCM) for solving partial differential equations with random input data is proposed. The uncertainty in the input dat...
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Reference Work Entry In depth
Least Squares Finite Element Methods
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Article
Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains
Approximations of solutions of fractional Laplacian equations on bounded domains are considered. Such equations allow global interactions between points separated by arbitrarily large distances. Two approximat...
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Chapter and Conference Paper
An Applied/Computational Mathematician’s View of Uncertainty Quantification for Complex Systems
Uncertainty quantification (UQ) is defined differently by different disciplines. Here, we first review an applied and computational mathematician’s definition of UQ for complex systems, especially in the conte...
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Article
An Improved Discrete Least-Squares/Reduced-Basis Method for Parameterized Elliptic PDEs
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-basis method into the DLS framewo...
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Chapter
Piecewise Polynomial Approximation of Probability Density Functions with Application to Uncertainty Quantification for Stochastic PDEs
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions ar...
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Article
A Multifidelity Monte Carlo Method for Realistic Computational Budgets
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each wi...
