6 Result(s)
-
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...
-
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...
-
Chapter and Conference Paper
A Locally Conservative Mimetic Least-Squares Finite Element Method for the Stokes Equations
Least-squares finite element methods (LSFEMs) for the incompressible Stokes equations that use nodal C 0 elements conserve mass approximately. This has led to the common and widespread misconcepti...
-
Chapter and Conference Paper
Bridging Methods for Coupling Atomistic and Continuum Models
We review some recent developments in the coupling of atomistic and continuum models based on the blending of the two models in a bridge region connecting the other two regions in which the models are separate...
-
Chapter and Conference Paper
Reduced-Order Modeling of Complex Systems with Multiple System Parameters
The computational approximation of solutions of complex systems such as the Navier-Stokes equations is often a formidable task. For example, in feedback control settings where one often needs solutions of the ...
-
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...
