Research Articles, Interdisciplinary Center for Applied Mathematics (ICAM)
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Local improvements to reducedorder models using sensitivity analysis of the proper orthogonal decomposition
(Cambridge University Press, 200906)The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis ... 
Shape Sensitivity Analysis in Flow Models Using a FiniteDifference Approach
(Hindawi Publishing Corporation, 2010)Reducedordermodels have a number of practical engineering applications for unsteady flows that require either lowdimensional approximations for analysis and control or repeated simulation over a range of parameter values. ... 
Issues related to leastsquares finite element methods for the stokes equations
(Siam Publications, 199810)Leastsquares finite element methods have become increasingly popular for the approximate solution of firstorder systems of partial differential equations. Here, after a brief review of some existing theories, a number ... 
On efficient solutions to the continuous sensitivity equation using automatic differentiation
(Siam Publications, 200006)Shape sensitivity analysis is a tool that provides quantitative information about the influence of shape parameter changes on the solution of a partial differential equation (PDE). These shape sensitivities are described ... 
Inexact KleinmanNewton method for Riccati equations
(Siam Publications, 200903)In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver ... 
Mesh independence of KleinmanNewton iterations for Riccati equations in Hilbert space
(Siam Publications, 2008)In this paper we consider the convergence of the infinite dimensional version of the KleinmanNewton algorithm for solving the algebraic Riccati operator equation associated with the linear quadratic regulator problem in ... 
On the LawrenceDoniach and Anisotropic GinzburgLandau models for layered superconductors
(Siam Publications, 199502)The authors consider two models, the LawrenceDoniach and the anisotropic GinzburgLandau models for layered superconductors such as the recently discovered hightemperature superconductors. A mathematical description of ... 
comment on "a numerical study of periodic disturbances on twolayer couette flow" phys. fluids 10, 3056 (1998)
(AIP Publishing, 199910) 
a numerical study of periodic disturbances on twolayer Couette flaw
(AIP Publishing, 199812)The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semiimplicit Stokes solver to enable computations at low Reynolds numbers, and a secondorder velocity ...