Interdisciplinary Center for Applied Mathematics (ICAM)
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Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition
(Cambridge University Press, 2009-06)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 Finite-Difference Approach
(Hindawi Publishing Corporation, 2010)Reduced-ordermodels have a number of practical engineering applications for unsteady flows that require either low-dimensional approximations for analysis and control or repeated simulation over a range of parameter values. ... -
Issues related to least-squares finite element methods for the stokes equations
(Siam Publications, 1998-10)Least-squares finite element methods have become increasingly popular for the approximate solution of first-order 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, 2000-06)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 Kleinman-Newton method for Riccati equations
(Siam Publications, 2009-03)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 Kleinman-Newton iterations for Riccati equations in Hilbert space
(Siam Publications, 2008)In this paper we consider the convergence of the infinite dimensional version of the Kleinman-Newton algorithm for solving the algebraic Riccati operator equation associated with the linear quadratic regulator problem in ... -
On the Lawrence-Doniach and Anisotropic Ginzburg-Landau models for layered superconductors
(Siam Publications, 1995-02)The authors consider two models, the Lawrence-Doniach and the anisotropic Ginzburg-Landau models for layered superconductors such as the recently discovered high-temperature superconductors. A mathematical description of ... -
comment on "a numerical study of periodic disturbances on two-layer couette flow" phys. fluids 10, 3056 (1998)
(AIP Publishing, 1999-10) -
a numerical study of periodic disturbances on two-layer Couette flaw
(AIP Publishing, 1998-12)The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds numbers, and a second-order velocity ...
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