Virginia Forstall

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The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space, and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem, which provides an accurate estimate(More)
This work presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by a non-invariant symmetric-positive-definite matrix. As opposed to typical truncation strategies used in recycling such as deflation, we propose a truncation method inspired by goal-oriented proper orthogonal(More)
The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem, which provides an accurate estimate(More)
The goal of this project is to efficiently solve a steady-state diffusion equation with a random diffusion coefficient. Although, such equations can be solved using Monte-Carlo methods, the lengthy computation time can be constraining. Using a Karhunen-Loéve expansion allows the random coefficient to be approximated with a finite sum of random variables.(More)
Title of dissertation: ITERATIVE SOLUTION METHODS FOR REDUCED-ORDER MODELS OF PARAMETERIZED PARTIAL DIFFERENTIAL EQUATIONS Virginia Forstall, Doctor of Philosophy, 2015 Dissertation directed by: Professor Howard Elman Department of Computer Science This dissertation considers efficient computational algorithms for solving parameterized discrete partial(More)
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