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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)

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)

- Virginia Forstall, Howard Elman
- 2012

The goal of this project is to explore computational methods designed to solve the steady-state diffusion equation with a random coefficient. Although such equations can be solved using Monte-Carlo methods, the lengthy computation time can be constraining. Using a Karhunen-Lò eve expansion allows the random coefficient to be approximated with a finite sum… (More)

- Virginia Forstall, Howard Elman
- 2011

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)

- Virginia Forstall, Howard Elman
- 2011

The goal of this project is to efficiently solve a steady state diffusion equation with a random 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. This… (More)

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