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Estimating parameters for reactive contaminant transport models can be a very computationally intensive. Typically this involves solving a forward problem many times, with many degrees of freedom that must be computed each time. We show that reduced order modeling (ROM) by proper orthogonal decomposition (POD) can be used to approximate the solution to the forward model using many fewer degrees of freedom. We provide background on the finite element method and reduced order modeling in one spatial dimension, and apply both methods to a system of linear uncoupled time-dependent equations simulating reactive transport in a column. By comparing the reduced order and finite element approximations, we demonstrate that the reduced model, while having many fewer degrees of freedom to compute, gives a good approximation of the high-dimensional (finite element) model. Our results indicate that one may substitute a reduced model in place of a high-dimensional model to solve the forward problem in parameter estimation with many fewer degrees of freedom.
A Thesis submitted to the Department of Scientiﬁc Computing in partial fulfillment of the requirements for the degree of Master of Science.
Includes bibliographical references.
Janet Peterson, Professor Directing Thesis; Ming Ye, Professor Co-Directing Thesis; Sachin Shanbhag, Committee Member.
Florida State University
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