IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Ninth Annual Graduate Student Mini-conference in Computational Mathematics

Olcay Ciftci
Auburn University
Abstract

Application of the discrete empirical interpolation method to variable density flow and solute transport equations

  • Feb. 17, 2018
  • 11:20 a.m.
  • LeConte 412

The variable-density flow and solute transport's (VDFST) model is a time dependent, coupled nonlinear PDE, widely used to simulate seawater intrusion and related problems. The aim of this project is to investigate reduced order models for these equations.

The standard POD-Galerkin technique is a well-known reduced order model, but the complexity of evaluating the nonlinear term, which arises from the finite difference (FD) or finite element (FE) discretization of time dependent PDEs and/or parametrically dependent steady state problems remains that of the original problem.

The discrete empirical interpolation method (DEIM) is a suitable method to reduce the complexity of evaluating these nonlinear terms. We applied DEIM to an ODE arising from the FE discretization of a parametrically dependent Reaction Diffusion PDE, but the main purpose of my study is to develop mathematical and numerical methods to simulate VDFST and reduce the computational cost via DEIM.

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