An Efficient Algorithm to Construct the Reduced Stiffness and Mass Matrices in a Reduced Order Groundwater Flow Model

Abstract:

An algorithm is developed to reduce the computational burden of constructing the reduced stiffness and mass matrices for a reduced order groundwater model. A reduced order groundwater model can be developed by projecting the full groundwater model onto a subspace whose range spans the range of the full model space. This is done through the use of a projection matrix. Although reduced order groundwater models have been shown to be able to make accurate estimates of the full model solution at a greatly reduced dimension, the computational cost of projecting the stiffness and mass matrices onto the subspace of the reduced model can be very demanding. To alleviate this difficulty, an algorithm is developed that is able to reduce the effort and cost of constructing the reduced stiffness and mass matrices of the reduced model. The algorithm is based on the concept of approximating the value of a function at some point by use of the first-order Taylor series approximation. The developed algorithm is applied to both a 1-D test case and a 2-D test case. In both cases the algorithm is able to reduce the effort and cost of constructing the reduced order model by several orders of magnitude while losing little to no accuracy.