An efficient parameter estimation technique for a solute transport equation in porous media

Abstract

Many parameter estimation problems arising in the solute transport equations in porous media involve numerous time integrations. An efficient adaptive numerical method is introduced in this paper. The method reduces the computational costs significantly compared with those of the conventional time-marching schemes due to the single time-integration, the spatial adaptiveness, and the O(log(N)) effects of the method, where N is the spatial approximation dimension. The efficiency and accuracy of the proposed algorithm is shown through a simple one-dimensional model. However, the methodology can be applied for more general multi-dimensional models.