Accelerated Smoothing and Construction of Prolongation Operators for the Multiscale Restricted-Smoothed Basis Method on Distributed Memory Systems

Abstract

During the last two decades, several multiscale solvers have been developed in an attempt to reduce the computational cost of reservoir simulations. One such method is the recently proposed and promising multiscale restricted-smoothed basis method. As with other multiscale methods, it relies on capturing local variations in form of basis functions, which are represented by a prolongation operator. The prolongation operator is used to develop a coarse system, and after this system has been solved, the operator is used once more to construct a fine-scale pressure approximation from the coarse-scale solution. The basis functions are solutions to local flow problems, and are formed by an iterative algorithm that gradually makes them algebraically smooth while restricting them to remain local and preserving partition of unity for the union of basis functions.

The work presented in this thesis has been made to advance the computational efficiency in the construction of the prolongation operator. A modified version of the preexisting construction algorithm is presented, which has shown to be more numerically stable. Further, two Gauss-Seidel type smoothers are proposed as alternatives to the currently used relaxed Jacobi smoother. Numerical evidence is presented which suggests that the new smoothers have improved convergence rate. The second contribution in this thesis is a program able to compute the prolongation operator on distributed memory systems. Results show that a high speedup of the iteration algorithm can be achieved, but it greatly depends on the number of connections in the reservoir model.