A functional program describing a simple reservoir model and its potential for parallel computation

Results of using a functional programming language, Miranda, to solve a simple reservoir modeling problem are presented. The algorithm uses Miranda´s function form to determine a parallel decomposition of a reservoir modeling problem. There is discussion on both discerning the parallel decomposition and the ease of specifying the problem in functional form. Finite element discretization of a reservoir model yields linear equations of the form Ax=b, where A is a large, sparse, banded matrix, and x and b are dense vectors. Each step of the simulation uses the conjugate gradient method to solve the sparse linear system. Matrices are represented as quads in Miranda to take advantage of their sparsity. Vectors are represented as lists of numbers. Other data structures yielded worse performance. Results of simulations for reservoirs which yield sparse matrices up to size 4096×4096 and estimates for matrices up to size 262144×262144 are presented