Fractional Steps methods are suitable for modeling transient processes
that are central to many geological applications. Low memory
requirements and modest computational complexity facilitates
calculations on high-resolution three-dimensional models. An efficient
implementation of Alternating Direction Implicit/Locally One-Dimensional
schemes for an Opteron-based shared memory system is presented. The
memory bandwidth usage, the main bottleneck on modern computer
architectures, is specially addressed. High efficiency of above 2 GFlops
per CPU is sustained for problems of I billion degrees of freedom. The
optimized sequential implementation of all I D sweeps is comparable in
execution time to copying the used data in the memory. Scalability of
the parallel implementation on up to 8 CPUs is close to perfect.
Performing one timestep of the Locally One-Dimensional scheme on a
system of 10003 unknowns on 8 CPUs takes only 11 s. We validate the LOD
scheme using a computational model of an isolated inclusion subject to a
constant far field flux. Next, we study numerically the evolution of a
diffusion front and the effective thermal conductivity of composites
consisting of multiple inclusions and compare the results with
predictions based on the differential effective medium approach.
Finally, application of the developed parabolic solver is suggested for
a real-world problem of fluid transport and reactions inside a
reservoir. (C) 2008 Elsevier B.V. All rights reserved.