The size and complexity of many scientific and enterprise-level applications require a high degree of parallelization in order to produce outputs within an acceptable period of time. This often necessitates the uses of high performance computing clusters (HPCCs) and parallelized applications which are carefully designed and optimized. A myriad of papers study the various factors which influence performance and then attempt to quantify the maximum theoretical speedup that can be achieved by a cluster relative to a sequential processor. The studies tend to only investigate the influences in isolation, but in practice these factors tend to be interdependent. It is the interaction rather than any solitary influence which normally creates the bounds of the design trade space. In the attempt to address this disconnect, this thesis blends the studies into an expanded speedup model which captures the interplay. The model is intended to help the cluster engineer make initial estimates during the early phases of design while the system is not mature enough for refinement using timing studies. The model pulls together factors such as problem scaling, resource allocation, critical sections, and the problem's inherent parallelizability. The derivation was examined theoretically and then validated by timing studies on a physical HPCC. The validation studies found that the model was an adequate generic first approximation. However, it was also found that customizations may be needed in order to account for application-specific influences such as bandwidth limitations and communication delays which are not readily incorporated into a generic model. / Master of Science

Transport codes are beginning to be parallelized in order to allow more complex add-ons, such as geochemical packages, to utilize finer, more accurate grids, and to reduce solution times making stochastic and Monte Carlo simulations more feasible. Most codes parallelized via MPI (message passing interface) offer good results, but require the development of a new parallel code. OpenMP, the shared-memory standard, offers incremental parallelization, allowing sequential codes to remain relatively intact with minimal changes or additions. OpenMP allows speedup to be seen on personal computers with dual processors or greater, unlike some other parallelization approaches that require a supercomputer. An operator-split strategy creates an environment for easy parallelization by decoupling the transport and reactions of species. The transport, when decoupled from the reactions, is dependent on surrounding nodes and not on species. Therefore, each species transport can be solved on a different processor. The reactions, when decoupled from the transport, are dependant on the other species concentrations and not on the surrounding nodes, allowing the concentrations for all species to be solve for at a given node as if in a batch reactor. This allows a parallelization of the nodes. Two codes are parallelized in this work. The first is a 100-species 1D theoretical problem. The second is RT3D, a modular computer code for simulating reactive multi-species transport in 3-dimensional groundwater systems written and developed by Dr. T. Prabhakar Clement. RT3D is a sub-component of a parent code, MT3DMS, which utilizes RT3D to solve reaction terms. A speedup factor of 3.91 is seen on four processors, accomplishing a processor efficiency of approximately 98% while spent in RT3D itself.