GPU-Accelerated Sparse Matrix Solvers for Large-Scale Simulations

Many large-scale numerical simulations can be broken down into common mathematical routines. While the applications may differ, the need to perform functions such as matrix solves, Fourier transforms, or eigenvalue analysis routinely arise. Consequently, targeting fast, efficient implementations of these methods will benefit a large number of applications. Graphics Processing Units (GPUs) are emerging as an attractive platform to perform these types of simulations. There FLOPS/Watt and FLOPS/dollar figures are far below competing alternatives. In previous work, EM Photonics has implemented dense matrix solvers using a hybrid GPU/multicore microprocessor approach. This has shown the ability to significantly outperform either platform when used independently. In this project, we will develop a complimentary library focused on performing routines on sparse matrices. This will be extremely valuable to a wide set of users including those doing finite-element analysis and computational fluid dynamics. Using GPUs, users are able to build single workstations with an excess of four teraFLOPS of computational power as well as create large, high-performance computing systems that are efficient in terms of both cost and power. By leveraging libraries such as the ones we will develop for this project, the user is shielded from the intricacies of GPU programming while still able to access their computational performance.

The need to solve sparse matrices arises from numerous scientific computing and numerical analysis applications. One major category that requires sparse matrix solutions includes solvers that use finite element analysis. This technique can be used for fields such as electromagnetics, heat transfer, structural analysis, chemical interactions, and environmental phenomena, among many others. Additionally, sparse matrices can arise in image processing, classification, combustion analysis, and fluid modeling techniques. It is extremely common for numerical algorithms to result in the need to solve sparse matrices. By significantly accelerating such solvers, you have the opportunity to affect an extremely wide range of fields.

A suite of sparse linear algebra solvers will be particularly useful to NASA. Sparse computations arise from finite element methods and in various areas of the CFD space. The importance of these solution spaces cannot be overstated. NASA has many CFD efforts, especially related to space missions. Analyzing the fluid flows, aero-acoustic properties, and mechanical characteristics accurately and speedily allows engineers to more quickly turn around designs. Sparse solvers have applications in the entire FEM space, which further expands the applicability of our project to mechanical analysis and computational electromagnetic analysis.

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