Accelerated Linear Algebra Solvers for Multi-Core GPU-Based Computing Architectures

Many large-scale numerical simulations can be broken down into common mathematical routines. While the applications may differ, they often need to perform standard functions such as system solves, Fourier transforms, or eigenvalue calculations. Consequently, producing fast, efficient implementations of these methods will benefit a broad range of Air Force applications. Graphics Processing Units (GPUs) have emerged as an attractive platform to perform complex numerical computations. Their 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, which has resulted in a product we have released to the public called CULA. 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 and extend both families of solvers to work in multi-GPU environments. The solver package developed in this project with will be applicable to a wide range of applications from finite element analysis to computational fluid dynamics to image processing while being scalable from a single desktop PC to large, GPU-based high-performance computing systems. BENEFIT: A suite of sparse and dense linear algebra solvers will be particularly useful to air force. Sparse computations arise from finite element methods and in various areas of the CFD space. The importance of these solution spaces cannot be overstated. The Air Force 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. Since sparse solvers have applications in the entire FEM space, that further expands the applicability of our project to mechanical analysis and computational electromagnetic analysis. Dense solvers arise in scientific computing disciplines such as electromagnetic analysis for radar signatures and communications and system analysis with eigenvalues. Also image and signal processing techniques such as beam forming and compression are often done with dense matrix routines. 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.