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

ABSTRACT: High-performance computing (HPC) programmers and domain experts, such as those in the Air Force's research divisions, develop solvers for a wide variety of application areas such as modeling next generation aircraft and weapons designs and advanced image processing analysis. When developing software for HPC systems, the programmer should not spend the majority of their time optimizing their program. Instead, the programmer should have access to optimized fundamental libraries with which they can more quickly develop solvers in their unique domain. An emerging technology in HPC is vector-based coprocessors optimized for math computations, lead by graphics processing units (GPUs). With so-called hybrid systems consisting of a mix of CPUs and GPUs claiming 3 of the top 4 spots on the Top500 list of supercomputers, it is vital that the supporting software libraries catch up to the hardware. EM Photonics has gained recognition as a leader in the hybrid computing community as producers of the CULA library for accelerated dense linear algebra computations. In our Phase I, we showed that producing scalable linear algebra solvers in the dense and sparse domains is feasible, and in Phase II we intend to vastly broaden the scope of our existing library solutions. BENEFIT: A suite of sparse and dense linear algebra solvers will be particularly useful to the Air Force, especially when given the ability to scale across hybrid/heterogeneous computing clusters. 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/CSD efforts, especially for analyzing the properties of moving aircraft. 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. Dense solvers arise in scientific computing disciplines such as electromagnetic analysis for radar signatures and communications and system analysis with eigenvalues. Image and signal processing techniques such as beam forming and compression are often done with dense matrix routines. Outside of the Air Force, the commercial space finds these solvers appealing for many of the same reasons. Our users have requested each feature we intend to develop many times over, and while the end applications may differ (e.g., stress and strain on a building, modeling of cell phone antennas, or analysis of airflow through a HVAC system), the techniques employ many of the same underlying mathematics. Moreover, those who purchase clusters or supercomputers often desire as much speed as possible for as little power and space as possible. An optimized and scalable underlying library can reduce power consumption and/or node count considerably.