GPU-Accelerated Sparse Matrix Solvers for Large-Scale Simulations

At the heart of scientific computing and numerical analysis are linear algebra solvers. In scientific computing, the focus is on the partial differential equations (PDEs) that arise from computational fluid dynamics (CFD), climate modeling, astrophysics, and structural and heat analysis that cannot be solved analytically. Certain problem formulations lead to sparse matrices, in which the majority of matrix elements are zero. Special attention is required when computing on sparse matrices in order to avoid using unrealistic amounts of memory or produce ill-performing software. Such topics have been the subject of considerable research and the limits of CPU-based performance have been reached. Recently, the graphics processing unit (GPU) has emerged as an attractive platform for high performance computing. The modern GPU boasts over 1 TFLOPS performance and as much as 6 GB onboard memory, but harnessing the power can be challenging. A library-based approach is common for HPC, with most applications using several libraries to offload well-known tasks. EM Photonics maintains a library of GPU-accelerated dense linear algebra solvers that has over 5000 users. In this project we will extend this library to include a wide range of sparse solvers, including many that have direct relevance to NASA projects.

Sparse solvers have applications in the entire FVM and FEM space that further expands the applicability of our project to a large number of fields involved with modeling and simulation. For instance, the models used by circuit simulation, heat transfer, and structural mechanics can all be represented by very large sparse matrices. Accelerated sparse solvers will allow engineers to more quickly turn around designs with increased detail and accuracy. Large sparse matrices commonly arise in other fields involving statistics and optimization where a large amount number of elements have various interactions. For example, electrical power systems, traffic flow optimization, economics, search index rankings, and the modeling of chemical processes are just a small sample of fields where the interaction of a large number coupled elements are represented through sparse matrices. Accelerated sparse solvers and decompositions will allow scientists to rapidly study larger problems in less time.

Sparse computations arise in finite element and finite volume methods (FEM, FVM) common in the computational fluid dynamics (CFD) space, an area where NASA has many important efforts especially related to space missions and weather prediction. For example, the CFD code Overflow is widely used by NASA when designing launch and re-reentry vehicles and is used to study the air loads on the NASA space shuttles. The INS3D code is used by the space directorate to solve the incompressible Navier-Stokes equations for steady-state and time varying flow, which has been used to study the gravitational effects of blood flow in the human brain. NASA also has a vested interest in CFD-based weather prediction models. For example, the NASA Finite Volume General Circulation Model (fvGCM) and Parallel Ocean Program (POP) codes are large-scale climate prediction models important for analyzing weather effects such as global warming and hurricane predictions.

This is a mature technology (TRL 7) — the realistic path in is usually NASA's Technology Transfer Program: licensing an existing NASA patent, or a Space Act Agreement to use NASA facilities/expertise directly. NASA also runs a startup licensing program with no upfront fee for companies formed to commercialize a specific NASA technology.

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