Fast, High-Order algorithms for Many-Core and GPU-based Computer Architectures

We propose algorithm development and efficient GPU implementation of numerical PDE solvers based on four novel high-order methodologies: 1) High-order Discontinuous Galerkin approaches, 2) Fast High-Order boundary integral methods, 3) Convergent FFT-based methodologies for evaluation of computational boundary conditions, and 4) Fourier Continuation methods. These methodologies are applicable to a vast array of problems of critical interest to the Air Force, encompassing computational electromagnetics and computational acoustics (including the convective wave equation), isotropic and anisotropic elasticity, heat transfer and fluid-dynamics (including gas-dynamics, incompressible hydrodynamics, shock-dynamics and slow viscous flow). Parallel CPU implementations of such solvers have provided some of the most efficient PDE solution methods in existence today: in some cases, our algorithms are up to one-thousand times faster than the best alternative solvers. We have further demonstrated that GPU implementations of DG solvers can outperform corresponding CPU implementations, in comparably priced multi-core CPUs, by factors of fifty. The proposed effort thus seeks to combine the power of two game-changing emerging paradigms: fast high-order PDE solvers and many-core/GPU computer architectures. We believe the resulting methodologies will significantly advance the state of the art in computational science, and will play central roles in science and engineering in years to come. BENEFIT: The PDE software needs of large high-tech companies, government labs and DoD (such as Lockheed Martin, Northrop Grumman, NASA, DoD agencies, etc.) are massive. MathSys Inc. is well positioned to cater to the needs of such entities, and has open ties at key levels of such organizations. We are certain that the successful completion of the proposed development effort will find manifold uses and it will generate significant business opportunities for our company.