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In this dissertation we provide new numerical algorithms for use in conjunction with simulation based design codes. These algorithms are designed and best suited to run on emerging heterogenous computing architectures which contain a combination of traditional multi-core processors and new programmable many-core graphics processing units (GPUs). We have developed the following numerical algorithms (i) a new Multidirectional Search (MDS) method for PDE constrained optimization that utilizes a Multigrid (MG) strategy to accelerate convergence, this algorithm is well suited for use on GPU clusters due to its parallel nature and is more scalable than adjoint methods (ii) a new GPU accelerated point implicit solver for the NASA FUN3D code (unstructured Navier-Stokes) that is written in the Compute Unified Device Architecture (CUDA) language, and which employs a novel GPU sharing model, (iii) novel GPU accelerated smoothers (developed using PGI Fortran with accelerator compiler directives) used to accelerate the multigrid preconditioned conjugate gradient method (MGPCG) on a single rectangular grid, and (iv) an improved pressure projection solver for adaptive meshes that is based on the MGPCG method which requires fewer grid point calculations and has potential for better scalability on hetergeneous clusters. It is shown that a multigrid - multidirectional search (MGMDS) method can run up to 5.5X faster than the MDS method when used on a one dimensional data assimilation problem. It is also shown that the new GPU accelerated point implicit solver of FUN3D is up to 5.5X times faster than the CPU version and that the solver can perform up to 40% faster on a single GPU being shared by four CPU cores. It is found that GPU accelerated smoothers for the MGPCG method on uniform grids can run over 2X faster than the non-accelerated versions for 2D problems, and that the new MGPCG pressure projection solver for adaptive grids is up to 4X faster than the previous MG algorithm.
Adaptive Mesh Refinement, High Performance Computing, Computational Fluid Dynamics, Adjoint Methods, Multidirectional Search, Multigrid, Graphics Processing Unit
Date of Defense
March 15, 2011.
A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
Mark Sussman, Professor Directing Dissertation; M. Yousuﬀ Hussaini, Professor Co-Directing Dissertation; Robert Van Engelen, University Representative; Nick Cogan, Committee Member; Kyle Gallivan, Committee Member.
Florida State University
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