Abstract

A GPU accelerated approach to numerical linear algebra and matrix analysis with CFD applications is presented. The works objectives are to (1) develop stable and efficient algorithms utilizing multiple NVIDIA GPUs with CUDA to accelerate common matrix computations, (2) optimize these algorithms through CPU/GPU memory allocation, GPU kernel development, CPU/GPU communication, data transfer and bandwidth control to (3) develop parallel CFD applications for Navier Stokes and Lattice Boltzmann analysis methods. Special consideration will be given to performing the linear algebra algorithms under certain matrix types (banded, dense, diagonal, sparse, symmetric and triangular). Benchmarks are performed for all analyses with baseline CPU times being determined to find speed-up factors and measure computational capability of the GPU accelerated algorithms. The GPU implemented algorithms used in this work along with the optimization techniques performed are measured against preexisting work and test matrices available in the NIST Matrix Market. CFD analysis looked to strengthen the assessment of this work by providing a direct engineering application to analysis that would benefit from matrix optimization techniques and accelerated algorithms. Overall, this work desired to develop optimization for selected linear algebra and matrix computations performed with modern GPU architectures and CUDA developer which were applied directly to mathematical and engineering applications through CFD analysis.

Notes

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Thesis Completion

2014

Semester

Spring

Advisor

Shivamoggi, Bhimsen

Degree

Bachelor of Science (B.S.)

College

College of Sciences

Department

Mathematics

Subjects

Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic

Format

PDF

Identifier

CFH0004605

Language

English

Access Status

Open Access

Length of Campus-only Access

None

Document Type

Honors in the Major Thesis

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Included in

Mathematics Commons

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