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An Implementation of the Longman's Integration Method on Graphics Hardware

E. Mesquita1, J.Labaki 1 and L.O.S.Ferreira1
1 University of Campinas, SP, Brazil.

Computer Modeling in Engineering & Sciences 2009, 51(2), 143-168.


There is a growing trend towards solving problems of computational mechanics by parallelization strategies. The traditional approach is to implement the parallelization procedures on CPUs based on the MPI or OpenMP paradigms. Recent efforts have been made to implement computational tasks on general-purpose programmable graphics hardware (GPGPU). The GPU is specially well-suited to address problems that can be formulated in form of data-parallel computations with high arithmetic intensity. This work addresses the implementation of the Longman's integration method on graphics hardware. A serial implementation of Longman's method was rewritten under the SIMD (Single Input Multiple Data) parallel programming paradigm. The code was developed on an NVidia CUDA programming environment and executed on a graphics card hosted by a regular dual-cored CPU. The structure of a GPU as visible from the CUDA programming language is briefly described in order to assess the possible strategies for parallel implementation on the graphics card. The accuracy and efficiency of the implemented strategies are investigated by solving the improper integral of a simple, but representative, oscillatory and decaying function possessing closed-form solution. The paper reports the performances of the GPU and the CPU on solving different numbers of integrals for distinct parameters of the integrand and required degrees of accuracy. For a large number of integrals the GPU has shown a speedup capacity ranging from one to two order of magnitudes compared to the CPU.


High Performance Computing, Graphics Hardware, Improper Numerical Integration, Oscillatory-Decaying Functions, Numerical Inversion of Integral Transforms.

Cite This Article

Mesquita, E., , J. (2009). An Implementation of the Longman's Integration Method on Graphics Hardware. CMES-Computer Modeling in Engineering & Sciences, 51(2), 143–168.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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