A GPU application for high-order compact finite difference scheme

Tutkun, Bulent; Edis, Fırat Oğuz

doi:10.1016/j.compfluid.2011.10.016

Cited by 29 publications

(12 citation statements)

References 19 publications

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“…At present, neither running simulations with long divergence times between populations nor any scenario where the number of extant mutations in the simulation rises to too high a proportion of the total number of sites is theoretically consistent with the Poisson Random Field model underpinning the current version of GO Fish. Beyond GO Fish, solving Wright–Fisher diffusion equations in programs like δaδi ( Gutenkunst et al 2009 ) can likewise be sped up through parallelization on the GPU ( Lions et al 2001 ; Komatitsch et al 2009 ; Micikevicius 2009 ; Tutkun and Edis 2012 ).…”

Section: Resultsmentioning

confidence: 99%

Accelerating Wright–Fisher Forward Simulations on the Graphics Processing Unit

Lawrie¹

2017

G3 Genes|Genomes|Genetics

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Forward Wright–Fisher simulations are powerful in their ability to model complex demography and selection scenarios, but suffer from slow execution on the Central Processor Unit (CPU), thus limiting their usefulness. However, the single-locus Wright–Fisher forward algorithm is exceedingly parallelizable, with many steps that are so-called “embarrassingly parallel,” consisting of a vast number of individual computations that are all independent of each other and thus capable of being performed concurrently. The rise of modern Graphics Processing Units (GPUs) and programming languages designed to leverage the inherent parallel nature of these processors have allowed researchers to dramatically speed up many programs that have such high arithmetic intensity and intrinsic concurrency. The presented GPU Optimized Wright–Fisher simulation, or “GO Fish” for short, can be used to simulate arbitrary selection and demographic scenarios while running over 250-fold faster than its serial counterpart on the CPU. Even modest GPU hardware can achieve an impressive speedup of over two orders of magnitude. With simulations so accelerated, one can not only do quick parametric bootstrapping of previously estimated parameters, but also use simulated results to calculate the likelihoods and summary statistics of demographic and selection models against real polymorphism data, all without restricting the demographic and selection scenarios that can be modeled or requiring approximations to the single-locus forward algorithm for efficiency. Further, as many of the parallel programming techniques used in this simulation can be applied to other computationally intensive algorithms important in population genetics, GO Fish serves as an exciting template for future research into accelerating computation in evolution. GO Fish is part of the Parallel PopGen Package available at: http://dl42.github.io/ParallelPopGen/.

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Section: Resultsmentioning

confidence: 99%

Accelerating Wright–Fisher Forward Simulations on the Graphics Processing Unit

Lawrie¹

2017

G3 Genes|Genomes|Genetics

View full text Add to dashboard Cite

show abstract

“…At present, neither running simulations with long divergence times between populations nor any scenario where the number of extant mutations in the simulation rises to too high a proportion of the total number of sites is theoretically consistent with the Poisson Random Field model underpinning the current version of GO Fish. Beyond GO Fish, solving Wright-Fisher diffusion equations in programs like δaδi [15] can likewise be sped up through parallelization on the GPU [43][44][45][46].…”

Section: Resultsmentioning

confidence: 99%

Accelerating Wright-Fisher Forward Simulations on the Graphics Processing Unit

Lawrie¹

2016

Preprint

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Forward Wright-Fisher simulations are powerful in their ability to model complex demography and selection scenarios, but suffer from slow execution on the CPU, thus limiting their usefulness. The single-locus Wright-Fisher forward algorithm is, however, exceedingly parallelizable, with many steps which are so-called embarrassingly parallel, consisting of a vast number of individual computations that are all independent of each other and thus capable of being performed concurrently. The rise of modern Graphics Processing Units (GPUs) and programming languages designed to leverage the inherent parallel nature of these processors have allowed researchers to dramatically speed up many programs that have such high arithmetic intensity and intrinsic concurrency. The presented GPU Optimized Wright-Fisher simulation, or GO Fish for short, can be used to simulate arbitrary selection and demographic scenarios while running over 250-fold faster than its serial counterpart on the CPU. Even modest GPU hardware can achieve an impressive speedup of well over two orders of magnitude. With simulations so accelerated, one can not only do quick parametric bootstrapping of previously estimated parameters, but also use simulated results to calculate the likelihoods and summary statistics of demographic and selection models against real polymorphism dataall without restricting the demographic and selection scenarios that can be modeled or requiring approximations to the single-locus forward algorithm for efficiency. Further, as many of the parallel programming techniques used in this simulation can be applied to other computationally intensive algorithms important in population genetics, GO Fish serves as an exciting template for future research into accelerating computation in evolution. GO Fish is part of the Parallel PopGen Package available at: http://dl42.github.io/ParallelPopGen/

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“…Tutkun and Edis [23] applied this method on Lele's compact scheme, which generates a tridiagonal system. Following Tutkun and Edis's work, the Matmul method is optimized and applied to a bidiagonal system.…”

Section: The Matmul Methodsmentioning

confidence: 99%

“…Bolz et al [22] applied the same method to the same 2D laminar, incompressible Navier-Stokes equation simulation, and developed the multigrid technique on a GPU. Tutkun and Edis [23] investigated Lele's 6th order compact scheme [24] which generated tridiagonal matrices on a CFD code. The generated tridiagonal matrices were directly solved by inverting the coefficient matrix.…”

Section: Alphanumeric Symbolsmentioning

confidence: 99%