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Statements

Subject Item
n2:RIV%2F00025615%3A_____%2F13%3A%230001899%21RIV14-MSM-00025615
rdf:type
skos:Concept n8:Vysledek
dcterms:description
The progress in computer development makes it possible to solve many problems of physical geodesy just by means of numerical arrangements unimaginable before. Nevertheless, considering a precise evaluation of spheroidal (spherical and ellipsoidal) harmonic functions in our typical task, we still observe a huge performance gap between numerical demands and capabilities of the present CPUs. Known methods for evaluation of Legendre functions (of the first as well as 2nd kind) are basically recurrent and thus sequential, where one step involves just a few arithmetic operations. Therefore, it seems to be challenging, but still feasible, to arrange an evaluation of Legendre functions in a way that admits wide SIMD parallelism. Regarding this aim, we provide Open Computing Language (OpenCL) implementation of the streaming-parallel algorithm for evaluation of ellipsoidal harmonic functions and their derivatives. The developed algorithm is free of assumptions about the function arguments, maximal degree/order or number of points to be evaluated and can be utilized on any vector data types of float, double or integer numbers. Besides, it addresses also floating-point issues in Legendre functions numerical treatment. We demonstrate the implementation on a GPGPU hardware, where anyone can easily obtain a computational power of several TFlops today. Several benchmarks are provided, including EGM2008, leading to conclusion about significant speedup of a single GPGPU over multi-core CPU device by a factor of 100, without any accuracy penalty. Moreover, thanks to OpenCL standard, we can benefit from excellent portability and scalability over heterogeneous parallel platforms, involving also hybrid MPI-OpenCL implementations. The topic presented is, of course, matter of importance in many application fields, not only in physical geodesy. The progress in computer development makes it possible to solve many problems of physical geodesy just by means of numerical arrangements unimaginable before. Nevertheless, considering a precise evaluation of spheroidal (spherical and ellipsoidal) harmonic functions in our typical task, we still observe a huge performance gap between numerical demands and capabilities of the present CPUs. Known methods for evaluation of Legendre functions (of the first as well as 2nd kind) are basically recurrent and thus sequential, where one step involves just a few arithmetic operations. Therefore, it seems to be challenging, but still feasible, to arrange an evaluation of Legendre functions in a way that admits wide SIMD parallelism. Regarding this aim, we provide Open Computing Language (OpenCL) implementation of the streaming-parallel algorithm for evaluation of ellipsoidal harmonic functions and their derivatives. The developed algorithm is free of assumptions about the function arguments, maximal degree/order or number of points to be evaluated and can be utilized on any vector data types of float, double or integer numbers. Besides, it addresses also floating-point issues in Legendre functions numerical treatment. We demonstrate the implementation on a GPGPU hardware, where anyone can easily obtain a computational power of several TFlops today. Several benchmarks are provided, including EGM2008, leading to conclusion about significant speedup of a single GPGPU over multi-core CPU device by a factor of 100, without any accuracy penalty. Moreover, thanks to OpenCL standard, we can benefit from excellent portability and scalability over heterogeneous parallel platforms, involving also hybrid MPI-OpenCL implementations. The topic presented is, of course, matter of importance in many application fields, not only in physical geodesy.
dcterms:title
An OpenCL implementation of ellipsoidal harmonics An OpenCL implementation of ellipsoidal harmonics
skos:prefLabel
An OpenCL implementation of ellipsoidal harmonics An OpenCL implementation of ellipsoidal harmonics
skos:notation
RIV/00025615:_____/13:#0001899!RIV14-MSM-00025615
n8:predkladatel
n9:ico%3A00025615
n3:aktivita
n15:I n15:P
n3:aktivity
I, P(ED1.1.00/02.0090)
n3:dodaniDat
n13:2014
n3:domaciTvurceVysledku
n10:7619413 n10:3365093
n3:druhVysledku
n18:A
n3:duvernostUdaju
n12:S
n3:entitaPredkladatele
n6:predkladatel
n3:idSjednocenehoVysledku
60404
n3:idVysledku
RIV/00025615:_____/13:#0001899
n3:jazykVysledku
n17:eng
n3:klicovaSlova
evaluation of Legendre functions; recurrent relations; SIMD parallelism; floating-point issues; GPGPU hardware
n3:klicoveSlovo
n4:recurrent%20relations n4:SIMD%20parallelism n4:floating-point%20issues n4:evaluation%20of%20Legendre%20functions n4:GPGPU%20hardware
n3:kodPristupu
n14:L
n3:kontrolniKodProRIV
[7D127CAAB76B]
n3:mistoVydani
Rome
n3:objednatelVyzkumneZpravy
International Assocoation of Geodesy
n3:obor
n5:DE
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:projekt
n16:ED1.1.00%2F02.0090
n3:rokUplatneniVysledku
n13:2013
n3:tvurceVysledku
Nesvadba, Otakar Holota, Petr