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1	A New Subgroup Chain for the Finite Affine Group Lingenbrink, David Alan, Jr. 01 January 2014 (has links) The finite affine group is a matrix group whose entries come from a finite field. A natural subgroup consists of those matrices whose entries all come from a subfield instead. In this paper, I will introduce intermediate sub- groups with entries from both the field and a subfield. I will also examine the representations of these intermediate subgroups as well as the branch- ing diagram for the resulting subgroup chain. This will allow us to create a fast Fourier transform for the group that uses asymptotically fewer opera- tions than the brute force algorithm. 20G05 Representation theory 20H20 Other matrix groups over fields Algebra Harmonic Analysis and Representation
2	PFFT - An Extension of FFTW to Massively Parallel Architectures Pippig, Michael 12 July 2012 (has links) (PDF) We present a MPI based software library for computing the fast Fourier transforms on massively parallel, distributed memory architectures. Similar to established transpose FFT algorithms, we propose a parallel FFT framework that is based on a combination of local FFTs, local data permutations and global data transpositions. This framework can be generalized to arbitrary multi-dimensional data and process meshes. All performance relevant building blocks can be implemented with the help of the FFTW software library. Therefore, our library offers great flexibility and portable performance. Likewise FFTW, we are able to compute FFTs of complex data, real data and even- or odd-symmetric real data. All the transforms can be performed completely in place. Furthermore, we propose an algorithm to calculate pruned FFTs more efficiently on distributed memory architectures. For example, we provide performance measurements of FFTs of size 512^3 and 1024^3 up to 262144 cores on a BlueGene/P architecture. parallel Fourier-Transformation MPI FFT parallel Fourier transform MPI FFT 65T50 65Y05 ddc:004 ddc:518 Schnelle Fourier-Transformation MPI <Schnittstelle> Parallelverarbeitung
3	Parallel Three-Dimensional Nonequispaced Fast Fourier Transforms and Their Application to Particle Simulation Pippig, Michael, Potts, Daniel 31 August 2012 (has links) (PDF) In this paper we describe a parallel algorithm for calculating nonequispaced fast Fourier transforms on massively parallel distributed memory architectures. These algorithms are implemented in an open source software library called PNFFT. Furthermore, we derive a parallel fast algorithm for the computation of the Coulomb potentials and forces in a charged particle system, which is based on the parallel nonequispaced fast Fourier transform. To prove the high scalability of our algorithms we provide performance results on a BlueGene/P system using up to 65536 cores. parallel nichtäquidistant Fourier-Transformation schnelle summation FFT NFFT parallel nonequispaced Fourier transform fast summation particle mesh FFT NFFT 65T50 65Y05 ddc:518 ddc:004 Schnelle Fourier-Transformation Paralleler Algorithmus Parallelverarbeitung MPI <Schnittstelle>
4	PFFT - An Extension of FFTW to Massively Parallel Architectures Pippig, Michael January 2012 (has links) We present a MPI based software library for computing the fast Fourier transforms on massively parallel, distributed memory architectures. Similar to established transpose FFT algorithms, we propose a parallel FFT framework that is based on a combination of local FFTs, local data permutations and global data transpositions. This framework can be generalized to arbitrary multi-dimensional data and process meshes. All performance relevant building blocks can be implemented with the help of the FFTW software library. Therefore, our library offers great flexibility and portable performance. Likewise FFTW, we are able to compute FFTs of complex data, real data and even- or odd-symmetric real data. All the transforms can be performed completely in place. Furthermore, we propose an algorithm to calculate pruned FFTs more efficiently on distributed memory architectures. For example, we provide performance measurements of FFTs of size 512^3 and 1024^3 up to 262144 cores on a BlueGene/P architecture. info:eu-repo/classification/ddc/004 ddc:004 info:eu-repo/classification/ddc/518 ddc:518 parallel, Fourier transform, MPI, FFT 65T50, 65Y05
5	Parallel Three-Dimensional Nonequispaced Fast Fourier Transforms and Their Application to Particle Simulation Pippig, Michael, Potts, Daniel January 2012 (has links) In this paper we describe a parallel algorithm for calculating nonequispaced fast Fourier transforms on massively parallel distributed memory architectures. These algorithms are implemented in an open source software library called PNFFT. Furthermore, we derive a parallel fast algorithm for the computation of the Coulomb potentials and forces in a charged particle system, which is based on the parallel nonequispaced fast Fourier transform. To prove the high scalability of our algorithms we provide performance results on a BlueGene/P system using up to 65536 cores. info:eu-repo/classification/ddc/518 ddc:518 info:eu-repo/classification/ddc/004 ddc:004 65T50, 65Y05

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