Parallel Eigensolvers for a Discretized Radiative Transfer Problem

Vasconcelos, Paulo B.; Marques, Osni; Román, José E.

doi:10.1007/978-3-540-92859-1_30

Cited by 5 publications

(2 citation statements)

References 10 publications

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“…This problem can be solved via discretization, that is, by projection onto a finite dimensional subspace X n , resulting in an algebraic eigenvalue problem A n x n = θ n x n of dimension n, where A n is the restriction of the projected operator to X n . Further details can be found in [37].…”

Section: Test Casesmentioning

confidence: 99%

MPI-CUDA parallel linear solvers for block-tridiagonal matrices in the context of SLEPc’s eigensolvers

Daviña

Román

2018

Parallel Computing

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We consider the computation of a few eigenpairs of a generalized eigenvalue problem Ax = λBx with block-tridiagonal matrices, not necessarily symmetric, in the context of Krylov methods. In this kind of computation, it is often necessary to solve a linear system of equations in each iteration of the eigensolver, for instance when B is not the identity matrix or when computing interior eigenvalues with the shift-and-invert spectral transformation. In this work, we aim to compare different direct linear solvers that can exploit the block-tridiagonal structure. Block cyclic reduction and the Spike algorithm are considered. A parallel implementation based on MPI is developed in the context of the SLEPc library. The use of GPU devices to accelerate local computations shows to be competitive for large block sizes.

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Section: Test Casesmentioning

confidence: 99%

MPI-CUDA parallel linear solvers for block-tridiagonal matrices in the context of SLEPc’s eigensolvers

Daviña

Román

2018

Parallel Computing

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Section: Block-tridiagonal Casementioning

confidence: 99%

Dense and sparse parallel linear algebra algorithms on graphics processing units

Daviña¹

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I thank again to José Román for his unique humor sense. To Carmen, for showing me the way and for all her good advices. To Enrique, who helped me to get rolling. And to the former members Andrés and Eloy, to whom I had the opportunity to meet and who enliven the group meals. I will keep good memories from these years. I do not want to forget to mention to Xavier Cartoixà, Jeff Steward and Altuǧ Aksoy, great researchers with whom I have had the opportunity to collaborate. The afternoon snacks would not have been the same without the excellent discussions and comments of Fernando, David and of course Salva, who, without noticing it, also helped to improve this dissertation. Last, I would like to thank to José Luis, IT staff of the department, for his high valuable work behind the scenes and his promptly response to any incidence. To all of you who have supported me, thank you. v de matriz de forma directa. Nosotros hemos implementado varios algoritmos para calcular las funciones de matrices raíz cuadrada y exponencial, en las que el uso de GPUs permite acelerar el cálculo. vi Contents List of Figures xi List of Tables xv List of Algorithms xvii

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