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    Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities

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    Type
    Conference Paper
    Authors
    Paszyńska, Anna
    Jopek, Konrad
    Banaś, Krzysztof
    Paszyński, Maciej
    Gurgul, Piotr
    Lenerth, Andrew
    Nguyen, Donald
    Pingali, Keshav
    Dalcin, Lisandro
    Calo, Victor M. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Earth Science and Engineering Program
    Numerical Porous Media SRI Center (NumPor)
    Physical Science and Engineering (PSE) Division
    Date
    2015-06-01
    Online Publication Date
    2015-06-01
    Print Publication Date
    2015
    Permanent link to this record
    http://hdl.handle.net/10754/556723
    
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    Abstract
    This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.
    Citation
    Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities 2015, 51:2744 Procedia Computer Science
    Publisher
    Elsevier BV
    Journal
    Procedia Computer Science
    Conference/Event name
    International Conference on Computational Science, ICCS 2002
    DOI
    10.1016/j.procs.2015.05.415
    Additional Links
    http://linkinghub.elsevier.com/retrieve/pii/S1877050915012235
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.procs.2015.05.415
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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