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    An efficient Poisson solver for complex embedded boundary domains using the multi-grid and fast multipole methods

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    Type
    Article
    Authors
    Rapaka, Narsimha Reddy cc
    Samtaney, Ravi cc
    KAUST Department
    Fluid and Plasma Simulation Group (FPS)
    Mechanical Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2020-03-09
    Online Publication Date
    2020-03-09
    Print Publication Date
    2020-06
    Submitted Date
    2019-06-29
    Permanent link to this record
    http://hdl.handle.net/10754/662105
    
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    Abstract
    We present an efficient method to solve the Poisson equation in embedded boundary (EB) domains. The original problem is divided into an inhomogeneous problem without the effects of EB and a homogeneous problem that imposes the effects of EB. The inhomogeneous problem is efficiently solved through a geometric multi-grid (GMG) solver and the homogenous problem is solved through a boundary element method (BEM) utilizing the free space Green’s function. Our method is robust and can handle sharp geometric features without any special treatment. Analytical expressions are presented for the boundary and the domain integrals in BEM to reduce the computational cost and integration error relative to numerical quadratures. Furthermore, a fast multipole method (FMM) is employed to evaluate the boundary integrals in BEM and reduce the computational complexity of BEM. Our method inherits the complementary advantages of both GMG and FMM and presents an efficient alternative with linear computational complexity even for problems involving complex geometries. We observe that the overall computational cost is an order of magnitude lower compared with a stand-alone FMM and is similar to that of an ideal GMG solver.
    Citation
    Rapaka, N. R., & Samtaney, R. (2020). An efficient Poisson solver for complex embedded boundary domains using the multi-grid and fast multipole methods. Journal of Computational Physics, 109387. doi:10.1016/j.jcp.2020.109387
    Sponsors
    The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST).
    Publisher
    Elsevier BV
    Journal
    Journal of Computational Physics
    DOI
    10.1016/j.jcp.2020.109387
    Additional Links
    https://linkinghub.elsevier.com/retrieve/pii/S0021999120301613
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2020.109387
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Mechanical Engineering Program

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