Factorizing the factorization - a spectral-element solver for elliptic equations with linear operation count

JOURNAL OF COMPUTATIONAL PHYSICS

卷:346

Article

Huismann, Immo^1,2  Stiller, Joerg^1,2  Froehlich, Jochen^1,2 

[1] Tech Univ Dresden, Inst Fluid Mech, George Bahr Str 3c, D-01062 Dresden, Germany

[2] Cfaed, Helmholtz Str 10, D-01062 Dresden, Germany

关键词: Spectral-element method;    Elliptic equations;    Substructuring;    Static condensation;   

DOI  :  10.1016/j.jcp.2017.06.012

来源: Elsevier

【 摘 要 】

The paper proposes a novel factorization technique for static condensation of a spectralelement discretization matrix that yields a linear operation count of just 13N multiplications for the residual evaluation, where N is the total number of unknowns. In comparison to previous work it saves a factor larger than 3 and outpaces unfactored variants for all polynomial degrees. Using the new technique as a building block for a preconditioned conjugate gradient method yields linear scaling of the runtime with N which is demonstrated for polynomial degrees from 2 to 32. This makes the spectral-element method cost effective even for low polynomial degrees. Moreover, the dependence of the iterative solution on the element aspect ratio is addressed, showing only a slight increase in the number of iterations for aspect ratios up to 128. Hence, the solver is very robust for practical applications. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free