A fourth‐order Hermitian box‐scheme with fast solver for the Poisson problem in a cube | Zendy

Abbas Ali | Zendy

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A fourth‐order Hermitian box‐scheme with fast solver for the Poisson problem in a cube

Author(s) -

Abbas Ali

Publication year - 2015

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.21807

Subject(s) - mathematics , hermitian matrix , cube (algebra) , scheme (mathematics) , extension (predicate logic) , norm (philosophy) , mathematical analysis , combinatorics , pure mathematics , computer science , political science , law , programming language

We present a fourth‐order Hermitian box‐scheme (HB‐scheme) for the Poisson problem in a cube. A single‐nonstaggered regular grid is used supporting the discrete unknowns u and ∇ u . The scheme is fourth‐order accurate for u and ∇ u inL ∞norm. The fast numerical resolution uses a matrix capacitance method, resulting in a computational complexity of O ( N 3log 2 ( N ) ) . Numerical results are reported on several examples including nonseparable problems. The present scheme is the extension to the three‐dimensional case of the HB‐scheme presented in Abbas and Croisille [J Sci Comp 49 (2011), 239–267]. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 609–629, 2015

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