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An evaluation of the cost effectiveness of Chebyshev spectral and p ‐finite element solutions to the scalar wave equation
Author(s) -
Dauksher Walter,
Emery Ashley F.
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990720)45:8<1099::aid-nme622>3.0.co;2-5
Subject(s) - chebyshev filter , mathematics , discretization , scalar (mathematics) , finite element method , chebyshev nodes , bilinear interpolation , chebyshev equation , finite difference , chebyshev iteration , mathematical analysis , chebyshev polynomials , geometry , physics , statistics , orthogonal polynomials , thermodynamics , classical orthogonal polynomials
The computational efficiency of finite elements using Chebyshev basis functions is compared with that of standard equispaced lower order (bilinear and biquadratic) and higher order (bicubic and greater) p ‐elements in the solution of the two‐dimensional scalar wave equation when using explicit time integration. All solutions use a central‐difference‐in‐time temporal discretization and both consistent and lumped mass matrices are considered. The Chebyshev finite elements are shown to possess significant advantages in accuracy and in computational efficiency with respect to p ‐elements for an equivalent number of nodes. Copyright © 1999 John Wiley & Sons, Ltd.