Hypergeometric summation algorithms for high-order finite elements

DOI10.1007/s00607-006-0179-xzbMath1113.65105OpenAlexW1974515217MaRDI QIDQ858177

Carsten Schneider, A. Bećirović, Paule, Peter, Axel Riese, Joachim Schöberl, Veronika Pillwein

Publication date: 8 January 2007

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-006-0179-x

zbMATH Keywords

Sobolev spacespreconditioningcondition numberMathematicacomputer algebra algorithmshigh order finite elementsblock-Jacobi preconditioners

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Boundary value problems for second-order elliptic equations (35J25) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

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Uses Software

• gfun
• Mathematica
• SIGMA
• GeneratingFunctions

Cites Work

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• Plane partitions. VI: Stembridge's TSPP theorem
• A new Sigma approach to multi-summation
• Polynomial Liftings on a Tetrahedron and Applications to the h-p Version of the Finite Element Method in Three Dimensions
• Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions
• Basis Functions for Triangular and Quadrilateral High-Order Elements
• GFUN
• Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements