Symbolic Evaluation of hp-FEM Element Matrices

Tim Haubold; Veronika Pillwein; Sven Beuchler

doi:10.1002/pamm.201900446

Symbolic Evaluation of hp-FEM Element Matrices

Tim Haubold, Veronika Pillwein, Sven Beuchler

Research Institute for Symbolic Computation

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

Abstract In this paper we consider higher order shape functions for finite elements on a triangle. On the reference element Dubiner-like ansatz functions based on suitable integrated Jacobi polynomials are chosen. It can be proved that the corresponding mass and stiffness matrices are sparse for all polynomial degree p. Due to the orthogonal relations between Jacobi polynomials the exact values of the entries of mass and stiffness matrix can be determined. Using symbolic computation, we can find simple recurrence relations which allow us to compute the remaining nonzero entries in optimal arithmetic complexity.

Original language	English
Title of host publication	Proceedings in Applied Mathematics and Mechanics (PAMM)
Editors	Gesellschaft für Angewandte Mathematik und Mechanik (GAMM)
Number of pages	2
Volume	19
DOIs	https://doi.org/10.1002/pamm.201900446
Publication status	Published - 2019

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

JKU Focus areas

Digital Transformation

Access to Document

10.1002/pamm.201900446

Cite this

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title = "Symbolic Evaluation of hp-FEM Element Matrices",

abstract = "Abstract In this paper we consider higher order shape functions for finite elements on a triangle. On the reference element Dubiner-like ansatz functions based on suitable integrated Jacobi polynomials are chosen. It can be proved that the corresponding mass and stiffness matrices are sparse for all polynomial degree p. Due to the orthogonal relations between Jacobi polynomials the exact values of the entries of mass and stiffness matrix can be determined. Using symbolic computation, we can find simple recurrence relations which allow us to compute the remaining nonzero entries in optimal arithmetic complexity.",

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N2 - Abstract In this paper we consider higher order shape functions for finite elements on a triangle. On the reference element Dubiner-like ansatz functions based on suitable integrated Jacobi polynomials are chosen. It can be proved that the corresponding mass and stiffness matrices are sparse for all polynomial degree p. Due to the orthogonal relations between Jacobi polynomials the exact values of the entries of mass and stiffness matrix can be determined. Using symbolic computation, we can find simple recurrence relations which allow us to compute the remaining nonzero entries in optimal arithmetic complexity.

AB - Abstract In this paper we consider higher order shape functions for finite elements on a triangle. On the reference element Dubiner-like ansatz functions based on suitable integrated Jacobi polynomials are chosen. It can be proved that the corresponding mass and stiffness matrices are sparse for all polynomial degree p. Due to the orthogonal relations between Jacobi polynomials the exact values of the entries of mass and stiffness matrix can be determined. Using symbolic computation, we can find simple recurrence relations which allow us to compute the remaining nonzero entries in optimal arithmetic complexity.

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DO - 10.1002/pamm.201900446

M3 - Conference proceedings

VL - 19

BT - Proceedings in Applied Mathematics and Mechanics (PAMM)

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