The intrinsic partition of unity method

Thomas Peter Fries, Ted Belytschko

Research output: Contribution to journalArticleResearchpeer-review

Abstract

A method is presented which enables the global enrichment of the approximation space without introducing additional unknowns. Only one shape function per node is used. The shape functions are constructed by means of the moving least-squares method with an intrinsic basis vector and weight functions based on finite element shape functions. The enrichment is achieved through the intrinsic basis. By using polynomials in the intrinsic basis, optimal rates of convergence can be achieved even on distorted elements. Special enrichment functions can be chosen to enhance accuracy for solutions that are not polynomial in character. Results are presented which show optimal convergence on randomly distorted elements and improved accuracy for the oscillatory solution of the Helmholtz equation.

Original languageEnglish
Pages (from-to)803-814
Number of pages12
JournalComputational mechanics
Volume40
Issue number4
DOIs
Publication statusPublished - Sep 2007

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Partition of Unity Method
Shape Function
Moving Least Squares
Oscillatory Solution
Optimal Rate of Convergence
Polynomial
Approximation Space
Helmholtz Equation
Least Square Method
Weight Function
Polynomials
Helmholtz equation
Finite Element
Unknown
Vertex of a graph

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Applied Mathematics
  • Safety, Risk, Reliability and Quality

Cite this

The intrinsic partition of unity method. / Fries, Thomas Peter; Belytschko, Ted.

In: Computational mechanics, Vol. 40, No. 4, 09.2007, p. 803-814.

Research output: Contribution to journalArticleResearchpeer-review

Fries, Thomas Peter ; Belytschko, Ted. / The intrinsic partition of unity method. In: Computational mechanics. 2007 ; Vol. 40, No. 4. pp. 803-814.
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