Quadrature representation of finite element variational forms

Kristian Breum Ølgaard, Garth N. Wells

Publikation: Bidrag til bog/antologi/rapport/konference proceedingBidrag til bog/antologiUndervisningpeer review

Resumé

This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations. An alternative to the run-time quadrature approach is the tensor representation presented in Chapter 8. Both the quadrature and tensor approaches are implemented in FFC (see Chapter 11). In this chapter we discuss four strategies for optimizing the quadrature representation for run-time performance of the generated code and show that optimization strategies lead to a dramatic improvement in run-time performance over a naive implementation. We also examine performance aspects of the quadrature and tensor approaches for different equations, and this will motivate the desirability of being able to choose between the two representations
OriginalsprogEngelsk
TitelAutomated Solution of Differential Equations by the Finite Element Methods : The FeniCS Book
RedaktørerAnders Logg, Kent-Andre Mardal, Garth Wells
Publikationsdato2012
Sider147-158
Kapitel7
ISBN (Trykt)978-3-642-23098-1
ISBN (Elektronisk)978-3-642-23099-8
StatusUdgivet - 2012
NavnLecture Notes in Computational Science and Engineering
Vol/bind84
ISSN1439-7358

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Tensors

Emneord

  • Local element tensors
  • Finite Element
  • Run-Time performance

Citer dette

Ølgaard, K. B., & Wells, G. N. (2012). Quadrature representation of finite element variational forms. I A. Logg, K-A. Mardal, & G. Wells (red.), Automated Solution of Differential Equations by the Finite Element Methods: The FeniCS Book (s. 147-158). Lecture Notes in Computational Science and Engineering, Bind. 84
Ølgaard, Kristian Breum ; Wells, Garth N. / Quadrature representation of finite element variational forms. Automated Solution of Differential Equations by the Finite Element Methods: The FeniCS Book. red. / Anders Logg ; Kent-Andre Mardal ; Garth Wells. 2012. s. 147-158 (Lecture Notes in Computational Science and Engineering, Bind 84).
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Ølgaard, KB & Wells, GN 2012, Quadrature representation of finite element variational forms. i A Logg, K-A Mardal & G Wells (red), Automated Solution of Differential Equations by the Finite Element Methods: The FeniCS Book. Lecture Notes in Computational Science and Engineering, bind 84, s. 147-158.

Quadrature representation of finite element variational forms. / Ølgaard, Kristian Breum; Wells, Garth N.

Automated Solution of Differential Equations by the Finite Element Methods: The FeniCS Book. red. / Anders Logg; Kent-Andre Mardal; Garth Wells. 2012. s. 147-158 (Lecture Notes in Computational Science and Engineering, Bind 84).

Publikation: Bidrag til bog/antologi/rapport/konference proceedingBidrag til bog/antologiUndervisningpeer review

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Ølgaard KB, Wells GN. Quadrature representation of finite element variational forms. I Logg A, Mardal K-A, Wells G, red., Automated Solution of Differential Equations by the Finite Element Methods: The FeniCS Book. 2012. s. 147-158. (Lecture Notes in Computational Science and Engineering, Bind 84).