### Resumé

Originalsprog | Engelsk |
---|---|

Titel | Automated Solution of Differential Equations by the Finite Element Methods : The FeniCS Book |

Redaktører | Anders Logg, Kent-Andre Mardal, Garth Wells |

Publikationsdato | 2012 |

Sider | 147-158 |

Kapitel | 7 |

ISBN (Trykt) | 978-3-642-23098-1 |

ISBN (Elektronisk) | 978-3-642-23099-8 |

Status | Udgivet - 2012 |

Navn | Lecture Notes in Computational Science and Engineering |
---|---|

Vol/bind | 84 |

ISSN | 1439-7358 |

### Fingerprint

### Emneord

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

### Citer dette

*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

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*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.

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Bidrag til bog/antologi › Undervisning › peer review

TY - CHAP

T1 - Quadrature representation of finite element variational forms

AU - Ølgaard, Kristian Breum

AU - Wells, Garth N.

PY - 2012

Y1 - 2012

N2 - 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

AB - 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

KW - Local element tensors

KW - Finite Element

KW - Run-Time performance

KW - Local Element Tensors

KW - Finite Element

KW - Run-time performance

M3 - Book chapter

SN - 978-3-642-23098-1

SP - 147

EP - 158

BT - Automated Solution of Differential Equations by the Finite Element Methods

A2 - Logg, Anders

A2 - Mardal, Kent-Andre

A2 - Wells, Garth

ER -