| 1. |
- Alnaes, Martin S., et al.
(författare)
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UFC: a Finite Element Code Generation Interface
- 2012
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Ingår i: Automated Solution of Differential Equations by the Finite Element Method. Anders Logg, Kent-Andre Mardal, Garth Wells (Eds.). - Heidelberg : Springer. - 9783642230981 ; , s. 283-302
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- A central component of FEniCS is the UFC interface (Unified Form-assembly Code). UFC is an 8703 interface between problem-specific and general-purpose components of finite element programs. In 8704 particular, the UFC interface defines the structure and signature of the code that is generated by 8705 the form compilers FFC and SFC for DOLFIN. The UFC interface applies to a wide range of finite 8706 element problems (including mixed finite elements and discontinuous Galerkin methods) and may be 8707 used with libraries that differ widely in their design.
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| 2. |
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| 3. |
- Kirby, Robert C., et al.
(författare)
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Common and Unusual Finite Elements
- 2012
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Ingår i: Automated Solution of Differential Equations by the Finite Element Method. Anders Logg, Kent-Andre Mardal, Garth Wells (Eds.). - Heidelberg : Springer. - 9783642230981 ; , s. 95-119
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This chapter provides a glimpse of the considerable range of finite elements in the literature. Many of the elements presented here are implemented as part of the FEniCS project already; some are future work. The universe of finite elements extends far beyond what we consider here. In particular, we consider only simplicial, polynomial-based elements. We thus bypass elements defined on quadrilaterals and hexahedra, composite and macro-element techniques, as well as XFEM-type methods. Even among polynomial-based elements on simplices, the list of elements can be extended. Nonetheless, this chapter presents a comprehensive collection of some the most common, and some more unusual, finite elements.
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| 4. |
- Kirby, Robert C., et al.
(författare)
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Discrete Optimization of Finite Element Matrix Evaluation
- 2012
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Ingår i: Automated Solution of Differential Equations by the Finite Element Method. Anders Logg, Kent-Andre Mardal, Garth Wells (Eds.). - Heidelberg : Springer. - 9783642230981 ; , s. 163-169
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- The tensor contraction structure for the computation of the element tensor AT obtained in Chapter 8,enables not only the construction of a compiler for variational forms,but an optimizing compiler.For typical variational forms,the reference tensor A0 has significant structure that allows the element tensor AT to be computed on an arbitrary cell T at a lower computational cost.
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| 5. |
- Kirby, Robert C., et al.
(författare)
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FErari: an Optimizing Compiler for Variational Forms
- 2012
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Ingår i: Automated Solution of Differential Equations by the Finite Element Method. Anders Logg, Kent-Andre Mardal, Garth Wells (Eds.). - Heidelberg : Springer. - 9783642230981 ; , s. 239-246
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In Chapter 8, we presented a framework for efficient evaluation of multilinear forms based on 7311 expressing the multilinear form as a special tensor contraction. This allows generation of efficient 7312 low-level code for assembly of a range of multilinear forms.
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| 6. |
- Kirby, Robert C., et al.
(författare)
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Finite Element Variational Forms
- 2012
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Ingår i: Automated Solution of Differential Equations by the Finite Element Method. Anders Logg, Kent-Andre Mardal, Garth Wells (Eds.). - Heidelberg : Springer. - 9783642230981 ; , s. 133-140
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Much of the FEniCS software is devoted to the formulation of variational forms (UFL), the discretization of variational forms (FIAT, FFC, SyFi) and the assembly of the corresponding discrete operators (UFC, DOLFIN). This chapter summarizes the notation for variational forms used throughout FEniCS.
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| 7. |
- Kirby, Robert C., et al.
(författare)
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Tensor Representation of Finite Element Variational Forms
- 2012
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Ingår i: Automated Solution of Differential Equations by the Finite Element Method. Anders Logg, Kent-Andre Mardal, Garth Wells (Eds.). - Heidelberg : Springer. - 9783642230981 ; , s. 159-162
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In Chapter 6, we saw that an important step in the assembly of matrices and vectors for the 4523 discretization of finite element variational problems is the evaluation of the cell (element) tensor AT 4524 defined by 4525 AT,i = aT(f T,r ir,...,fT,2 i2,fT,1 i1 ).
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| 8. |
- Kirby, Robert C., et al.
(författare)
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The Finite Element Method
- 2012
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Ingår i: Automated Solution of Differential Equations by the Finite Element Method. Anders Logg, Kent-Andre Mardal, Garth Wells (Eds.). - Heidelberg : Springer. - 9783642230981 ; , s. 77-94
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- The finite element method has emerged as a universal method for the solution of differential equations. Much of the success of the finite element method can be attributed to its generality and elegance, allowing a wide range of differential equations from all areas of science to be analyzed and solved within a common framework. Another contributing factor to the success of the finite element method is the flexibility of formulation, allowing the properties of the discretization to be controlled by the choice of approximating finite element spaces.
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| 9. |
- Logg, Anders, 1976, et al.
(författare)
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DOLFIN: a C++/Python Finite Element Library
- 2012
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Ingår i: Automated Solution of Differential Equations by the Finite Element Method. Anders Logg, Kent-Andre Mardal, Garth Wells (Eds.). - Heidelberg : Springer. - 9783642230981 ; , s. 173-225
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- DOLFIN is a C++/Python library that functions as the main user interface of FEniCS. In this 4806 chapter, we review the functionality of DOLFIN. We also discuss the implementation of some key 4807 features of DOLFIN in detail.
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| 10. |
- Logg, Anders, 1976, et al.
(författare)
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FFC: the FEniCS Form Compiler
- 2012
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Ingår i: Automated Solution of Differential Equations by the Finite Element Method. Anders Logg, Kent-Andre Mardal, Garth Wells (Eds.). - Heidelberg : Springer. - 9783642230981 ; , s. 227-238
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- One of the key features of FEniCS is automated code generation for the general and efficient 7018 solution of finite element variational problems. This automated code generation relies on a form 7019 compiler for offline or just-in-time compilation of code for individual forms. Two different form 7020 compilers are available as part of FEniCS.
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