| 1. |
- Alnæs, Martin S., et al.
(författare)
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The FEniCS Project Version 1.5
- 2015
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Ingår i: Archive of Numerical Software. - 2197-8263 .- 2197-8263. ; 3:100, s. 9-23
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Tidskriftsartikel (refereegranskat)abstract
- The FEniCS Project is a collaborative project for the development of innovative concepts and tools for automated scientific computing, with a particular focus on the solution of differential equations by finite element methods. The FEniCS Projects software consists of a collection of interoperable software components, including DOLFIN, FFC, FIAT, Instant, UFC, UFL, and mshr. This note describes the new features and changes introduced in the release of FEniCS version 1.5.
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| 2. |
- Alnaes, Martin, et al.
(författare)
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Unified Form Language: A Domain-Specific Language for Weak Formulations of Partial Differential Equations
- 2014
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Ingår i: ACM Transactions on Mathematical Software. - 0098-3500. ; 40:2, s. artikel nr 9-
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Tidskriftsartikel (refereegranskat)abstract
- We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies for multifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted.
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| 3. |
- Larsson, Karl, 1981-
(författare)
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Finite Element Methods for Thin Structures with Applications in Solid Mechanics
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers.In the first paper we introduce a thread model for use in interactive simulation. Based on a three-dimensional beam model, a corotational approach is used for interactive simulation speeds in combination with adaptive mesh resolution to maintain accuracy.In the second paper we present a family of continuous piecewise linear finite elements for thin plate problems. Patchwise reconstruction of a discontinuous piecewise quadratic deflection field allows us touse a discontinuous Galerkin method for the plate problem. Assuming a criterion on the reconstructions is fulfilled we prove a priori error estimates in energy norm and L2-norm and provide numerical results to support our findings.The third paper deals with the biharmonic equation on a surface embedded in R3. We extend theory and formalism, developed for the approximation of solutions to the Laplace-Beltrami problem on an implicitly defined surface, to also cover the biharmonic problem. A priori error estimates for a continuous/discontinuous Galerkin method is proven in energy norm and L2-norm, and we support the theoretical results by numerical convergence studies for problems on a sphere and on a torus.In the fourth paper we consider finite element modeling of curved beams in R3. We let the geometry of the beam be implicitly defined by a vector distance function. Starting from the three-dimensional equations of linear elasticity, we derive a weak formulation for a linear curved beam expressed in global coordinates. Numerical results from a finite element implementation based on these equations are compared with classical results.
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| 4. |
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| 5. |
- 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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| 6. |
- 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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| 7. |
- Logg, Anders, 1976, et al.
(författare)
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Finite Element Assembly
- 2012
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Ingår i: Automated Solution of Differential Equations by the Finite Element Method. - Heidelberg : Springer. - 9783642230981 ; , s. 141-146
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- The finite element method may be viewed as a method for forming a discrete linear system 4064 AU = b or nonlinear system b(U) = 0 corresponding to the discretization of the variational form of a 4065 differential equation.A central part of the implementation of finite element methods is therefore the 4066 computation of matrices and vectors from variational forms.In this chapter, we describe the standard 4067 algorithm for computing the discrete operator (tensor) A.
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| 8. |
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