| 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. |
- Alnæs, M.S., et al.
(författare)
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Unified framework for finite element assembly
- 2009
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Ingår i: International Journal of Computational Science and Engineering. - 1742-7185 .- 1742-7193. ; 4:4, s. 231-244
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Tidskriftsartikel (refereegranskat)abstract
- At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain. Copyright © 2009, Inderscience Publishers.
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| 3. |
- Ames, Ellery, et al.
(författare)
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Cosmic string and black hole limits of toroidal Vlasov bodies in general relativity
- 2019
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Ingår i: Physical Review D. - : AMER PHYSICAL SOC. - 2470-0010 .- 2470-0029. ; 99:2
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Tidskriftsartikel (refereegranskat)abstract
- We numerically investigate limits of a two-parameter family of stationary solutions to the Einstein-Vlasov system. The solutions are toroidal and have nonvanishing angular momentum. As the parameters are tuned to more relativistic solutions (measured e.g., by an increasing redshift) we provide evidence for a sequence of solutions which approaches the extreme Kerr black hole family. Solutions with angular momentum larger than the square of the mass are also investigated, and in the relativistic limit the near-field geometry of such solutions is observed to become locally rotationally symmetric about the matter density. The existence of a deficit angle in these regions is investigated.
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| 4. |
- Ames, Ellery, 1984, et al.
(författare)
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On axisymmetric and stationary solutions of the self-gravitating Vlasov system
- 2016
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 33:15
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Tidskriftsartikel (refereegranskat)abstract
- Axisymmetric and stationary solutions are constructed to the Einstein-Vlasov and Vlasov-Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein-Vlasov system which contain ergoregions.
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| 5. |
- Arnold, Douglas N., et al.
(författare)
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Periodic Table of the Finite Elements
- 2014
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Ingår i: SIAM News. - 0036-1437. ; 47:9
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Tidskriftsartikel (refereegranskat)abstract
- The finite element method is one of the most powerful and widely applicable techniques for the numerical solution of partial differential equations and, therefore, for the simulation of the physical world. First proposed by engineers in the 1950s as a practical numerical method for predicting the deflection and stress of structural components of aircraft, the method has since been continuously extended and refined. It is now used in almost all application areas modeled by PDEs: solid and fluid dynamics, electromagnetics, biophysics, and even finance, to name just a few. Much as the chemical elements can be arranged in a periodic table based on their electron structure and recurring chemical properties, a broad assortment of finite elements can be arranged in a table that clarifies their properties and relationships. This arrangement, which is based on expression of the finite element function spaces in the language of differential forms, is one of the major outcomes of the theory known as finite element exterior calculus, or FEEC. Just as the arrangement of the chemical elements in a periodic table led to the discovery of new elements, the periodic table of finite elements has not only clarified existing elements but also highlighted holes in our knowledge and led to new families of finite elements suited for certain purposes.
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| 6. |
- Borgqvist, Johannes, 1990, et al.
(författare)
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Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability
- 2021
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Ingår i: Npj Systems Biology and Applications. - : Springer Science and Business Media LLC. - 2056-7189. ; 7:1
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Tidskriftsartikel (refereegranskat)abstract
- The GTPase Cdc42 is the master regulator of eukaryotic cell polarisation. During this process, the active form of Cdc42 is accumulated at a particular site on the cell membrane called the pole. It is believed that the accumulation of the active Cdc42 resulting in a pole is driven by a combination of activation-inactivation reactions and diffusion. It has been proposed using mathematical modelling that this is the result of diffusion-driven instability, originally proposed by Alan Turing. In this study, we developed, analysed and validated a 3D bulk-surface model of the dynamics of Cdc42. We show that the model can undergo both classic and non-classic Turing instability by deriving necessary conditions for which this occurs and conclude that the non-classic case can be viewed as a limit case of the classic case of diffusion-driven instability. Using three-dimensional Spatio-temporal simulation we predicted pole size and time to polarisation, suggesting that cell polarisation is mainly driven by the reaction strength parameter and that the size of the pole is determined by the relative diffusion.
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| 7. |
- Eriksson, Kenneth, 1952, et al.
(författare)
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Explicit time-stepping for stiff ODES
- 2003
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Ingår i: SIAM Journal on Scientific Computing. - 1064-8275 .- 1095-7197. ; 25:4, s. 1142-1157
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Tidskriftsartikel (refereegranskat)abstract
- We present a new strategy for solving stiff ODEs with explicit methods. By adaptively taking a small number of stabilizing small explicit time steps when necessary, a stiff ODE system can be stabilized enough to allow for time steps much larger than what is indicated by classical stability analysis. For many stiff problems the cost of the stabilizing small time steps is small, so the improvement is large. We illustrate the technique on a number of well-known stiff test problems.
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| 8. |
- Jansson, Johan, et al.
(författare)
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Algorithms and Data Structures for Multi-Adaptive Time-Stepping
- 2008
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Ingår i: ACM Transactions on Mathematical Software. - : Association for Computing Machinery (ACM). - 0098-3500 .- 1557-7295. ; 35:3
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Tidskriftsartikel (refereegranskat)abstract
- Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the multi-adaptive methods allow individual and adaptive time steps to be used for different components or in different regions of space. We present algorithms for efficient multi-adaptive time-stepping, including the recursive construction of time slabs and adaptive time step selection. We also present data structures for efficient storage and interpolation of the multi-adaptive solution. The efficiency of the proposed algorithms and data structures is demonstrated for a series of benchmark problems.
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| 9. |
- Jansson, Johan, 1978, et al.
(författare)
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Computational modeling of dynamical systems
- 2005
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Ingår i: Mathematical Models and Methods in Applied Sciences. - 0218-2025. ; 15:3, s. 471-481
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Tidskriftsartikel (refereegranskat)abstract
- In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be very costly. By resolving the fast time scales in a short time simulation, a model for the effect of the small time scale variation on large time scales can be determined, making solution possible on a long time interval. This process of computational modeling can be completely automated. Two examples are presented, including a simple model problem oscillating at a time scale of 10-9 computed over the time interval [0, 100], and a lattice consisting of large and small point masses. © World Scientific Publishing Company.
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| 10. |
- Johansson, August, et al.
(författare)
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High order cut finite element methods for the Stokes problem
- 2015
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Ingår i: Advanced Modeling and Simulation in Engineering Sciences. - : Springer. - 2213-7467. ; 2:1, s. 1-23
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Tidskriftsartikel (refereegranskat)abstract
- We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on a Nitsche formulation of the interface condition together with a stabilization term. Starting from inf-sup stable spaces on the two meshes, we prove that the resulting composite method is indeed inf-sup stable and as a consequence optimal a priori error estimates hold.
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