| 1. |
- Hoffman, Johan, 1974-, et al.
(författare)
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DOLFIN: Dynamic Object oriented Library for FINite element computation
- 2002
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this report, we present a new software project intended to provide a platform for daptive finite element computation in both research and education. The software DOLFIN is implemented in C++ and provides an object-oriented powerful and flexible environment in which finnite element methods for differential equations can be easily implemented. The current version of DOLFIN already includes a nnumber of modules for special differential equations, including the incompressible Navier-Stokes equations. DOLFIN is free and open source, which we believe is a key point in creating truly useful software.
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| 2. |
- Hoffman, Johan, 1974-, et al.
(författare)
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The FEniCS project
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The goal of the FEniCS project is to develop open-source software for the automation of Computational Mathematical Modeling (CMM). FEniCS is a joint project between the Toyota Technological Institute at Chicago, the University of Chicago, and Chalmers University of Technology. The vision of FEniCS is to set a new standard in CMM, which can be described as the Automation of CMM, towards the goals of generality, efficiency, and simplicity, concerning mathematical methodology, implementation, and application.
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| 3. |
- Jansson, Johan, 1978-, et al.
(författare)
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Automated error control in finite element methods withapplications in fluid flow
- 2014
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we present a new adaptive finite element method for thesolution of linear and non-linear partial differential equationsdirectly using the a posteriori error representation as a local errorindicator, with the primal and dual solutions approximated in the samefinite element space, here piecewise continuous linear functions onthe same mesh. Since this approach gives a global a posteriori errorrepresentation that is zero due to Galerkin orthogonality, the errorrepresentation has traditionally been thought to contain noinformation about the error. However, for elliptic andconvection-diffusion model problems we show the opposite, that locallythe orthogonal error representation behaves very similar to thenon-orthogonal error representation using a higher order approximationof the dual. We have previously proved an a priori estimate of thelocal error indicator for elliptic problems, and in this paper weextend the proof to convection-reaction problems. We also present aversion of the method for non-elliptic and non-linear problems using astabilized finite element method where the a posteriori errorrepresentation is no longer orthogonal. We apply this method to thestationary incompressible Navier-Stokes equation and perform detailednumerical experiments which show that the a posteriori error estimateis within a factor 2 of the error based on a reference value on a finemesh, except in a few data points on very coarse meshes for anon-smooth test case where it is within a factor 3.
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| 7. |
- Hoffman, Johan, 1974, et al.
(författare)
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Mathematics and Computation
- 2004
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Ingår i: Stockholm Intelligencer: Fourth European Congress of Mathematics.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 8. |
- Hoffman, Johan, et al.
(författare)
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Subgrid modeling for convection-diffusion-reaction in one space dimension using a Haar Multiresolution analysis
- 2005
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 194:1, s. 19-44
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we propose and study a subgrid model for linear convection-diffusion-reaction equations with fractal rough coefficients. The subgrid model is based on scale extrapolation of a modeling residual from coarser scales using a computed solution on a finest scale as reference. We show in experiments that a solution with subgrid model on a scale h in most cases corresponds to a solution without subgrid model on a scale less than h/4. We also present error estimates for the modeling error in terms of modeling residuals.
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| 9. |
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| 10. |
- Degirmenci, Niyazi Cem, 1982-
(författare)
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Adaptive Finite Element Methods for Fluid Structure Interaction Problems with Applications to Human Phonation
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This work presents a unified framework for numerical solution of Fluid Structure Interaction (FSI) and acoustics problems with focus on human phonation. The Finite Element Method is employed for numerical investigation of partial differential equations that model conservation of momentum and mass. Since the resulting system of equations is very large, an efficient open source high performance implementation is constructed and provided. In order to gain accuracy for the numerical solutions, an adaptive mesh refinement strategy is employed which reduces the computational cost in comparison to a uniform refinement. Adaptive refinement of the mesh relies on computable error indicators which appear as a combination of a computable residual and the solution of a so-called dual problem acting as weights on computed residuals. The first main achievement of this thesis is to apply this strategy to numerical simulations of a benchmark problem for FSI. This FSI model is further extended for contact handling and applied to a realistic vocal folds geometry where the glottic wave formation was captured in the numerical simulations. This is the second achievement in the presented work. The FSI model is further coupled to an acoustics model through an acoustic analogy, for vocal folds with flow induced oscillations for a domain constructed to create the vowel /i/. The comparisons of the obtained pressure signal at specified points with respect to results from literature for the same vowel is reported, which is the final main result presented.
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