| 1. |
- Sorgentone, Chiara, et al.
(författare)
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A new high order energy and enstrophy conserving Arakawa-like Jacobian differential operator
- 2015
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 301, s. 167-177
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Tidskriftsartikel (refereegranskat)abstract
- A new high order Arakawa-like method for the incompressible vorticity equation in two-dimensions has been developed. Mimetic properties such as skew-symmetry, energy and enstrophy conservations for the semi-discretization are proved for periodic problems using arbitrary high order summation-by-parts operators. Numerical simulations corroborate the theoretical findings.
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| 2. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
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Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
- 2009
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Denna rapport studerar hur begreppen matematisk modell och matematisk modellering behandlats i kursplanerna i matematik för motsvarande svenska gymnasieskolans naturvetenskapliga program mellan åren 1965 och 2000. En översikt över sex kursplaners olika form och innehåll ges och tre olika analyser på tre olika nivåer genomförs; en innehållsanalys, en kvalitativ analys, och en analys som beaktar relationen mellan begreppen modellering, tillämpningar och problemlösning. Analysen visar att matematiska modeller och modellering förekommit implicit sedan kursplanen från 1965, men att begreppen främst i de två senaste kursplanerna lyfts fram explicit och fått en central position i kursplanerna. I den nuvarande kursplanen Gy2000 framgår att matematiska modeller kan tolkas både som ett undervisningsmål i sig och som ett didaktiskt hjälpmedel att lära matematik.
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| 3. |
- Berntsson, Fredrik, et al.
(författare)
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Numerical Solution of the Cauchy Problem for the Helmholtz Equation
- 2014
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The Cauchy problem for the Helmholtz equation appears in applications related to acoustic or electromagnetic wave phenomena. The problem is ill–posed in the sense that the solution does not depend on the data in a stable way. In this paper we give a detailed study of the problem. Specifically we investigate how the ill–posedness depends on the shape of the computational domain and also on the wave number. Furthermore, we give an overview over standard techniques for dealing with ill–posed problems and apply them to the problem.
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| 4. |
- Cengiz, Cigdem, et al.
(författare)
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High-dimensional profile analysis
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The three tests of profile analysis: test of parallelism, test of level and test of flatness have been studied. Likelihood ratio tests have been derived. Firstly, a traditional setting, where the sample size is greater than the dimension of the parameter space, is considered. Then, all tests have been derived in a high-dimensional setting. In high-dimensional data analysis, it is required to use some techniques to tackle the problems which arise with the dimensionality. We propose a dimension reduction method using scores which was first proposed by Läuter et al. (1996).
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| 5. |
- Eriksson, Sofia, et al.
(författare)
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Finite difference schemes with transferable interfaces for parabolic problems
- 2018
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Ingår i: Journal of Computational Physics. - Linköping : Elsevier. - 0021-9991 .- 1090-2716. ; 375, s. 935-949
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Tidskriftsartikel (refereegranskat)abstract
- We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent. (C) 2018 Elsevier Inc. All rights reserved.
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| 6. |
- Frenander, Hannes, et al.
(författare)
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Spurious solutions for the advection-diffusion equation using wide stencils for approximating the second derivative.
- 2014
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A one dimensional steady-state advection-diffusion problem using summation-by-parts operators has been investigated. For approximating the second derivative, a wide stencil has been used, which has spurious, oscillating, modes for all mesh-sizes. We show that the size of the spurious modes are equal to the size of the truncation error for a stable approximation. The theoretical results are veried with numerical experiments.
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| 7. |
- Ghasemi Zinatabadi, Fatemeh, 1988-, et al.
(författare)
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An Energy Stable Coupling Procedure for the Compressible and Incompressible Navier-Stokes Equations
- 2019
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Ingår i: Journal of Computational Physics. - Linköping : Linköping University Electronic Press. - 0021-9991 .- 1090-2716. ; 396, s. 280-302
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The coupling of the compressible and incompressible Navier-Stokes equations is considered. Our ambition is to take a first step towards a provably well posed and stable coupling procedure. We study a simplified setting with a stationary planar interface and small disturbances from a steady background ow with zero velocity normal to the interface.The simplified setting motivates the use of the linearized equations, and we derive interface conditions such that the continuous problem satisfy an energy estimate. The interface conditions can be imposed both strongly and weakly. It is shown that the weak and strong interface imposition produce similar continuous energy estimates.We discretize the problem in time and space by employing finite difference operators that satisfy a summation-by-parts rule. The interface and initial conditions are imposed weakly using a penalty formulation. It is shown that the results obtained for the weak interface conditions in the continuous case, lead directly to stability of the fully discrete problem.
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| 8. |
- Ghasemi Zinatabadi, Fatemeh, 1988-, et al.
(författare)
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On conservation and dual consistency for summation-by-parts based approximations of parabolic problems
- 2019
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We consider the coupling of parabolic problems discretized using difference operators on summation-by-parts (SBP) form with interface conditions imposed weakly. In, it was shown that conservation and dual consistency are equivalent concepts for linear conservation laws. Here, we show that these concepts are equivalent also for symmetric or symmetrizable parabolic problems, exemplified by the heat equation. We rewrite the heat equation as first order system as in the local discontinuous Galerkin method and show the equivalence of dual consistency and conservation for both the first and second order forms.
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| 9. |
- Ghasemi Zinatabadi, Fatemeh, 1988-, et al.
(författare)
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The Relation Between Primal and Dual Boundary Conditions for Hyperbolic Systems of Equations
- 2019
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we study boundary conditions for linear hyperbolic systems of equations and the corresponding dual problems. In particular, we show that the primal and dual boundary conditions are related by a simple scaling relation. It is also shown that the weak dual problem can be derived directly from the weak primal problem.Based on the continuous analysis, we discretize and perform computations with a high-order finite difference scheme on summation-by-parts form with weak boundary conditions. It is shown that the results obtained in the continuous analysis lead directly to stability results for the primal and dual discrete problems. Numerical experiments corroborate the theoretical results.
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| 10. |
- Kopriva, David A., et al.
(författare)
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Error boundedness of discontinuous Galerkin spectral element approximations of hyperbolic problems
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We examine the long time error behavior of discontinuous Galerkin spectral element approximations to hyperbolic equations. We show that the choice of numerical flux at interior element boundaries affects the growth rate and asymptotic value of the error. Using the upwind flux, the error reaches the asymptotic value faster, and to a lower value than a central flux gives, especially for low resolution computations. The differences in the error caused by the numerical flux choice decrease as the solution becomes better resolved.
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