| 1. |
- Appelo, D., et al.
(författare)
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An energy-based discontinuous Galerkin method for coupled elasto-acoustic wave equations in second-order form
- 2019
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 119:7, s. 618-638
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Tidskriftsartikel (refereegranskat)abstract
- We consider wave propagation in a coupled fluid-solid region separated by a static but possibly curved interface. The wave propagation is modeled by the acoustic wave equation in terms of a velocity potential in the fluid, and the elastic wave equation for the displacement in the solid. At the fluid solid interface, we impose suitable interface conditions to couple the two equations. We use a recently developed energy-based discontinuous Galerkin method to discretize the governing equations in space. Both energy conserving and upwind numerical fluxes are derived to impose the interface conditions. The highlights of the developed scheme include provable energy stability and high order accuracy. We present numerical experiments to illustrate the accuracy property and robustness of the developed scheme.
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| 2. |
- Bernland, Anders, et al.
(författare)
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Acoustic shape optimization using cut finite elements
- 2018
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Ingår i: International Journal for Numerical Methods in Engineering. - Hoboken : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 113:3, s. 432-449
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Tidskriftsartikel (refereegranskat)abstract
- Fictitious domain methods are attractive for shape optimization applications, since they do not require deformed or regenerated meshes. A recently developed such method is the CutFEM approach, which allows crisp boundary representations and for which uniformly well-conditioned system matrices can be guaranteed. Here, we investigate the use of the CutFEM approach for acoustic shape optimization, using as test problem the design of an acoustic horn for favorable impedance-matching properties. The CutFEM approach is used to solve the Helmholtz equation, and the geometry of the horn is implicitly described by a level-set function. To promote smooth algorithmic updates of the geometry, we propose to use the nodal values of the Laplacian of the level-set function as design variables. This strategy also improves the algorithm's convergence rate, counteracts mesh dependence, and, in combination with Tikhonov regularization, controls small details in the optimized designs. An advantage with the proposed method is that the exact derivatives of the discrete objective function can be expressed as boundary integrals, as opposed to when using a traditional method that uses mesh deformations. The resulting horns possess excellent impedance-matching properties and exhibit surprising subwavelength structures, not previously seen, which are possible to capture due to the fixed mesh approach.
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| 3. |
- Burman, Erik, et al.
(författare)
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Augmented Lagrangian and Galerkin least-squares methods for membrane contact
- 2018
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 114:11, s. 1179-1191
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose a stabilized finite element method for the numerical solution of contact between a small deformation elastic membrane and a rigid obstacle. We limit ourselves to friction-free contact, but the formulation is readily extendable to more complex situations.
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| 4. |
- Burman, Erik, et al.
(författare)
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CutFEM : Discretizing geometry and partial differential equations
- 2015
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 104:7, s. 472-501
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Tidskriftsartikel (refereegranskat)abstract
- We discuss recent advances on robust unfitted finite element methods on cut meshes. These methods are designed to facilitate computations on complex geometries obtained, for example, from computer-aided design or image data from applied sciences. Both the treatment of boundaries and interfaces and the discretization of PDEs on surfaces are discussed and illustrated numerically.
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| 5. |
- Carlsson, Kristoffer, 1989, et al.
(författare)
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Bounds on the effective response for gradient crystal inelasticity based on homogenization and virtual testing
- 2019
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 119:4, s. 281-304
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents the application of variationally consistent selective homogenization applied to a polycrystal with a subscale model of gradient-enhanced crystal inelasticity. Although the full gradient problem is solved on Statistical Volume Elements (SVEs), the resulting macroscale problem has the formal character of a standard local continuum. A semi-dual format of gradient inelasticity is exploited, whereby the unknown global variables are the displacements and the energetic micro-stresses on each slip-system. The corresponding time-discrete variational formulation of the SVE-problem defines a saddle point of an associated incremental potential. Focus is placed on the computation of statistical bounds on the effective energy, based on virtual testing on SVEs and an argument of ergodicity. As it turns out, suitable combinations of Dirichlet and Neumann conditions pertinent to the standard equilibrium and the micro-force balance, respectively, will have to be imposed. Whereas arguments leading to the upper bound are quite straightforward, those leading to the lower bound are significantly more involved; hence, a viable approximation of the lower bound is computed in this paper. Numerical evaluations of the effective strain energy confirm the theoretical predictions. Furthermore, heuristic arguments for the resulting macroscale stress-strain relations are numerically confirmed.
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| 6. |
- Casselbrant, Anna, 1970, et al.
(författare)
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Effects of fixation on electrophysiology and structure of human jejunal villi
- 2018
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Ingår i: Microscopy Research and Technique. - : Wiley. - 1059-910X. ; 81:4, s. 376-383
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Tidskriftsartikel (refereegranskat)abstract
- The villi of human jejunum vary in size and shape during different functional conditions. In the base the lamina propria is isotonic with blood, in the tip hyperosmotic. Here we study electrophysiological and morphological effects of incubation in hypotonic, isotonic, or hypertonic solutions, and to test various isotonic fixatives for microscopy. Samples of jejunal mucosae, obtained during surgery in obese patients, were studied in Ussing chambers where electrical parameters were registered during incubation in Krebs solution at various osmolarities, and during fixation in formaldehyde, glutaraldehyde, or osmium tetroxide (OsO4). The same fixatives were used for other jejunal specimens that were fixed directly for light microscopy. Morphometry was carried out to determine size and height of villi, proportion of lamina propria, and surface enlargement due to villi. Ussing chamber incubation in fluids with low osmolarity resulted in increased electrical resistance and epithelial swelling. Opposite results were obtained at high osmolality. Fixation was faster in formaldehyde than in glutaraldehyde or OsO4. In biopsies processed directly for light microscopy the proportions of lamina propria of the mucosa, and of lamina propria of villi, were significantly larger in biopsies fixed in formaldehyde than after fixation in glutaraldehyde or OsO4. The villus tips sometimes ended with a bleb with prominent spaces between the epithelial cells. In summary, jejunal villi swell in vitro when exposed to hypotonic solutions, and shrink in hypertonic solutions. Much of the morphological changes occurring during fixation can be related to the physiological hyperosmolar milieu in villus tips.
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| 7. |
- Cenanovic, Mirza, et al.
(författare)
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Minimal surface computation using a finite element method on an embedded surface
- 2015
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 104:7, s. 502-512
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Tidskriftsartikel (refereegranskat)abstract
- We suggest a finite element method for finding minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is carried out on the piecewise planar isosurface using the shape functions from the background three-dimensional mesh used to represent the distance function. A recently suggested stabilized scheme for finite element approximation of the mean curvature vector is a crucial component of the method.
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| 8. |
- Ekre, Fredrik, 1992, et al.
(författare)
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On error controlled numerical model reduction in FE2-analysis of transient heat flow
- 2019
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 119:1, s. 38-73
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Tidskriftsartikel (refereegranskat)abstract
- Numerical model reduction is exploited for solving the two-scale problem that arises from the computational homogenization of a model problem of transient heat flow. Since the problem is linear, an orthogonal basis is obtained via the method of spectral decomposition. A key feature is the construction of a symmetrized version of the space-time variational format, by which it is possible to estimate the error from the model reduction in (i) energy norm and in (ii) a given quantity of interest. In previous work by the authors, this strategy has been applied to the solution of an individual representative volume element problem, whereas the error transport to the macroscale problem in the finite element squared (FE2) approach was ignored. In this paper, such transport of error is included in the error estimate. It is remarkable that it is (still) possible to obtain guaranteed bounds on the error, as compared to the fully resolved discrete finite element problem, while using only the reduced basis and with minor extra computational effort. The performance of the error estimates is demonstrated via numerical results, whereby the subscale is modeled in three dimensions, whereas the macroscale problem is either one or two dimensional.
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| 9. |
- Främby, Johannes, 1983, et al.
(författare)
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Adaptive modelling of delamination initiation and propagation using an equivalent single-layer shell approach
- 2017
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 112:8, s. 882-908
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Tidskriftsartikel (refereegranskat)abstract
- A major challenge for crash failure analysis of laminated composites is to find a modelling approach, which is both sufficiently accurate, for example, able to capture delaminations, and computationally efficient to allow full-scale vehicle crash simulations. Addressing this challenge, we propose a methodology based on an equivalent single-layer shell formulation which is adaptively through-the-thickness refined to capture initiating and propagating delaminations. To be specific, single shell elements through the laminate thickness are locally and adaptively enriched using the extended finite element method such that delaminations can be explicitly modelled without having to be represented by separate elements. Furthermore, the shell formulation is combined with a stress recovery technique which increases the accuracy of predicting delamination initiations. The paper focuses on the parameters associated with identifying, introducing and extending the enrichment areas; especially on the impact of these parameters on the resulting structural deformation behaviour. We conclude that the delamination enrichment must be large enough to allow the fracture process to be accurately resolved, and we propose a suitable approach to achieve this. The proposed methodology for adaptive delamination modelling shows potential for being computationally efficient, and thereby, it has the potential to enable efficient and accurate full vehicle crash simulations of laminated composites.
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| 10. |
- Gaborit, Mathieu, et al.
(författare)
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Coupling of Finite-Element and Plane Waves Discontinuous Galerkin methods for time-harmonic problems
- 2018
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 116:7, s. 487-503
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Tidskriftsartikel (refereegranskat)abstract
- A coupling approach is presented to combine a wave‐based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation problems. While wave‐based methods can significantly reduce the computational cost, especially at high frequencies, their efficiency is hampered by the need to use small elements to resolve complex geometric features. This can be alleviated by using a standard finite element model close to the surfaces to model geometric details and create large, simply‐shaped areas to model with a wave‐based method. This strategy is formulated and validated in this paper for the wave‐based discontinuous Galerkin method together with the standard finite element method. The coupling is formulated without using Lagrange multipliers and results demonstrate that the coupling is optimal in that the convergence rates of the individual methods are maintained.
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