| 1. |
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| 2. |
- Ahlkrona, Josefin, et al.
(författare)
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A cut finite element method for non-Newtonian free surface flows in 2D : application to glacier modelling
- 2021
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Ingår i: Journal of Computational Physics: X. - : Elsevier. - 2590-0552. ; 11
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Tidskriftsartikel (refereegranskat)abstract
- In ice sheet and glacier modelling, the Finite Element Method is rapidly gaining popularity. However, constructing and updating meshes for ice sheets and glaciers is a non-trivial and computationally demanding task due to their thin, irregular, and time dependent geometry. In this paper we introduce a novel approach to ice dynamics computations based on the unfitted Finite Element Method CutFEM, which lets the domain boundary cut through elements. By employing CutFEM, complex meshing and remeshing is avoided as the glacier can be immersed in a simple background mesh without loss of accuracy. The ice is modelled as a non-Newtonian, shear-thinning fluid obeying the p-Stokes (full Stokes) equations with the ice atmosphere interface as a moving free surface. A Navier slip boundary condition applies at the glacier base allowing both bedrock and subglacial lakes to be represented. Within the CutFEM framework we develop a strategy for handling non-linear viscosities and thin domains and show how glacier deformation can be modelled using a level set function. In numerical experiments we show that the expected order of accuracy is achieved and that the method is robust with respect to penalty parameters. As an application we compute the velocity field of the Swiss mountain glacier Haut Glacier d'Arolla in 2D with and without an underlying subglacial lake, and simulate the glacier deformation from year 1930 to 1932, with and without surface accumulation and basal melt.
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| 3. |
- Björnham, Oscar, et al.
(författare)
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BioCon - A model for pathogens and biofilm in drinking water distribution systems
- 2024
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- En modell för biologisk kontamination av dricksvattensystem är utvecklad som ett komplement till kommersiella mjukvaror. Modellen benämns Biofilm contamination model (BioCon), vilken utgörs av delmodeller för transport och biofilmer. De dominerande processerna beskrivs genom ett system av partiella differentialekvationer. BioCon inkluderar även en numerisk lösare för de biofysikaliska modellerna och visualisering av den tidsupplösta kontaminationen i systemet. BioCon är utformad för att kunna hantera många olika biologiska agens och miljöparametrar genom parametrisering av de styrande ekvationerna. De två patogenerna Escherichia coli och Cryptosporidium spp. utgör pilotagens i denna rapport och relevanta egenskaper hos dem diskuteras. Förslag på parametrisering ges för E. coli baserad främst på publicerad litteratur men också till del från preliminär data från laboratorieexperiment genomförda under detta projekt. Modellstrukturen av de viktigaste komponenterna såsom transport, inbindning/dissociation, utveckling av biofilm, och påverkan av temperatur, desinfektionsmedel och näringsämnen, är utformade för att ge upphov till beteenden som överensstämmer med rapporterade experimentell data och teoretiska modeller. Huvuddragen i BioCon har på detta sätt blivit verifierade med avseende på nuvarande kunskapsläge, vilket presenteras i denna rapport. Däremot har en omfattande och kvantitativ validering av BioCon, genom jämförelse med experimentell data för samma system av agens, miljöfaktorer och flöden, ej kunnat genomföras inom ramen för detta projekt. Detta rekommenderas som en framtida studie.
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| 4. |
- Burman, Erik, et al.
(författare)
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A cut finite element method for the Bernoulli free boundary value problem
- 2017
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 317, s. 598-618
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Tidskriftsartikel (refereegranskat)abstract
- We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion. This leads to so called cut elements in the vicinity of the boundary. To obtain a stable method, stabilization terms are added in the vicinity of the cut elements penalizing the gradient jumps across element sides. The stabilization also ensures good conditioning of the resulting discrete system. We develop a method for shape optimization based on moving the distance function along a velocity field which is computed as the H1 Riesz representation of the shape derivative. We show that the velocity field is the solution to an interface problem and we prove an a priori error estimate of optimal order, given the limited regularity of the velocity field across the interface, for the velocity field in the H1norm. Finally, we present illustrating numerical results.
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| 5. |
- Burman, Erik, et al.
(författare)
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Cut topology optimization for linear elasticity with coupling to parametric nondesign domain regions
- 2019
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 350, s. 462-479
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Tidskriftsartikel (refereegranskat)abstract
- We develop a density based topology optimization method for linear elasticity based on the cut finite element method. More precisely, the design domain is discretized using cut finite elements which allow complicated geometry to be represented on a structured fixed background mesh. The geometry of the design domain is allowed to cut through the background mesh in an arbitrary way and certain stabilization terms are added in the vicinity of the cut boundary, which guarantee stability of the method. Furthermore, in addition to standard Dirichlet and Neumann conditions we consider interface conditions enabling coupling of the design domain to parts of the structure for which the design is already given. These given parts of the structure, called the nondesign domain regions, typically represent parts of the geometry provided by the designer. The nondesign domain regions may be discretized independently from the design domains using for example parametric meshed finite elements or isogeometric analysis. The interface and Dirichlet conditions are based on Nitsche's method and are stable for the full range of density parameters. In particular we obtain a traction-free Neumann condition in the limit when the density tends to zero.
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| 6. |
- Burman, Erik, et al.
(författare)
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Hybridized CutFEM for Elliptic Interface Problems
- 2019
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Ingår i: SIAM Journal on Scientific Computing. - : Society for Industrial and Applied Mathematics. - 1064-8275 .- 1095-7197. ; 41:5, s. A3354-A3380
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Tidskriftsartikel (refereegranskat)abstract
- We design and analyze a hybridized cut finite element method for elliptic interface problems. In this method very general meshes can be coupled over internal unfitted interfaces, through a skeletal variable, using a Nitsche type approach. We discuss how optimal error estimates for the method are obtained using the tools of cut finite element methods and prove a condition number estimate for the Schur complement. Finally, we present illustrating numerical examples.
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| 7. |
- Burman, Erik, et al.
(författare)
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Shape and topology optimization using CutFEM
- 2017
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Ingår i: Simulation for Additive Manufacturing 2017, Sinam 2017. - : International Center for Numerical Methods in Engineering (CIMNE). ; , s. 208-209, s. 208-209
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Konferensbidrag (refereegranskat)abstract
- We present a shape and topology optimization method based on the cut finite element method, see [1],[2], and [3], for the optimal compliance problem in linear elasticity and problems involving restrictionson the stresses.The elastic domain is defined by a level-set function, and the evolution of the domain is obtained bymoving the level-set along a velocity field using a transport equation. The velocity field is defined tobe the largest decreasing direction of the shape derivative that resides in a certain Hilbert space and iscomputed by solving an elliptic problem, associated with the bilinear form in the Hilbert space, with theshape derivative as right hand side. The velocity field may thus be viewed as the Riesz representationof the shape derivative on the chosen Hilbert space.We thus obtain a coupled problem involving three partial differential equations: (1) the elasticity problem,(2) the elliptic problem that determines the velocity field, and (3) the transport problem for thelevelset function. The elasticity problem is solved using a cut finite element method on a fixed backgroundmesh, which completely avoids re–meshing when the domain is updated. The levelset functionand the velocity field is approximated by standard conforming elements on the background mesh. Wealso employ higher order cut approximations including isogeometric analysis for the elasticity problem.In this case the levelset function and the velocity field are represented using linear elements on a refinedmesh in order to simplify the geometric and quadrature computations on the cut elements. To obtain astable method, stabilization terms are added in the vicinity of the cut elements at the boundary, whichprovides control of the variation of the solution in the vicinity of the boundary. We present numericalexamples illustrating the performance of the method.We also study an anisotropic material model that accounts for the orientation of the layers in an additivemanufacturing process and by including the orientation in the optimization problem we determine theoptimal choice of orientation.We present numerical results including test problems and engineering applications in additive manufacturing.References[1] E. Burman, S. Claus, P. Hansbo, M. G. Larson, and A. Massing. CutFEM: discretizing geometryand partial differential equations. Internat. J. Numer. Methods Engrg., 104(7):472–501, 2015.[2] E. Burman, D. Elfverson, P. Hansbo, M. G. Larson, and K. Larsson. Shape optimization using thecut finite element method. Technical report, 2016. arXiv:1611.05673.[3] E. Burman, D. Elfverson, P. Hansbo, M. G. Larson, and K. Larsson. A cut finite element method forthe Bernoulli free boundary value problem. Comput. Methods Appl. Mech. Engrg., 317:598–618,2017.
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| 8. |
- Burman, Erik, et al.
(författare)
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Shape optimization using the cut finite element method
- 2018
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - Lausanne : Elsevier. - 0045-7825 .- 1879-2138. ; 328, s. 242-261
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Tidskriftsartikel (refereegranskat)abstract
- We present a cut finite element method for shape optimization in the case of linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by moving the level-set along a velocity field using a transport equation. The velocity field is the largest decreasing direction of the shape derivative that satisfies a certain regularity requirement and the computation of the shape derivative is based on a volume formulation. Using the cut finite element method no re-meshing is required when updating the domain and we may also use higher order finite element approximations. To obtain a stable method, stabilization terms are added in the vicinity of the cut elements at the boundary, which provides control of the variation of the solution in the vicinity of the boundary. We implement and illustrate the performance of the method in the two-dimensional case, considering both triangular and quadrilateral meshes as well as finite element spaces of different order.
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| 9. |
- Elfverson, Daniel
(författare)
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A discontinuous Galerkin multiscale method for convection–diffusion problems
- 2015
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Ingår i: Computing Research Repository. ; :1509.03523
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- We propose an discontinuous Galerkin local orthogonal decomposition multiscale method for convection-diffusion problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the discontinuous Galerkin method allows us to better cope with multiscale features as well as interior/boundary layers in the solution. In the proposed method the trail and test spaces are spanned by a corrected basis computed on localized patches of size O(Hlog(H−1)), where H is the mesh size. We prove convergence rates independent of the variation in the coefficients and present numerical experiments which verify the analytical findings.
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| 10. |
- Elfverson, Daniel, et al.
(författare)
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A Multilevel Monte Carlo Method for Computing Failure Probabilities
- 2016
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Ingår i: SIAM-ASA Journal on Uncertainty Quantification. - : Society for Industrial & Applied Mathematics (SIAM). - 2166-2525. ; 4:1, s. 312-330
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Tidskriftsartikel (refereegranskat)abstract
- We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or above) some critical value. By combining recent results on quantile estimation and the multilevel Monte Carlo method, we develop a method that reduces computational cost without loss of accuracy. We show how the computational cost of the method relates to error tolerance of the failure probability. For a wide and common class of problems, the computational cost is asymptotically proportional to solving a single accurate realization of the numerical model, i.e., independent of the number of samples. Significant reductions in computational cost are also observed in numerical experiments.
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