| 1. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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An adaptive low-order FE-scheme for Stokes flow with cavitation
- 2010
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Ingår i: Journal of Numerical Mathematics. - 1570-2820 .- 1569-3953. ; 18:3, s. 177-185
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Tidskriftsartikel (refereegranskat)abstract
- In this note we derive a posteriori error bounds for FE-discretisations for a fluid problem with cavitation. The underlying model is the Stokes system together with an inequality constraint for the pressure. In order to avoid suboptimal behavior of the error bounds we propose to employ a Lagrange setting yielding an improved estimate. Numerical tests confirm our theoretical results.
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| 2. |
- Amouzgar, Kaveh
(författare)
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Metamodel based multi-objective optimization
- 2015
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- As a result of the increase in accessibility of computational resources and the increase in the power of the computers during the last two decades, designers are able to create computer models to simulate the behavior of a complex products. To address global competitiveness, companies are forced to optimize their designs and products. Optimizing the design needs several runs of computationally expensive simulation models. Therefore, using metamodels as an efficient and sufficiently accurate approximate of the simulation model is necessary. Radial basis functions (RBF) is one of the several metamodeling methods that can be found in the literature.The established approach is to add a bias to RBF in order to obtain a robust performance. The a posteriori bias is considered to be unknown at the beginning and it is defined by imposing extra orthogonality constraints. In this thesis, a new approach in constructing RBF with the bias to be set a priori by using the normal equation is proposed. The performance of the suggested approach is compared to the classic RBF with a posteriori bias. Another comprehensive comparison study by including several modeling criteria, such as problem dimension, sampling technique and size of samples is conducted. The studies demonstrate that the suggested approach with a priori bias is in general as good as the performance of RBF with a posteriori bias. Using the a priori RBF, it is clear that the global response is modeled with the bias and that the details are captured with radial basis functions.Multi-objective optimization and the approaches used in solving such problems are briefly described in this thesis. One of the methods that proved to be efficient in solving multi-objective optimization problems (MOOP) is the strength Pareto evolutionary algorithm (SPEA2). Multi-objective optimization of a disc brake system of a heavy truck by using SPEA2 and RBF with a priori bias is performed. As a result, the possibility to reduce the weight of the system without extensive compromise in other objectives is found.Multi-objective optimization of material model parameters of an adhesive layer with the aim of improving the results of a previous study is implemented. The result of the original study is improved and a clear insight into the nature of the problem is revealed.
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| 3. |
- Becker, Roland, et al.
(författare)
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A finite element method for domain decomposition with non-matching grids
- 2003
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Ingår i: Mathematical Modelling and Numerical Analysis. - : EDP Sciences. - 0764-583X .- 1290-3841. ; 37:2, s. 209-225
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Tidskriftsartikel (refereegranskat)abstract
- In this note, we propose and analyse a method for handling interfaces between nonmatching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson's equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.
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| 4. |
- Becker, R., et al.
(författare)
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A finite element time relaxation method
- 2011
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Ingår i: Comptes Rendus Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 349:5-6, s. 353-356
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Tidskriftsartikel (refereegranskat)abstract
- We discuss a finite element time-relaxation method for high Reynolds number flows. The method uses local projections on polynomials defined on macroelements of each pair of two elements sharing a face. We prove that this method shares the optimal stability and convergence properties of the continuous interior penalty (CIP) method. We give the formulation both for the scalar convection-diffusion equation and the time-dependent incompressible Euler equations and the associated convergence results. This note finishes with some numerical illustrations. (C) 2010 Academic des sciences. Published by Elsevier Masson SAS. All rights reserved.
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| 5. |
- Becker, R., et al.
(författare)
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A hierarchical NXFEM for fictitious domain simulations
- 2011
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 86:4-5, s. 549-559
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Tidskriftsartikel (refereegranskat)abstract
- We suggest a fictitious domain method, based on the Nitsche XFEM method of (Comput. Meth. Appl. Mech. Engrg 2002; 191: 5537-5552), that employs a band of elements adjacent to the boundary. In contrast, the classical fictitious domain method uses Lagrange multipliers on a line (surface) where the boundary condition is to be enforced. The idea can be seen as an extension of the Chimera method of (ESAIM: Math. Model Numer. Anal. 2003; 37: 495-514), but with a hierarchical representation of the discontinuous solution field. The hierarchical formulation is better suited for moving fictitious boundaries since the stiffness matrix of the underlying structured mesh can be retained during the computations. Our technique allows for optimal convergence properties irrespective of the order of the underlying finite element method.
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| 6. |
- Becker, Roland, et al.
(författare)
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A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity
- 2009
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 198:41-44, s. 3352-3360
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Tidskriftsartikel (refereegranskat)abstract
- In this note we propose a finite element method for incompressible (or compressible) elasticity problems with discontinuous modulus of elasticity (or, if compressible, Poisson’s ratio). The problem is written on mixed form using P1-continuous displacements and elementwise P0 pressures, leading to the possibility of eliminating the pressure beforehand in the compressible case. In the incompressible case, the method is augmented by a stabilization term, penalizing the pressure jumps. We show a priori error estimates under certain regularity hypothesis. In particular we prove that if the exact solution is sufficiently smooth in each subdomain then the convergence order is optimal.
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| 7. |
- Becker, Roland, et al.
(författare)
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A simple pressure stabilization method for the Stokes equation
- 2008
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Ingår i: Communications in Numerical Methods in Engineering. - : Wiley. - 1069-8299 .- 1099-0887. ; 24:11, s. 1421-1430
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider a stabilization method for the Stokes problem, using equal-order interpolation of the pressure and velocity, which avoids the use of the mesh size parameter in the stabilization term. We show that our approach is stable for equal-order interpolation in the case of piecewise linear and piecewise quadratic polynomials on triangles. In the case of linear polynomials, we retrieve a well-known idea of using mass lumping as a stabilization mechanism.
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| 8. |
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| 9. |
- Becker, Roland, et al.
(författare)
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Energy norm a posteriori error estimation for discontinuous Galerkin methods
- 2003
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 192:5-6, s. 723-733
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a residual-based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous Galerkin approximations of elliptic problems. The theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed. We also present some illustrating numerical examples.
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| 10. |
- Burman, Erik, et al.
(författare)
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A cut discontinuous Galerkin method for the Laplace–Beltrami operator
- 2017
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Ingår i: IMA Journal of Numerical Analysis. - : Oxford University Press. - 0272-4979 .- 1464-3642. ; 37:1, s. 138-169
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Tidskriftsartikel (refereegranskat)abstract
- We develop a discontinuous cut finite element method for the Laplace–Beltrami operator on a hypersurface embedded in R. The method is constructed by using a discontinuous piecewise linear finite element space defined on a background mesh in R. The surface is approximated by a continuous piecewise linear surface that cuts through the background mesh in an arbitrary fashion. Then, a discontinuous Galerkin method is formulated on the discrete surface and in order to obtain coercivity, certain stabilization terms are added on the faces between neighbouring elements that provide control of the discontinuity as well as the jump in the gradient. We derive optimal a priori error and condition number estimates which are independent of the positioning of the surface in the background mesh. Finally, we present numerical examples confirming our theoretical results.
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