MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1237 products
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33/2014 - 08/06/2014
Canuto, C.; Simoncini, V.; Verani, M.
Contraction and optimality properties of an adaptive Legendre-Galerkin method: the multi-dimensional case | Abstract | | We analyze the theoretical properties of an adaptive Legendre-Galerkin method in the multidimensional case. After the recent investigations for Fourier-Galerkin methods in a periodic box and for Legendre-Galerkin methods in the one dimensional setting, the present study represents a further step towards a mathematically rigorous understanding of adaptive spectral/hp discretizations of elliptic boundary-value problems. The main contribution of the paper is a careful construction of a multidimensional Riesz basis in H^1, based on a quasi-orthonormalization procedure. This allows us to design an adaptive algorithm, to prove its convergence by a contraction argument, and to discuss its optimality properties (in the sense of non-linear approximation theory) in certain sparsity classes of Gevrey type. |
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32/2014 - 08/04/2014
Agosti, A.; Formaggia, L.;Scotti, A.
Analysis of a model for precipitation and dissolution coupled with a Darcy flux | Abstract | | In this paper we deal with the numerical analysis of an upscaled model of a reactive flow in a porous medium, which describes the transport of solutes undergoing precipitation and dissolution, leading to the formation/degradation of crystals inside the porous matrix. The model is defined at the Darcy scale, and it is coupled to a Darcy flow characterized by a permeability field that changes in space and time according to the precipitated crystal concentration. The model involves a non-linear multi-valued reaction term, which is treated exactly by solving an inclusion problem for the solutes and the crystals dynamics. We consider a weak formulation for the coupled system of equations expressed in a dual mixed form for the Darcy field and in a primal form for the solutes and the precipitate, and show its well posedness without resorting to regularization of the reaction term. Convergence to the weak solution is proved for its finite element approximation. We perform numerical experiments to study the behavior of the system and to assess the effectiveness of the proposed discretization strategy. In particular we show that a method that captures the discontinuity yields sharper dissolution fronts with respect to methods that regularize the discontinuous term. |
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31/2014 - 08/03/2014
Corno, J.; de Falco, C.; De Gersem, H.; Schöps, S.
Isogeometric Simulation of Lorentz Detuning in Superconducting Accelerator Cavities | Abstract | | Cavities in linear accelerators suffer from eigenfrequency shifts due to mechanical de- formation caused by the electromagnetic radiation pressure, a phenomenon known as Lorentz detuning. Estimating the frequency shift up to the needed accuracy by means of standard Finite Element Methods, is a very complex task due to the poor representation of the geometry and to the necessity for mesh refinement due to the typical use of low order basis functions. In this paper, we use Isogeometric Analysis for discretising both mechanical deformations and electromagnetic fields in a coupled multiphysics simulation approach. The combined high-order approximation of both leads to high accuracies at a substantially lower computational cost. |
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30/2014 - 07/23/2014
Ferroni, A.; Formaggia, L.; Fumagalli, A.;
Numerical analysis of Darcy problem on surfaces | Abstract | | Surface problems play a key role in several theoretical and applied fields. In this work the main focus is the presentation of a detailed analysis of the approximation of the classical flow porous media problem: the Darcy equation, where the domain is a regular surface. The formulation require the mixed form and the numerical approximation consider the classical pair of finite element spaces: piecewise constant for the scalar fields and Raviart-Thomas for vector fields, both written on the tangential space of the surface. The main result is the proof of the order of convergence where the discretization error, due to the finite element approximation, is coupled with a geometrical error. The latter takes into account the approximation of the real surface with a discretized one. Several examples are presented to show the correctness of the analysis, including surfaces without boundary. |
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29/2014 - 07/22/2014
Arioli, G.; Koch, H.
Some symmetric boundary value problems and non-symmetric solutions | Abstract | | We consider the equation −∆u = wf′(u) on a symmetric bounded domain in Rn with Dirichlet boundary conditions. Here w is a positive function or measure that is invariant under the (Euclidean) symmetries of the domain. We focus on solutions u that are positive and/or have a low Morse index. Our results are concerned with the existence of non-symmetric solutions and the non-existence of symmetric solutions. In particular, we construct a solution u for the disk in R2 that has index 2 and whose modulus |u| has only one reflection symmetry. |
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28/2014 - 07/13/2014
Antonietti, P; Panfili, P.; Scotti, A.; Turconi, L. ; Verani, M.; Cominelli,A.; Formaggia,L.
Optimal techniques to simulate flow in fractured reservoirs | Abstract | | Simulation of multiphase flow in fractured reservoir is a computational challenge. A key issue is the effective coupling between flow in the porous matrix and in the fracture network. It requires computational grids honouring as much as possible the fracture geometry without degenerated/distorted elements. Standard techniques may degrade efficiency and are not a foolproof solution. Moreover, two point flux approximation (TPFA) demands a good quality of the mesh to mitigate discretization error. In this work compare two different approaches. The first one has been proposed by B.T Mallison et al. in 2010. The second method we consider is the one originally proposed by H. Mustapha, in 2009. We evaluate the two techniques by means of 2D synthetic problems based on realistic discrete fracture networks. Steady state and unsteady state simulations are performed using TPFA. We also present results obtained with computational methods based on coupling the fracture network with mimetic finite differences or extended mixed finite elements. The latter two approaches, even though more complex, are more robust with respect to mesh geometry and can be beneficial for the problem at hand. |
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27/2014 - 07/12/2014
Vergara, C; Domanin, M; Guerciotti, B; Lancellotti, R.M.; Azzimonti, L; Forzenigo, L; Pozzoli, M.
Computational comparison of fluid-dynamics in carotids before and after endarterectomy | Abstract | | In this work we provide a computational comparison between the fluid-dynamics before and after carotid endarterectomy (CEA) to assess to influence of this surgical operation on some hemodynamic indices related to the plaque rupture. We perform the numerical simulations in real geometries of the same patients before and after CEA, and with patient-specific boundary data obtained by Echo-color Doppler measurements. The results show a reduction at the systole of the maximum wall shear stress by at least 83%, of the peak velocity by at least 56%, of the vorticity at the internal carotid by at least 57%, and of the pressure gradient across the plaque by at least 83%. Finally, we performed a comparison among measures acquired in internal points and related computed values, highlighting a satisfactory agreement (in any case less than 10%). |
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26/2014 - 07/03/2014
Discacciati, M.; Gervasio, P.; Quarteroni, A.
Interface Control Domain Decomposition (ICDD) Methods for Heterogeneous Problems | Abstract | | This paper is concerned with the solution of heterogeneous problems by the ICDD (Interface Control Domain Decomposition) method, a strategy introduced for the solution of partial differential equations (PDEs) in computational domains partitioned into subdomains that overlap. After reformulating the original boundary value problem by introducing new additional control variables, the unknown traces of the solution at internal subdomain interfaces, the latter are determined by requiring that the (a-priori) independent solutions in each subdomain undergo the minimization of a suitable cost functional. We provide an abstract formulation for coupled heterogeneous problems and a general theorem of wellposedness for the associated ICDD problem. Then, we illustrate and validate an efficient algorithm based on the solution of the Schur-complement system restricted solely to the interface control variables by considering two kinds of heterogeneous boundary value problems: the coupling between pure advection and advection-diffusion equations, and the coupling between Stokes and Darcy equations. In the latter case we also compare the ICDD method with a classical approach based on the Beavers-Joseph-Saffman conditions. |
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