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 1251 products
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10/2012 - 02/09/2012
Lassila, T.; Manzoni, A.; Quarteroni, A.; Rozza, G.
Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty | Abstract | | We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the the worst-case in terms of recirculation effects is inferred to correspond to a residual strong orifice flow through near-complete occlusion. Worst-case optimization is performed to identify an anastomosis angle and a cuffed shape that are robust with respect to a possible range of residual flows. We also consider a reduced order modelling framework based on reduced basis methods
in order to make the robust design problem computationally feasible. Keywords: optimal control, shape optimization, arterial bypass grafts, uncertainty, worst-case design, reduced order modelling, Navier-Stokes equations. |
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09/2012 - 01/30/2012
Mauri, L.; Perotto, S.; Veneziani, A.
Adaptive geometrical multiscale modeling for hydrodynamic problems | Abstract | | Hydrodynamic problems often feature geometrical configurations that allow a suitable dimensional model reduction. One-dimensional models may be
sometimes accurate enough for describing a dynamic of interest. In other cases, localized relevant phenomena require more precise models. To improve the computational efficiency, geometrical multiscale models have been proposed,
where reduced (1D) and complete (2D-3D) models are coupled in a unique numerical solver. In this paper we consider an adaptive geometrical multiscale modeling: the regions of the computational domain requiring more or less
accurate models are automatically and dynamically selected via a heuristic criterion. To the best of our knowledge, this is a first example of automatic geometrical multiscale model reduction. |
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08/2012 - 01/29/2012
Sangalli, L.M.; Ramsay, J.O.; Ramsay, T.O.
Spatial Spline Regression Models | Abstract | | We describe a model for the analysis of data distributed over irregularly shaped spatial domains with complex boundaries, strong concavities and interior holes. Adopting an approach typical of functional data analysis, we propose a Spatial Spline Regression model that is computationally efficient, allows for spatially distributed covariate information and can impose various conditions over the boundaries of the domain. Accurate surface estimation is achieved by the use of finite elements, which provide a basis for piecewise polynomial surfaces. |
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07/2012 - 01/28/2012
Perotto, S; Zilio, A.
Hierarchical model reduction: three different approaches | Abstract | | We present three different approaches to model, in a computationally cheap way, problems characterized by strong horizontal dynamics, even though
in the presence of transverse heterogeneities.
The three approaches move from the hierarchical model reduction setting introduced in S. Perotto, A. Ern, A. Veneziani 2010. |
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06/2012 - 01/27/2012
Micheletti, S.; Perotto, S.
Anisotropic recovery-based a posteriori error estimators for advection-diffusion-reaction problems | Abstract | | We combine the good properties of recovery-based error estimators with the richness of information typical of an anisotropic a posteriori analysis.
This merging yields error estimators which are general purpose yet simple and easy to implement, and automatically incorporate detailed geometric information about the computational mesh.
This allows us to devise an effective anisotropic mesh adaptation procedure suited to control the discretization error both in the energy norm and in a goal-oriented framework.
The advection-diffusion-reaction problem is considered as a computational paradigm.
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05/2012 - 01/21/2012
Ambrosi, D; Arioli, G; Koch, H.
A homoclinic solution for excitation waves on a contractile substratum | Abstract | | We analyze a model of electric signalling in biological tissues
and prove that this model admits a travelling wave solution.
Our result is based on a new technique for computing rigorous bounds on the stable and unstable manifolds at an equilibrium point of a dynamical system depending on a parameter. |
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04/2012 - 01/18/2012
Tumolo, G.; Bonaventura, L.; Restelli, M.
A semi-implicit, semi-Lagrangian, p-adaptive Discontinuous Galerkin method for the shallow water equations | Abstract | | A semi-implicit and semi-Lagrangian Discontinuous Galerkin (SISLDG) method for the shallow water equations is proposed, for applications to geophysical scale flows. A non conservative formulation of the advection equation is employed, in order to achieve a more treat- able form of the linear system to be solved at each time step. The method is equipped with a simple p−adaptivity criterion, that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution. Numerical results show that the method captures well the main features of gravity and inertial gravity waves, as well as reproducing correct solutions in nonlinear test cases with analytic solutions. The accuracy and effectiveness of the method are also demonstrated by numerical results obtained at high Courant numbers and with automatic choice of the local approximation degree. |
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03/2012 - 01/17/2012
Fumagalli, A.; Scotti, A.
A reduced model for flow and transport in fractured porous media with non-matching grids | Abstract | | In this work we focus on a model reduction approach for the treatment of fractures in a porous medium, represented as interfaces embedded in a n-dimensional domain, in the form of a (n- 1)-dimensional manifold, to describe fluid flow and transport in both domains. We employ a method that allows for non-matching grids, thus very advantageous if the position of the fractures is uncertain and multiple simulations are required. To this purpose we adopt an XFEM approach to
represent discontinuities of the variables at the interfaces, which can arbitrarily cut the elements of the grid. The method is applied to the numerical solution of the Darcy problem, and advection-diffusion problems in porous media. |
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