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 1275 products
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40/2011 - 11/23/2011
D Angelo, C.; Zunino, P.; Porpora, A.; Morlacchi, S.; Migliavacca, F.
Model reduction strategies enable computational analysis of controlled drug release from cardiovascular stents | Abstract | | Medicated cardiovascular stents, also called drug eluting stents (DES) represent a relevant application of controlled drug release mechanisms. Modeling of drug release from DES also represents a challenging problem for theoretical and computational analysis. In particular, the study of drug release may require to address models with singular behavior, arising for instance in the analysis of drug release in the small diffusion regime. Moreover, the application to realistic stent configurations requires to account for complex designs of the device. To efficiently obtain satisfactory simulations of DES we rely on a multiscale strategy, involving lumped parameter models (0D) to account for drug release, one dimensional models (1D) to efficiently handle complex stent patterns and fully three-dimensional models (3D) for drug transfer in the artery, including the lumen and the arterial wall. The application of these advanced mathematical models makes it possible to perform a computational analysis of the fluid dynamics and drug release for a medicated stent implanted into a coronary bifurcation, a treatment where clinical complications still have to be fully understood. |
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41/2011 - 11/23/2011
Burman, E.; Zunino, P.;
Numerical Approximation of Large Contrast Problems with the Unfitted Nitsche Method | Abstract | | These notes are concerned with the numerical treatment of the coupling between second order elliptic problems that feature large contrast between their characteristic coefficients. In particular, we study the application of Nitsche s method to set up a robust approximation of interface conditions in the framework of the finite element method. The notes are subdivided in three parts. Firstly, we review the weak enforcement of Dirichlet boundary conditions with particular attention to Nitsche s method and we discuss the extension of such technique to the coupling of Poisson equations. Secondly, we review the application of Nitsche s method to large contrast problems, discretised on computational meshes that capture the interface of discontinuity between coefficients. Finally, we extend the previous schemes to the case of unfitted meshes, which occurs when the computational mesh does not conform with the interface between subproblems. |
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39/2011 - 11/20/2011
Antonietti, P.F.; Ayuso de Dios, B.; Brenner, S.C.; Sung, L.-Y.
Schwarz methods for a preconditioned WOPSIP method for elliptic problems | Abstract | | We construct and analyze non-overlapping Schwarz methods for a preconditioned weakly over-penalized symmetric interior penalty (WOPSIP) method for elliptic problems. |
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38/2011 - 11/14/2011
Porpora A., Zunino P., Vergara C., Piccinelli M.
Numerical treatment of boundary conditions to replace lateral branches in haemodynamics | Abstract | | In this paper, we discuss a technique for weakly enforcing
ow rate
conditions in computational hemodynamics. In particular, we study the
e ectiveness of cutting lateral branches from the computational domain
and replacing them with non perturbing boundary conditions, in order
to simplify the geometrical reconstruction and the numerical simulation.
All these features are investigated both in the case of a rigid and of a
compliant wall. Several numerical results are presented in order to discuss
the reliability of the proposed method. |
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37/2011 - 11/10/2011
Ieva, F.; Paganoni, A.M.
Depth Measures For Multivariate Functional Data | Abstract | | The statistical analysis of functional data is a growing interest research area. In particular more and more frequently in the biomedical context the output of many clinical examinations are complex mathematical objects like images or curves. In this work we propose, analyze, and apply a new concept of depth for multivariate functional observations, i.e. statistical units where each component is a curve, in order to study them from a statistical perspective.
Robust statistics, such as the median function or trimmed mean, can be generalized to a multivariate functional framework using this new depth measure definition so that outliers detection and nonparametric tests can be carried out also within this more complex context. Mathematical properties of these new concepts are established and proved. Finally, an application to Electrocardiographic (ECG) signals is proposed, aimed at detecting outliers for identifying stable training set to be used in unsupervised classification procedures adopted to perform semi automatic diagnosis and at testing differences between pathological and physiological groups of patients. |
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36/2011 - 11/07/2011
Motamed, M.; Nobile, F.; Tempone, R.
A stochastic collocation method for the second order wave equation with a discontinuous random speed | Abstract | | In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We provide a rigorous convergence analysis and demonstrate different types of convergence of the Òprobability errorÓ with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems, the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence may only be algebraic. An exponential/fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data. We present numerical examples, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo method for this class of problems.
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35/2011 - 08/25/2011
Iapichino, L.; Quarteroni, A.; Rozza, G.
A Reduced Basis Hybrid Method for the coupling of parametrized domains represented by fluidic networks | Abstract | | In this paper we propose a reduced basis hybrid method (RBHM) for the approximation of partial differential equations in domains represented by complex networks where topological features are recurrent.
The RBHM is applied to Stokes equations in domains which are decomposable into smaller similar blocks that are properly coupled.
The RBHM is built upon the reduced basis element method (RBEM) and it takes advantage from both the reduced basis methods (RB) and the domain decomposition method. We move from the consideration that the blocks composing the computational domain are topologically similar to a few reference shapes. On the latter, representative solutions, corresponding to the same governing partial differential equations, are computed for different values of some parameters of interest, representing, for example, the deformation of the blocks. A generalized transfinite mapping is used in order to produce a global map from the reference shapes of each block to any deformed configuration.
The desired solution on the given original computational domain is recovered as projection of the previously precomputed solutions and then glued across sub-domain interfaces by suitable coupling conditions.
The geometrical parametrization of the domain, by transfinite mapping, induces non-affine parameter dependence: an empirical interpolation technique is used to recover an approximate affine parameter dependence and a sub--sequent offline/online decomposition of the reduced basis procedure. This computational decomposition yields a considerable reduction of the problem complexity. Results computed on some combinations of 2D and 3D geometries representing cardiovascular networks show the advantage of the method in terms of reduced computational costs and the quality of the coupling to guarantee continuity of both stresses, pressure and velocity at sub-domain interfaces. |
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34/2011 - 07/27/2011
Benacchio, T.; Bonaventura, L.
A spectral collocation method for the one dimensional shallow water equations on semi-infinite domains | Abstract | | We introduce a spectral collocation method for the discretization of the shallow water
equations on a one dimensional semi-infinite domain, employing suitably rescaled Laguerre basis functions to obtain an accurate description of the solutions on finite regions of arbitrary size. The time discretization is based on
a semi-implicit, semi-Lagrangian approach that allows to handle the highly inhomogeneous node distribution without loss of efficiency.
The method is first validated on standard test cases and then applied to the implementation of absorbing open boundary conditions by coupling the semi-infinite domain to a finite size domain on which the same equations are discretized by standard finite volume methods. Numerical experiments show that the proposed approach does not produce significant spurious reflections at the interface between the finite and infinite domain, thus providing a reliable tool for absorbing boundary conditions.
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