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 1349 products
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43/2011 - 12/09/2011
L. Formaggia, A. Quarteroni, C. Vergara
On the physical consistency of the coupling between three-dimensional compliant and one-dimensional problems in haemodynamics | Abstract | | In this work we discuss the reliability of the coupling among three-dimensional (3D)
and one-dimensional (1D) models, that describe blood flowing into the circulatory tree.
In particular, we study the physical consistency of the 1D model with respect to the
3D one. To this aim, we introduce a general criterion based on energy balance for the
proper choice of coupling conditions between models. We also propose a way to include
in the 1D model the effect of the external tissue surrounding the vessel and we discuss
its importance whenever this effect is considered in the 3D model. Finally, we propose
several numerical results in real human carotids, studying different configurations for
the 1D model and highlighting the best one in view of the physical consistency. |
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42/2011 - 11/27/2011
Antonietti, P.F.; Quarteroni, A.
Numerical performance of discontinuous and stabilized continuous Galerkin methods or convection-diffusion problems | Abstract | | We compare the performance of two classes of numerical methods for the approximation of linear steady-state convection-diffusion equations, namely, the discontinuous Galerkin (DG) method and the continuous streamline upwind Petrov-Galerkin (SUPG) method. We present a fair comparison of such schemes considering both diffusion--dominated and convection-dominated regimes, and present numerical results obtained on a series of test problems including smooth solutions, and test cases with sharp internal and boundary layers. |
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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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