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 1238 products
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20/2015 - 04/16/2015
Antonietti, P.F.; Formaggia, L.; Scotti, A.; Verani, M.; Verzotti, N.
Mimetic finite difference approximation of flows in fractured porous media | Abstract | | We present a possible framework for the numerical simulation of flow in fractured porous media that couples mimetic finite differences for the porous matrix with a finite volume scheme for the flow in the fractures. The resulting method is theoretically analyzed in the case of a single fracture. Moreover, several numerical experiments show the capability of the method to deal also with complicated networks of fractures. Thanks to the implementation of rather general coupling conditions, it encompasses both "conductive fractures", i.e., fractures with high permeability and "sealed fractures", i.e., fractures with low permeability which act as a flow barrier. |
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19/2015 - 04/11/2015
Palamara, S.; Lange, M.; Vergara, C.; Lassila, T.; Frangi, A.F.; Quarteroni, A.
A coupled 3D-1D numerical monodomain solver for cardiac electrical activation in the myocardium with detailed Purkinje network | Abstract | | We present a model for the electrophysiology in the heart to handle the
electrical propagation through the Purkinje system and in the myocardium,
with two-way coupling at the Purkinje-muscle junctions. In both the subproblems
the monodomain model is considered, whereas at the junctions a
resistor element is included that induces an orthodromic propagation delay
from the Purkinje network towards the heart muscle. We prove a sufficient
condition for convergence of a fixed-point iterative algorithm to the
numerical solution of the coupled problem. Numerical comparison of activation
patterns are made with two different combinations of models for
the coupled Purkinje network/myocardium system, the eikonal/eikonal and
the monodomain/monodomain models. Test cases are investigated for both
physiological and pathological activation of a model left ventricle. Finally,
we prove the reliability of the monodomain/monodimain coupling on a real
scenario. Our results underlie the importance of using physiologically realistic
Purkinje-trees with propagation solved using the monodomain model
for simulating cardiac activation |
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18/2015 - 04/09/2015
Masci, C,; Ieva, F.; Agasisti, T.; Paganoni, A.M.
Bivariate multilevel models for the analysis of mathematics and reading pupils' achievements | Abstract | | The purpose of this paper is to identify a relationship between pupils' mathematics and reading test scores and the characteristics of students themselves, stratifying for classes, schools and geographical areas. The dataset of interest contains detailed information about more than 500,000 students at the first year of junior secondary school in the year 2012/2013, provided by the Italian Institute for the Evaluation of Educational System (INVALSI). The innovation of this work is in the use of multivariate models, in which the outcome variable is bivariate: reading and mathematics achievements. Using the bivariate outcome enables researchers to analyze the correlations between achievement levels in the two fields and to estimate statistically significant school and class effects after adjusting for pupil's characteristics. The statistical model employed here explicates account for the potential covariance between the two topics, and at the same time it allows the school effect to vary among them. The results show that while for most cases the direction of school's effect is coherent for reading and mathematics (i.e. positive/negative), there are cases where internal school factors lead to differential performances in the two fields. |
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17/2015 - 04/09/2015
Nestola, M.G.C.; Faggiano, E.; Vergara, C.; Lancellotti, R.M.; Ippolito, S,; Filippi, S.; Quarteroni
Computational comparison of aortic root stresses in presence of stentless and stented aortic valve bio-prostheses | Abstract | | We provide a computational comparison of the performance of stentless and
stented aortic prostheses, in terms of aortic root displacements and internal
stresses. To this aim, we consider three real patients; for each of them
we draw the two prostheses configurations, which are characterized by different
mechanical properties. Moreover, for each patient, we consider also
the healthy configuration. For each scenario, we solve the fluid-structure
interaction problem arising between blood and aortic root, through Finite
Elements. The results show a better agreement between stentless and
healthy displacements and stresses, with respect to the stented case. |
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16/2015 - 03/31/2015
Fumagalli, I.; Manzoni, A.; Parolini, N.; Verani, M.
Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems | Abstract | | We develop a new reduced basis (RB) method for the rapid and reliable approximation of parametrized elliptic eigenvalue problems. The method hinges upon dual weighted residual type a posteriori error indicators which estimate, for any value of the parameters, the error between the high-fidelity finite element approximation of the first eigenpair and the corresponding reduced basis approximation. The proposed error estimators are exploited not only to certify the RB approximation with respect to the high-fidelity one, but also to set up a greedy algorithm for the offline construction of a reduced basis space. Several numerical experiments show the overall validity of the proposed RB approach. |
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15/2015 - 03/26/2015
Taffetani, M.; de Falco, C.; Penta, R.; Ambrosi, D.; Ciarletta, P.
Biomechanical modelling in nanomedicine: multiscale approaches and future challenges | Abstract | | Nanomedicine is the branch of nanotechnology devoted to the miniaturization of devices and to the functionalization of processes for the diagnosis and the design of tools of clinical use. In the perspective to develop patient-specific treatments and effective therapies against currently incurable diseases, biomechanical modelling plays a key role in enabling their translation to clinical practice. Establishing a dynamic interaction with experiments, a modelling approach is expected to allow investigating problems with lower economic burden, evaluating a larger range of conditions. Since biological systems have a wide range of typical characteristic length and timescales, a multiscale modelling approach is necessary both for providing a proper description of the biological complexity at the single scales and for keeping the largest amount of functional interdependence among them. This work starts with a survey both of the common frameworks for modelling a biological system, at scales from atoms to a continuous distribution of matter, and of the available multiscale methods that link the different levels of investigation. In the following, we define an original approach for dealing with the specific case of transport and diffusion of nanoparticles and/or drug-delivery carriers from the systemic circulation to a target tissue microstructure. Using a macro–micro viewpoint, we discuss the existing multiscale approaches and we propose few original strategies for overcoming their limitations in bridging scales. In conclusion, we highlight and critically discuss the future challenges of multiscale modelling for achieving the long-term objective to assist the nanomedical research in proposing more accurate clinical approaches for improved medical benefit. |
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14/2015 - 03/18/2015
Canuto, C.; Nochetto, R.H.; Stevenson R,; Verani, M.
Convergence and Optimality of hp-AFEM | Abstract | | We design and analyze an adaptive hp-finite element method
(hp-AFEM) in dimensions $n=1,2$.
The algorithm consists of iterating two routines:
HP-NEARBEST finds a near-best hp-approximation of the current
discrete solution and data to a desired accuracy, and
REDUCE improves the discrete solution to a finer but comparable accuracy.
The former hinges on a recent algorithm by Binev for adaptive
hp-approximation, and acts as a coarsening step. We prove
convergence and instance optimality.
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13/2015 - 03/17/2015
Bartezzaghi, A.; Dedè, L.; Quarteroni, A.;
Isogeometric Analysis of High Order Partial Differential Equations on Surfaces | Abstract | | We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-splines or NURBS, as for example the sphere, and we spatially discretize the PDEs by means of NURBS based Isogeometric Analysis in the framework of the standard Galerkin method. We numerically solve benchmark Laplace-Beltrami problems of the fourth and sixth order, as well as the corresponding eigenvalue problems, with the goal of analyzing the role of the continuity of the NURBS basis functions on closed surfaces. In this respect, we show that the use of globally high order continuous basis functions, as allowed by the construction of periodic NURBS, leads to the efficient solution of the high order PDEs. Finally, we consider the numerical solution of high order phase field problems on closed surfaces, namely the Cahn-Hilliard and crystal equations.
Key words. High order Partial Dierential Equations; Surfaces; Isogeometric Analysis; Error estimation; Laplace-Beltrami operators; Phase field models. |
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