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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53/2016 - 12/07/2016
Antonietti, P. F.; Manzini, G.; Verani, M.
The fully nonconforming Virtual Element method for biharmonic problems | Abstract | | In this paper we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbi- trary order of accuracy for biharmonic problems. The approximation space is made of possibly discontinuous functions, thus giving rise to the fully nonconforming virtual element method. We derive optimal error estimates in a suitable (broken) energy norm and present numer- ical results to assess the validity of the theoretical estimates. |
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52/2016 - 12/07/2016
Paolucci, R.; Evangelista, L.; Mazzieri, I.; Schiappapietra, E.
The 3D Numerical Simulation of Near-Source Ground Motion during the Marsica Earthquake, Central Italy, 100 years later | Abstract | | In this paper we show 3D physics-based numerical simulations of ground motion during one of the most devastating earthquakes in the recent Italian history, occurred on Jan 13, 1915, Marsica, Central Italy. The results provide a realistic estimate of the earthquake ground motion and fit reasonably well both the geodetic measurements of permanent ground settlement, and the observed macroseismic distribution of damage. In addition, these results provide a very useful benchmark to improve the current knowledge of near-source earthquake ground motion, including evaluation of the best distance metrics to describe the spatial variability of the peak values of ground motion, the relative importance of fault normal vs fault parallel components, the conditions under which vertical ground motion may prevail, as well as the adequacy of 1D vs 3D modelling of site amplification effects. |
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51/2016 - 12/04/2016
Guzzetti, S.; Perotto, S.; Veneziani, A.
Hierarchical Model Reduction for Incompressible Flows in Cylindrical Domains: The Axisymmetric Case | Abstract | | Hierarchical Model (HiMod) Reduction provides an efficient way to solve Partial Differential Equations in domains with a geometrically dominant direction, like slabs or pipes. The associated solution is regarded as the combination of mainstream dynamics driven by the geometry and trans- verse components. The latter are generally of secondary importance so to be described by few degrees of freedom of a spectral approximation in- troduced at the top of a finite element discretization of the mainstream. Thus, the 3D nature of the problem is broken into a basically 1D descrip- tion added by transverse details. The versatility of this approach is that the accuracy of the method can be adaptively refined when needed, by judi- ciously selecting the number of transverse modes - as opposed to purely 1D models popular in computational hemodynamics and gasdynamics. After having investigated the basic features of the method in slab-like domains - where the Cartesian tensor product framework facilitates the practical implementation, in this paper we consider cylindrical pipes with polar co- ordinates. The selection of a different coordinate system rises several issues in particular for the most appropriate selection of the modal basis func- tions. Having computational hemodynamics as reference application, we address here the HiMod approximation of Advection-Diffusion-Reaction as well as Incompressible Navier-Stokes equations in axisymmetric domains. |
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50/2016 - 11/23/2016
Ambrosi, D.; Pezzuto, S.; Riccobelli, D.; Stylianopoulos, T.; Ciarletta, P.
Solid tumors are poroelastic solids with a chemo--mechanical feedback on growth | Abstract | | The experimental evidence that a feedback exists between growth and stress in tumors poses challenging questions. First, the rheological properties
(the ``constitutive equations'') of aggregates of malignant cells are still a matter of debate. Secondly, the feedback law (the ``growth law'') that relates stress and mitotic--apoptotic rate is far to be identified.
We address these questions on the basis of a theoretical analysis of in vitro and in vivo experiments that involve the growth of tumor spheroids. We show that solid tumors exhibit several mechanical features of a poroelastic material, where the cellular component behaves like an elastic solid. When the solid component of the spheroid is loaded at the boundary, the cellular aggregate grows up to an asymptotic volume that depends on the exerted compression. Residual stress shows up when solid tumors are radially cut, highlighting a peculiar tensional pattern. By a novel numerical approach we correlate the measured opening angle and the underlying residual stress in a sphere. The features of the mechanobiological system can be explained in terms of a feedback of mechanics on the cell proliferation rate as modulated by the availability of nutrient, that is radially damped by the balance between diffusion and consumption. The volumetric growth profiles and the pattern of residual stress can be theoretically reproduced assuming a dependence of the target stress on the concentration of nutrient which is specific of the malignant tissue.
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49/2016 - 11/23/2016
Formaggia, L.; Scotti, A.; Sottocasa, F.
ANALYSIS OF A MIMETIC FINITE DIFFERENCE APPROXIMATION OF FLOWS IN FRACTURED POROUS MEDIA | Abstract | | We consider the mixed formulation for Darcy’s flow in fractured media. We give a well-posedness result that does not rely on the imposition of pressure in part of the boundary of the fracture network, thus including a fully immersed fracture network. We present and analyze a mimetic finite difference formulation for the problem, providing convergence results and numerical tests. |
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48/2016 - 11/23/2016
Scardulla, S.; Pasta, S.; D’Acquisto, L.; Sciacca, S.; Agnese, V.; Vergara, C.; Quarteroni, A.; Clemenza, F.; Bellavia, D.; Pilato, M.
Shear Stress Alterations in the Celiac Trunk of Patients with Continuous-Flow Left Ventricular Assist Device by In-Silico and In-Vitro Flow Analysis | Abstract | | Background: The use of left ventricular assist device (LVAD) to treat advanced cardiac heart failure is constantly increasing, although this device leads to high risk for gastrointestinal.
Methods: Using in-silico flow analysis, we quantified hemodynamic alterations due to continuous-flow LVAD (HeartWare Inc, Framingham, MA, USA) in the celiac trunk and major branches of the abdominal aorta and then explored the relationship between wall shear stress (WSS) and celiac trunk orientation. To assess outflow from aortic branch, a 3D printed patient-specific model of the celiac trunk reconstructed from a LVAD-supported patient was used to estimate echocardiographic outflow velocities under continuous-flow conditions and then to calibrate computational simulations. Moreover, flow pattern and resulting WSS were computed on 5 patients with LVAD implantation.
Results: Peak WSSs were estimated on the three branches of celiac trunk and the LVAD cannula. Mean values of WSS demonstrated that the left gastric artery experiences the greatest WSS of 9.08±5.45 Pa with an average flow velocity of 0.57±0.25 m/s when compared to that of other vessel districts. The common hepatic artery had the less critical WSS of 4.58±1.77 Pa. A positive correlation was found between the celiac trunk angulation and the WSS stress just distal the ostium of celiac trunk (R=0.9), and this may increase to vulnerability of this vessel to bleeding.
Conclusions: Although further studies are warranted to confirm these findings in a larger patient cohort, computational flow simulations may enhance the information of clinical image data and may have an application in clinical investigations of hemodynamic changes in LVAD-supported patients. |
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47/2016 - 11/17/2016
Canuto, C.; Nochetto, R. H.; Stevenson R.; Verani, M.
On p-Robust Saturation for hp-AFEM | Abstract | | For the Poisson problem in two dimensions,
we consider the standard adaptive finite element loop solve, estimate, mark, refine, with
estimate being implemented using the $p$-robust equilibrated flux estimator, and, mark being Dorfler marking.
As a refinement strategy we employ $p$-refinement. We investigate the question by which amount the local polynomial degree on any marked patch has to be increase in order to achieve a p-independent error reduction.
The resulting adaptive method can be turned into an instance optimal $hp$-adaptive method by the addition of a coarsening routine. |
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46/2016 - 11/17/2016
Lila, E.; Aston, J.A.D.; Sangalli, L.M.
Smooth Principal Component Analysis over two-dimensional manifolds with an application to Neuroimaging | Abstract | | Motivated by the analysis of high-dimensional neuroimaging signals located over the cortical surface, we introduce a novel Principal Component Analysis technique that can handle functional data located over a two-dimensional manifold. For this purpose a regularization approach is adopted, introducing a smoothing penalty coherent with the geodesic distance over the manifold. The model introduced can be applied to any manifold topology, can naturally handle missing data and functional
samples evaluated in different grids of points. We approach the discretization task by means of finite element analysis and propose an efficient iterative algorithm for its resolution. We compare the performances of the proposed algorithm with other approaches classically adopted in literature. We finally apply the proposed method to resting state functional magnetic resonance imaging data from the Human Connectome
Project, where the method shows substantial differential variations between
brain regions that were not apparent with other approaches. |
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