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 1249 products
-
53/2014 - 11/13/2014
Ieva, F.; Paganoni, A.M., Pietrabissa, T.
Dynamic clustering of hazard functions: an application to disease progression in chronic heart failure | Abstract | | We analyse data collected from the administrative datawarehouse of an Italian regional district (Lombardia) concerning patients affected by Chronic Heart Failure. The longitudinal data gathering for each patient hospital readmissions in time, as well as patient-specific covariates, is studied as a realization of non homogeneous Poisson process. Since the aim behind this study is to identify groups of patients behaving similarly in terms of disease progression (and then healthcare consumption), we conjectured the time segments between two consecutive hospitalizations to be Weibull distributed in each hidden cluster. Therefore, the comprehensive distribution for each time to event variable is modelled as a Weibull Mixture. We are then able to easily interpret the related hidden groups as healthy, sick, and terminally ill subjects. Adding a frailty term to take into account the unknown variability of each subject, the corresponding patient-specific hazard functions are reconstructed. |
-
52/2014 - 11/12/2014
Dede', L..; Quarteroni, A.; S. Zhu, S.
Isogeometric analysis and proper orthogonal decomposition for parabolic problems | Abstract | | We investigate the combination of Isogeometric Analysis (IGA) and proper orthogonal decomposition (POD) based on the Galerkin method for model order reduction of linear parabolic partial differential equations. For the proposed fully discrete scheme, the associated numerical error features three components due to spatial discretization by IGA, time discertization with the ?-scheme, and eigenvalue truncation by POD. First, we prove a priori error estimates of the spatial IGA semi-discrete scheme. Then, we show stability and prove a priori error estimates of the space-time discrete scheme and the fully discrete IGA-? -POD Galerkin scheme. Numerical tests are provided to show efficiency and accuracy of NURBS-based IGA for model order reduction in comparison with standard finite element-based POD techniques. |
-
51/2014 - 11/11/2014
Dassi, F.; Perotto, S.; Formaggia, L.
A priori anisotropic mesh adaptation on implicitly defined surfaces | Abstract | | Mesh adaptation on surfaces demands particular care due to the important role played by the fitting of the surface. We propose an adaptive procedure based on a new error analysis which combines a rigorous anisotropic estimator for the L1 -norm of the interpolation error with an anisotropic and more heuristic control of the geometric error. We resort to a metric-based adaptive algorithm which employs local operations to modify the initial mesh according to the information provided by the error analysis. An extensive numerical validation corroborates the robustness of the error analysis as well as of the adaptive procedure.
|
-
50/2014 - 11/10/2014
Bartezzaghi, A.; Cremonesi, M.; Parolini, N.; Perego, U.
An explicit dynamics GPU structural solver for thin shell finite elements | Abstract | | With the availability of user oriented software tools, dedicated architectures, such as NVIDIA CUDA (Compute Unified Device Architecture), and of improved, highly performing GPU boards, GPGPU (General Purpose programming on GPU) is attracting increasing interest in the engineering community, for the development of analysis tools suitable to be used in validation/verification and virtual reality applications. For their inherent explicit and decoupled structure, explicit dynamics finite element formulations appear to be particularly attractive for implementations on hybrid CPU/GPU or pure GPU architectures. The issue of an optimized, double-precision finite element GPU implementation of an explicit dynamics finite element solver for elastic shell problems in small strains and large displacements and rotation, using unstructured meshes, is here addressed. The conceptual difference between a GPU implementation directly adapted from a standard CPU approach and a new optimized formulation, specifically conceived for GPUs, is discussed and comparatively assessed. It is shown that a speedup factor of about 5 can be achieved by an optimized algorithm reformulation and careful memory management. A speedup of more than 40 is achieved with respect of state-of-the art commercial codes running on CPU, obtaining real-time simulations in some cases,on commodity hardware. When a last generation GPU board is used, it is shown that a problem with more than 16 millions degrees of freedom can be solved in just few hours of computing time, opening the way to virtualization approaches for real large scale engineering problems. Keywords: GPU, explicit dynamics, double-precision, shell finite elements.
|
-
49/2014 - 11/07/2014
Bonomi, D.; Vergara, C.; Faggiano, E.; Stevanella, M.; Conti, C.; Redaelli, A.; Puppini, G.; Faggian, G.; Formaggia, L.; Luciani, G.B.
Influence of the aortic valve leaflets on the fluid-dynamics in aorta in presence of a normally functioning bicuspid valve | Abstract | | In this work we consider the blood fluid-dynamics in the ascending aorta in presence of a normally functioning bicuspid aortic valve (BAV). In particular, we perform a computational study to assess the effect of the inclusion of the leaflets on the fluid-dynamic abnormalities characterizing BAV cases. Indeed, in previous works it has been shown that without leaflets it is possible to recover such abnormalities, in particular the strong systolic jet asymmetry, but it was not clear how the inclusion of the leaflets would have improve the results. To this aim we perform a comparison in two real geometries (a dilated and a non-dilated ones) among three scenarios which are built up for each geometry: BAV without leaflets, BAV with leaflets, and tricuspid case (TAV) with leaflets. Our results show that the inclusion of the leaflets increases the fluid-dynamics abnormalities which are quantified through the introduction of suitable synthetic indices. |
-
48/2014 - 10/27/2014
Penta, R; Ambrosi, D; Shipley, R.
Effective governing equations for poroelastic growing media | Abstract | | A new mathematical model is developed for the macroscopic behaviour of a porous, linear elastic solid, saturated with a slowly flowing incompressible, viscous fluid, with surface accretion of the solid phase. The derivation uses a formal two-scale asymptotic expansion to exploit the well-separated length scales of the material: the pores are small compared to the macroscale, with a spatially-periodic microstructure. Surface accretion occurs at the interface between the solid and fluid phases, resulting in growth of the solid phase through mass exchange from the fluid at a prescribed rate (and viceversa). The averaging derives a new poroelastic model, which reduces to the classical result of Burridge and Keller in the limit of no growth. The new model is of relevance to a large range of applications including packed snow, tissue growth, biofilms and subsurface rocks or soils. |
-
47/2014 - 10/26/2014
Penta, R; Ambrosi, D; Quarteroni, A.
Multiscale homogenization for fluid and drug transport in vascularized malignant tissues | Abstract | | A system of differential equations for coupled fluid and drug transport in vascularized (malignant) tissues is derived by a multiscale expansion. We start from mass and momentum balance equations, stated in the physical domain, geometrically characterized by the intercapillary distance (the microscale). The Kedem-Katchalsky equations are used to account for blood and drug exchange across the capillary walls. The multiscale technique (homogenization) is used to formulate continuum equations describing the coupling of fluid and drug transport on the tumor length scale (the macroscale), under the assumption of local periodicity; macroscale variations of the microstructure account for spatial heterogeneities of the angiogenic capillary network. A double porous medium model for the uid dynamics in the tumor is obtained, where the drug dynamics is represented by a double advection-diffusion-reaction model. The homogenized equations are straightforward to approximate, as the role of the vascular geometry is recovered at an average level by solving standard cell differential problems. Fluid and drug fluxes now read as effective mass sources in the macroscale model, which upscale the interplay between blood and drug dynamics on the tissue scale. We aim to provide a theoretical setting for a better understanding of the design of effective anti-cancer therapies. |
-
46/2014 - 10/25/2014
Penta, R; Ambrosi, D.
The role of the microvascular tortuosity in tumor transport phenomena | Abstract | | The role of the microvascular network geometry on transport phenomena in solid tumors and its interplay with the leakage and pressure drop across the vessels is qualitatively and quantitatively discussed. Our starting point is a multiscale homogenization, suggested by the sharp length scale separation that exists between the characteristic vessels and tumor tissue spatial scales, referred to as the microscale and the macroscale, respectively. The coupling between interstitial and capillary compartment is described by a double Darcy model on the macroscale, whereas the geometric information on the microvascular structure is encoded in the effective hydraulic conductivities, which are numerically computed solving classical differential problems on the microscale representative cell. Then, microscale information is injected into the macroscopic model, which is analytically solved in a prototypical geometry and compared with previous experimentally validated, phenomenological models. In this way, we are able to capture the role of the standard blood flow determinants in the tumor, such as the tumor radius, tissue hydraulic conductivity and vessels permeability, as well as the influence of the vascular tortuosity on fluid convection. The results quantitatively confirm that transport of blood (and, as a consequence, of any advected anti-cancer drug) can be dramatically impaired by increasing the geometrical complexity of the microvasculature. Hence, our quantitative analysis supports the argument that geometric regularization of the capillary network improve blood transport and drug delivery in the tumor mass. |
|
