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 1253 products
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09/2014 - 02/12/2014
Chen, P.; Quarteroni, A.
A new algorithm for high-dimensional uncertainty quantification problems based on dimension-adaptive and reduced basis methods | Abstract | | In this work we develop an adaptive and reduced computational framework based on dimension-adaptive hierarchical approximation and reduced basis method for solving high-dimensional uncertainty quantification (UQ) problems. In order to tackle the computational challenge of curse-of-dimensionality commonly faced by these problems, we employ a dimension-adaptive tensor-product algorithm [29] and propose a verified version to enable effective removal of the stagnation phenomenon besides automatically detecting the importance and interaction of different dimensions. To reduce the heavy computational cost of UQ problems modelled by partial differential equations (PDEs), we adopt a weighted reduced basis method [18] and develop an adaptive greedy algorithm in combination of the previous verified algorithm for efficient construction of an accurate reduced basis approximation space. The effectivity, efficiency and accuracy of this computational framework are demonstrated and compared to several other existing techniques by a variety of classical numerical examples. Keywords: uncertainty quantification, curse-of-dimensionality, generalized sparse grid, hierarchical surpluses, reduced basis method, adaptive greedy algorithm, weighted a posteriori error bound
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08/2014 - 02/03/2014
Cattaneo, L; Zunino, P.
A computational model of drug delivery through microcirculation to compare different tumor treatments | Abstract | | Starting from the fundamental laws of filtration and transport in biological tissues, we develop a computational model to capture the interplay between blood perfusion, fluid exchange with the interstitial volume, mass transport in the capillary bed, through the capillary walls and into the surrounding tissue. These phenomena are accounted at the microscale level, where capillaries and interstitial volume are viewed as two separate regions. The capillaries are described as a network of vessels carrying blood flow. We apply the model to study drug delivery to tumors. The model can be adapted to compare various treatment options. In particular, we consider delivery using drug bolus injection and nanoparticle injection into the blood stream. The computational approach is prone to a systematic quantification of the treatment performance, enabling the analysis of interstitial drug concentration levels, metabolization rates and cell surviving fractions. Our study suggests that for the treatment based on bolus injection, the drug dose is not optimally delivered to the tumor interstitial volume. Using nanoparticles as intermediate drug carriers overrides the shortcomings of the previous delivery approach. The present work shows that the proposed theoretical and computational framework represents a promising tool to compare the efficacy of different cancer treatments. |
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07/2014 - 01/31/2014
Agasisti, T.; Ieva, F.; Paganoni, A.M.
Heterogeneity, school-effects and achievement gaps across Italian regions: further evidence from statistical modeling | Abstract | | Catching the differences in educational attainments between groups of students and across schools is becoming increasingly interesting. With the aim of assessing the extent of these differences in the context of Italian educational system, the paper applies multilevel modeling to a new administrative dataset, containing detailed information for more than 500,000 students at grade 6 in the year 2011/12, provided by the Italian Institute for the Evaluation of Educational System. The results show that the national averages hide considerable heterogeneity both within and between schools, and that it is possible to estimate statistically significant school effects , i.e. the positive/negative impact of attending a specific school on the student s test score, after a case-mix adjustment. Therefore, the paper s most important message is that school effects are different in terms of magnitude and types in the three geographical macro-areas (Northern, Central and Southern Italy) and are dependent upon specific students characteristics. |
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06/2014 - 01/28/2014
Benzi, M.; Deparis, S.; Grandperrin, G.; Quarteroni, A.
Parameter estimates for the relaxed dimensional factorization preconditioner and application to hemodynamics | Abstract | | We present new results on the Relaxed Dimensional Factorization (RDF) preconditioner for solving saddle point problems, first introduced in [5]. This method contains a parameter α > 0, to be chosen by the user. Previous works provided an estimate of α in the 2D case using Local Fourier Analysis. Novel algebraic estimation techniques for finding a suitable value of the RDF parameter in both the 2D and the 3D case with arbitrary geometries are proposed. These techniques are tested on a variety of discrete saddle point problems arising from the approximation of the Navier–Stokes equations using a Marker-and-Cell scheme and a finite element one. We also show results for a large-scale problem relevant for hemodynamics simulation that we solve in parallel using up to 8196 cores.
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05/2014 - 01/27/2014
Rozza, G.; Koshakji, A.; Quarteroni, A.
Free Form Deformation Techniques Applied to 3D Shape Optimization Problems | Abstract | | The purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametrization, a technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the FFD technique by establishing a path, from the geometry definition, to the method implementation, and finally to the simulation and to the optimization of the shape. In particular, we have studied a bulb and a rudder of a race sailing boat as model applications, where we have tested a complete procedure from Computer-Aided-Design to build the geometrical model to discretization and mesh generation. |
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04/2014 - 01/26/2014
Palamara, S.; Vergara, C.; Catanzariti, D.; Faggiano, E.; Centonze, M.; Pangrazzi, C.; Maines, M.; Quarteroni, A.
Patient-specific generation of the Purkinje network driven by clinical measurements: The case of pathological propagations | Abstract | | To describe the electrical activity of the left ventricle is necessary to take into account the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times acquired during pathological propagations. In particular, we consider clinical data acquired on four subjects suffering from pathologies with different origins, from conduction problems in the muscle or in the Purkinje fibers to a pre-excitation ventricular syndrome. To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network with the ones obtained by using a not patient-specific network. The results showed that the mean absolute errors are reduced by a factor in the range 27%-54%, highlighting the importance of including a patient-specific Purkinje network in computational models. |
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03/2014 - 01/25/2014
Kashiwabara, T.; Colciago, C.M.; Dede, L.; Quarteroni, A.
Well-posedness, regulariy, and convergence analysis of the Finite Element approximation of a Generalized Robin boundary value problem | Abstract | | In this paper, we propose the mathematical and finite element analysis of a second order Partial Differential Equation endowed with a generalized Robin boundary condition which involves the Laplace–Beltrami operator, by introducing a function space H 1 (Ω; Γ) of H 1 (Ω)-functions with H 1 (Γ)-traces, where Γ ⊆ ∂Ω. Based on a variational method, we prove that the solution of the generalized Robin boundary value problem possesses a better regularity property on the boundary than in the case of the standard Robin problem. We numerically solve generalized Robin problems by means of the finite element method with the aim of validating the theoretical rates of convergence of the error in the norms associated to the space H 1 (Ω; Γ).
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02/2014 - 01/23/2014
Antonietti, P.F.; Sarti, M.; Verani, M.
Multigrid algorithms for high order discontinuous Galerkin methods | Abstract | | In this paper we study the performance of a W-cycle multigrid algorithm for high order Discontinuous Galerkin discretizations of the Poisson problem. We recover the well known uniformity of the rate of convergence with respect to the mesh size and the number of levels and study the dependence on the polyonomial order p employed. The theoretical estimates are verified by two- and three-dimensional numerical tests. |
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