Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1249 prodotti
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13/2014 - 21/04/2014
Ballarin, F.; Manzoni, A.; Quarteroni, A.; Rozza, G.
Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations | Abstract | | In this work we present a stable proper orthogonal decomposition (POD)-Galerkin approximation for parametrized steady Navier-Stokes equations. The stabilization is guaranteed by the use of supremizers solutions that enrich the reduced velocity space. Numerical results show that an equivalent inf-sup condition is fulfilled, yielding stability for both velocity and pressure. Our stability analysis is first carried out from a theoretical standpoint, then confirmed by numerical tests performed on a parametrized two-dimensional backward facing step flow. |
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12/2014 - 14/03/2014
Fumagalli, I; Parolini, N.; Verani, M.
Shape optimization for Stokes flow: a reference domain approach | Abstract | | In this paper we analyze a shape optimization problem, with Stokes equations as the state problem, defined on a domain with a part of the boundary that is described as the graph of the control function. The state problem formulation is mapped onto a reference domain, which is independent of the control function, and the analysis is mainly led on such domain. The existence of an optimal control function is proved, and optimality conditions are derived. After the analytical inspection of the problem, finite element discretization is considered for both the control function and the state variables, and a priori convergence error estimates are derived. Numerical experiments assess the validity of the theoretical results. |
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11/2014 - 28/02/2014
Taddei, T.; Quarteroni, A.; Salsa, S.
An offline-online Riemann solver for one-dimensional systems of conservation laws | Abstract | | In this paper we present a new technique based on two different phases, here called offline and online stages, for the solution of the Riemann problem for one-dimensional hyperbolic systems of conservation laws. After theoretically motivating our offline-online technique, we prove its effectiveness by means of two numerical examples. |
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10/2014 - 17/02/2014
Antonietti, P.F.; Dedner, A.; Madhavan, P.; Stangalino, S.; Stinner, B.; Verani, M.
High order discontinuous Galerkin methods on surfaces | Abstract | | We derive and analyze high order discontinuous Galerkin methods for
second-order elliptic problems on implicitely defined surfaces in R^3. This is done by carefully adapting the unified discontinuous Galerkin framework of [D.N. Arnold, F. Brezzi, B. Cockburn, and L.D. Marini, SIAM J. Numer. Anal., 2002] on a triangulated surface approximating the smooth surface. We prove optimal error estimates in both a (mesh dependent) energy and L^2 norms. |
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09/2014 - 12/02/2014
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 - 03/02/2014
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 - 31/01/2014
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 - 28/01/2014
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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