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 1349 prodotti
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60/2013 - 29/11/2013
Ghiglietti, A.; Paganoni, A.M.
An urn model to construct an efficient test procedure for response adaptive designs | Abstract | | We study statistical performance of different tests for comparing the mean effect of two treatments. Given a test T0, we determine which sample size and proportion allocation guarantee to a test T to be better than T0, in terms of (a) higher power and (b) fewer subjects assigned to the inferior treatment. The adoption of a response adaptive design to implement the random allocation procedure is necessary to ensure that both (a) and (b) are satisfied. In particular, we propose to use a Modified Randomly Reinforced Urn design (MRRU) and we show how to perform the model parameters selection for the purpose of this paper. The opportunity of relaxing some assumptions is examined. Results of simulation studies on the test performance are reported and a real case study is analyzed. |
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59/2013 - 25/11/2013
Aletti, M.; Bortolossi, A.; Perotto, S.; Veneziani, A.
One-dimensional surrogate models for advection-diffusion problems | Abstract | | Numerical solution of partial differential equations can be made more tractable
by model reduction techniques. For instance, when the problem at hand presents
a main direction of the dynamics (such as blood flow in arteries), it may be
conveniently reduced to a 1D model. Here we compare two strategies to obtain this
model reduction, applied to classical advection-diffusion equations in domains
where one dimension dominates the others. |
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58/2013 - 20/11/2013
Artina, M.; Fornasier, M.; Micheletti, S.; Perotto, S.
Anisotropic adaptive meshes for brittle fractures: parameter sensitivity | Abstract | | We deal with the Ambrosio-Tortorelli approximation of the well-known Mumford-Shah functional to model quasi-static crack propagation in brittle materials.
We employ anisotropic mesh adaptation to efficiently capture the crack path.
Aim of this work is to investigate the numerical sensitivity
of the crack behavior to the parameters involved in both the physical model
and in the adaptive procedure. |
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57/2013 - 17/11/2013
Antonietti, P.F.; Perugia, I.; Zaliani, D.
Schwarz domain decomposition preconditioners for plane wave discontinuous Galerkin methods | Abstract | | We construct Schwarz domain decomposition preconditioners for plane wave discontinuous Galerkin methods for Helmholtz boundary value problems. In particular, we consider additive and multiplicative non-overlapping Schwarz methods. Numerical tests show good performance of these preconditioners when solving the linear system of equations with GMRES. |
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56/2013 - 15/11/2013
Antonietti, P.F.; Ayuso de Dios, B.; Mazzieri, I.; Quarteroni, A.
Stability analysis for Discontinuous Galerkin approximations of the elastodynamics problem | Abstract | | We consider semi-discrete discontinuous Galerkin approximations of a general elastodynamics problem, in both displacement and displacement-stress formulations. We present the stability analysis of all the methods in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We include some numerical experiments in three dimensions to verify the theory. |
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54/2013 - 13/11/2013
Biasi, R.; Ieva, F.; Paganoni, A.M.; Tarabelloni, N.
Use of depth measure for multivariate functional data in disease prediction: an application to electrocardiographic signals | Abstract | | In this paper we develop statistical methods to compare two independent samples of multivariate functional data that differ in terms of covariance operators. In particular we generalize the concept of depth measure to this kind of data, exploiting the role of the covariance operators in weighting the components that define the depth.
Two simulation studies are carried out to validate the robustness of the proposed methods.
We present an application to Electrocardiographic (ECG) signals aimed at comparing physiological subjects and patients affected by Left Bundle Branch Block. The proposed depth measures computed on data are then used to perform a nonparametric comparison test among these two populations. They are also introduced into a generalized regression model aimed at classifying the ECG signals.
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55/2013 - 13/11/2013
Laadhari, A.; Ruiz-Baier, R.; Quarteroni, A.
Fully Eulerian finite element approximation of a fluid-structure interaction problem in cardiac cells | Abstract | | We propose in this paper an Eulerian finite element approximation of a coupled chemical fluid-structure interaction problem arising in the study of mesoscopic cardiac biomechanics. We simulate the active response of a myocardial cell (here considered as an anisotropic, hyperelastic, and incompressible material), the propagation of calcium concentrations inside it, and the presence of a surrounding Newtonian fluid. An active strain approach is employed to account for the mechanical activation, and the deformation of the cell membrane is captured using a level set strategy. We address in detail the main features of the proposed method, and we report several numerical experiments aimed at model validation. Copyright © 2013 John Wiley & Sons, Ltd.
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53/2013 - 12/11/2013
Micheletti, S.
A continuum variational approach based on optimal control to adaptive moving mesh methods | Abstract | | We cast mesh adaptation based on point relocation in a continuum mechanics analogy. The movement of the mesh points is thus interpreted as a displacement of points of the continuum. We describe our approach on the
Dirichlet problem for the Poisson equation in 2D. It is well known that, for a fixed mesh, the best approximation in the energy norm, |||·|||, to the exact solution, u, is the Galerkin approximation, uh , in a finite element space, and that uh minimizes also a suitable energy functional. The best error, however, still depends on the mesh. The energy functional is then rewritten in terms of the displacement through its displacement-gradient tensor.
Thus finding the optimal mesh, where |||u − uh ||| is a minimum, among a family of possible meshes, amounts to computing the displacement field
which minimizes the energy functional. This is carried out via the optimal control approach, after enforcing the constraint that the displacement satisfies a diffusion equation with the control functions in the role of a variable
diffusivity. This in turn yields the optimal movement of the mesh nodes. An algorithm based on a gradient flow delivers the actual adapted mesh.
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