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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59/2014 - 12/12/2014
Manzoni, A.; Pagani, S.; Lassila, T.
Accurate solution of Bayesian inverse uncertainty quantification problems using model and error reduction methods | Abstract | | Computational inverse problems related to partial differential equations (PDEs) often contain nuisance parameters that cannot be effectively identified but still need to be considered as part of the problem. The objective of this work is to show how to take advantage of projection-based reduced order models (ROMs) to speed up Bayesian inversion on the identifiable parameters of the system, while marginalizing away the (potentially large number of) nuisance parameters. The key ingredients are twofold. On the one hand, we rely on a reduced basis (RB) method, equipped with computable a posteriori error bounds, to speed up the solution of the forward problem. On the other hand, we develop suitable reduction error models (REM) to quantify the error between the full-order and the reduced-order model affecting the likelihood function, in order to gauge the effect of the ROM on the posterior distribution of the identifiable parameters. Numerical results dealing with inverse problems governed by elliptic PDEs in the case of both scalar parameters and parametric fields highlight the combined role played by ROM accuracy and REM effectivity. |
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60/2014 - 12/12/2014
Signorini, M.; Micheletti, S.; Perotto, S.
CMFWI: Coupled Multiscenario Full Waveform Inversion for seismic inversion | Abstract | | We present the new method Coupled Multiscenario Full Waveform Inversion (CMFWI) for the solution of the seismic inversion problem. As in the case of Full Waveform Inversion (FWI), the proposed method is based on seismic reflection signals and it tries to recover the subsoil velocity profile by minimizing a suitable misfit functional between recorded and computed data. CMFWI suitably combines data generated by shooting one source at a time, but sharing the effect of this signal with the other sources. Moreover, CMFWI differs from FWI employed with the same sources shot together, and we numerically show that it performs better than FWI. In particular, this comparison focuses on different types of boundary conditions, wave sources, initial guesses of the velocity profile, and signal-to-noise ratio.
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55/2014 - 12/02/2014
Antonietti, P. F.; Houston P.; Sarti, M.; Verani, M.
Multigrid algorithms for hp-version Interior Penalty Discontinuous Galerkin methods on polygonal and polyhedral meshes | Abstract | | In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polygonal/polyhedral meshes. We prove that the two-level method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large. An analogous result is obtained for the W-cycle multigrid algorithm, which is proved to be uniformly convergent with
respect to the mesh size, the polynomial approximation degree, and the number of levels, provided the latter remains bounded
and the number of smoothing steps is chosen sufficiently large. Numerical experiments are presented which underpin the theoretical predictions; moreover, the proposed multilevel solvers are shown to be convergent in practice, even when some of the theoretical assumptions are not fully satisfied. |
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56/2014 - 12/02/2014
Antonietti, P. F.; Sarti, M.; Verani, M.; Zikatanov, L. T.
A uniform additive Schwarz preconditioner for the hp-version of Discontinuous Galerkin approximations of elliptic problems | Abstract | | In this paper we design and analyze a uniform preconditioner for a class of high order Discontinuous Galerkin schemes. The preconditioner is based on a space splitting involving the high order conforming subspace and
results from the interpretation of the problem as a nearly-singular problem. We show that the proposed preconditioner exhibits spectral bounds that are uniform with respect to the discretization parameters, i.e., the mesh size, the polynomial degree and the penalization coefficient. The theoretical estimates obtained are supported by several numerical simulations. |
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54/2014 - 11/28/2014
Ferrario, E.; Pini, A.
Uncertainties in renewable energy generation systems: functional data analysis, monte carlo simulation, and fuzzy interval analysis | Abstract | | In this paper, aleatory and epistemic uncertainties in energy generation systems are investigated. The former are described by probability distributions, whereas the latter by possibility distributions. In particular, time-varying probability distributions elicited by Functional Data Analysis are considered for the representation of the aleatory uncertainty that evolves with time. Then, the joint propagation of both types of uncertainty is performed by Monte Carlo simulation and Fuzzy Interval Analysis. The method is applied to a model of an energy system made of a solar panel, a storage energy system and the loads. As a quantitative indicator of the analysis we evaluate the Expected Energy Not Supplied. |
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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. |
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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. |
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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.
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