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 1322 prodotti
-
56/2015 - 02/11/2015
Bonaventura, L.; Della Rocca, A.
Monotonicity, positivity and strong stability of the TR-BDF2 method and of its SSP extensions | Abstract | | We analyze the one-step method TR-BDF2 from the point of view
of monotonicity, strong stability and positivity. All these properties
are strongly related and reviewed in the common framework of abso-
lute monotonicity. The radius of absolute monotonicity is computed
and it is shown that the parameter value which makes the method
L-stable is also the value which maximizes the radius of monotonicity.
Two hybrid variants of TR-BDF2 are proposed, that reduce the for-
mal order of accuracy and maximize the absolute monotonicity radius,
while keeping the native L-stability useful in stiff problems. Numeri-
cal experiments compare these different hybridization strategies with
other methods commonly used in the presence of stiff and mildly stiff
source terms. The results show that both strategies provide a good
compromise between accuracy and robustness at high CFL numbers,
without suffering from the limitations of alternative approaches al-
ready available in literature.
|
-
55/2015 - 02/11/2015
Fumagalli, A.; Zonca, S.; Formaggia, L.
Advances in computation of local problems for a flow-based upscaling in fractured reservoirs | Abstract | | In this article we present some advances to increase the efficiency and applicability of a flow-based upscaling procedure to solve single and multi-phase flows in natural fractured reservoirs. These geological formations may be characterized by hundreds up to hundreds of thousands of fractures, ranging from small to medium scales, which spread all the reservoir. An explicit representation of all the fractures in real scenarios make soon unfeasible performing numerical simulations. An upscaling procedure is thus required. We assume that the reservoir can be modeled with a coarse corner-point grid where the fractures are geometrically uncoupled, by using an embedded discrete fracture model. To describe the scaled up problem, we consider a flow-based upscaling procedure where multiple sub-regions are used to derive transmissibilities, mean depths and pore volumes related to the coarse degrees of freedom associated with fractures and rock matrix. Our focus is to further enhance the upscaling process by allowing the splitting of unconnected rock matrix regions and to compare two ways of setting up the local problems used to compute the transmissibility between coarse cells. Numerical examples confirm the effectiveness of the proposed approach. |
-
54/2015 - 02/11/2015
Canuto, C.; Nochetto, R. H.; Stevenson, R.; Verani, M.
Adaptive Spectral Galerkin Methods with Dynamic Marking | Abstract | | The convergence and optimality theory of adaptive Galerkin methods is
almost exclusively based on the Dorfler marking. This entails a fixed
parameter and leads to a contraction constant bounded below away from
zero. For spectral Galerkin methods this is a severe limitation which affects performance. We present a dynamic marking strategy that allows for a super-linear relation between consecutive discretization errors, and show exponential convergence with linear computational complexity whenever the solution belongs to a Gevrey approximation class.
|
-
53/2015 - 19/10/2015
Menafoglio, A; Grujic, O.; Caers, J.
Universal kriging of functional data: trace-variography vs cross-variography? Application to forecasting in unconventional shales | Abstract | | In this paper we investigate the practical and methodological use of universal kriging of functional data to predict unconventional shale production in undrilled locations from known production data. In universal kriging of functional data, two approaches are considered: 1) estimation by means of cokriging of functional components (Universal Cokriging, UCok), requiring cross-variography and 2) estimation by means of trace-variography (Universal Trace-Kriging, UTrK), which avoids cross-variogram modeling. While theoretically, under known variogram structures, such approaches may be quite equivalent, the practical application yields marked differences. We investigate these difference by means of a real field application in the Barnett shale play and by a Monte Carlo study inspired from such real field application. We find that, for the studied cases, in terms of sum of squared errors (SSE), UTrK outperforms UCok. We speculate that the main reason lies in the robustness of estimating experimental trace-variography over the cross-variography and the possible loss of information induced by the functional decomposition required for cokriging.
|
-
52/2015 - 30/09/2015
Giverso, C.; Scianna, M.; Grillo, A.
Growing Avascular Tumours as Elasto-Plastic Bodies by the Theory of Evolving Natural Configurations | Abstract | | The aim of this article is to propose a simple way of describing a tumour as a linear elastic material from a reference configuration that is continuously evolving in time due to growth and remodelling. The main assumption allowing this simplification is that the tumour mass is a very ductile material, so that it can only sustain moderate stresses while the deformation induced by growth, that can actually be quite big, mainly induces a plastic reorganisation of malignant cells. In mathematical terms this means that the deformation gradient can be split into a volumetric growth term, a term describing the reorganisation of cells, and a term that can be approximated by means of the linear strain tensor. A dimensionless analysis of the importance of the different terms also allows to introduce a second simplification consisting in the decoupling of the equations describing the growth of the tumour mass from those describing the flow of the interstitial fluid. |
-
51/2015 - 30/09/2015
Ballarin, F.; Faggiano, E.; Ippolito, S.; Manzoni, A.; Quarteroni, A.; Rozza, G.; Scrofani, R.
Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD–Galerkin method and a vascular shape parametrization | Abstract | | In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach. |
-
50/2015 - 30/09/2015
Grillo, A.; Guaily, A.; Giverso, C.; Federico, S.
Non-Linear Model for Compression Tests on Articular Cartilage | Abstract | | Hydrated soft tissues, such as articular cartilage, are often modelled as biphasic systems with individually incompressible solid and fluid phases, and biphasic models are employed to fit experimental data in order to determine the mechanical and hydraulic properties of the tissues. Two of the most common experimental setups are confined and unconfined compression. Analytical solutions exist for the unconfined case with the linear, isotropic, homogeneous model of articular cartilage, and for the confined case with the non-linear, isotropic, homogeneous model. The aim of this contribution is to provide an easily implementable numerical tool to determine a solution to the governing differential equations of (homogeneous and isotropic) unconfined and (inhomogeneous and isotropic) confined compression under large deformations. The large-deformation governing equations are reduced to equivalent diffusive equations, which are then solved by means of Finite Difference methods. The solution strategy proposed here could be used to generate benchmark tests for validating complex user-defined material models within Finite Element implementations, and for determining the tissue's mechanical and hydraulic properties from experimental data. |
-
49/2015 - 30/09/2015
Ghiglietti, A.; Ieva, F.; Paganoni, A.M.
Statistical inference for stochastic processes: two sample hypothesis tests | Abstract | | In this paper, we present inferential procedures to compare the means of two samples of functional data. The proposed tests are based on a suitable generalization of Mahalanobis distance to the Hibert space of square integrable function defined on a compact interval. We do not require any specific distributional assumption on the processes generating the data. Test procedures are proposed for both the cases of known and unknown variance-covariance structures, and asymptotic properties of test statistics are deeply studied. A simulation study together with a real case data analysis are also presented. |
|
