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 1251 prodotti
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21/2018 - 10/04/2018
Gervasio, P.; Dede', L.; Chanon, O.; Quarteroni, A.
Comparing Isogeometric Analysis and Spectral Element Methods: accuracy and spectral properties | Abstract | | In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods (SEM) and NURBS-based Isogeometric Analysis (IGA) in the framework of the Galerkin method for the approximation of the Poisson problem. Our focus is on their convergence properties, the algebraic structure and the spectral properties of the corresponding discrete arrays (mass and stiffness matrices). We review the available theoretical results for these methods and verify them numerically by performing error analysis on the solution of the Poisson problem. Where theory is lacking, we use numerical investigation of the results to draw conjectures on the behavior of the corresponding theoretical laws in terms of the design parameters, such as the (mesh) element size, the local polynomial degree, the smoothness of the NURBS basis functions, the space dimension, and the total number of degrees of freedom involved in the computations. |
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20/2018 - 25/03/2018
Bassi, C. ; Abbà, A.; Bonaventura L.; Valdettaro, L.
A priori tests of a novel LES approach to compressible variable density turbulence | Abstract | | We assess the viability of a recently proposed novel approach to LES for compressible variable density flows by means of a priori tests. The a priori tests have been carried out filtering a two-dimensional
DNS database of the classic lock-exchange benchmark. The tests confirm that additional terms should be accounted for in subgrid scale modeling of variable density flows, with respect to the terms usually considered in the traditional approach. Several alternatives for the modeling of these terms are assessed and discussed. |
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19/2018 - 01/03/2018
Menghini, F.; Dede', L.; Quarteroni, A.
Variational Multiscale LES modeling of blood flow in an idealized left human heart | Abstract | | In this work we build a realistic, although idealized, computational model of the left human heart for the study of the blood flow dynamics. We prescribe the left heart wall displacement based on physiological data and we take into account the presence of both the mitral and aortic valves through a resistive method. We simulate the left heart hemodynamics by means of the Finite Element method and compare different numerical stabilization techniques to account for the transitional and nearly turbulent nature of the blood flow in a physiological regime. In particular, we apply a Variational Multiscale Large Eddy Simulation (LES) model and a Streamwise Upwind Petrov-Galerkin method and we critically analyze the corresponding numerical results. |
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18/2018 - 26/02/2018
Antonietti, P.F.; Bonaldi, F.; Mazzieri, I.
A high-order discontinuous Galerkin approach to the elasto-acoustic problem | Abstract | | We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid (elastic) domain and the fluid (acoustic) domain. We state and prove a well-posedness result for the strong formulation of the problem, present a stability analysis for the semi-discrete formulation, and finally prove an a priori hp-version error estimate for the resulting formulation in a suitable (mesh-dependent) energy norm. The conver- gence results are validated by numerical experiments carried out in a two-dimensional setting. |
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17/2018 - 24/02/2018
Agosti, A.; Giverso, C.; Faggiano, E.;Stamm,A.; Ciarletta, P.
A personalized mathematical tool for neuro-oncology: a clinical case study | Abstract | | This work evaluates the predictive ability of a novel personalised computational tool for simulating the growth of brain tumours using the neuroimaging data collected during one clinical case study.
The mathematical model consists in an evolutionary fourth-order partial differential equation with degenerate motility, in which the spreading dynamics of the multiphase tumour is coupled through a growth term with a parabolic equation determining the diffusing oxygen within the brain. The model also includes a reaction term describing the effects of radiotherapy, that is simulated in accordance to the clinical schedule.
We collect Magnetic Resonance (MRI) and Diffusion Tensor (DTI) imaging data for one patient at given times of key clinical interest, from the first diagnosis of a giant glioblastoma to its surgical removal and the subsequent radiation therapies.
These neuroimaging data allow reconstructing the patient-specific brain geometry in a finite element virtual environment, that is used for simulating the tumour recurrence pattern after the surgical resection. In particular, we characterize the different brain tissues and the tumour location from MRI data, whilst we extrapolate the heterogeneous nutrient diffusion parameters and cellular mobility from DTI data.
The numerical results of the simulated tumour are found in good qualitative and quantitative agreement with the volume and the boundaries observed in MRI data. Moreover, the simulations point out a consistent regression of the tumour mass in correspondence to the application of radiotherapy, with an average growth rate which is of the same order as the one calculated from the neuroimaging data. Remarkably, our results display the highest Jaccard index of the tumour region reported in the biomathematical literature.
In conclusion, this work represents an important proof-of-concept of the ability of this mathematical framework to predict the tumour recurrence and its response to therapies in a patient-specific manner. |
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16/2018 - 24/02/2018
Calissano, A.; Vantini, S.; Arnaboldi, M.
An elephant in the room: Twitter samplingmethodology. | Abstract | | The usage of social media data is spreading among the broad scientific community: 30000 papers dealing with this type of data are indexed in Scopus in the last decade. On the one hand, this data are very appealing, creating a rich bucket of information. On the other one, gathering them through a repeatable sampling strategy is increasing in complexity (or maybe becoming impossible?). The aim of this paper is to map the scientific community awareness about the sampling strategies used to download on-line data, focusing on the most studied social media: Twitter. This review unveils two unexpected results: the downloaded data are typically far from being randomly sampled, and around 99% of papers does not explicitly declare the sampling strategy used to download the data. These two facts pose some worrisome doubts about the trustworthiness of all the results presented in this stream of literature. |
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15/2018 - 24/02/2018
Simona, A.; Bonaventura, L.; Pugnat, T.; Dalena, B.
High order time integrators for the simulation of charged particle motion in magnetic quadrupoles | Abstract | | Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider.
In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the accelerator must be simulated, thus leading to the necessity to preserve numerically invariants of motion over a long time interval and to a substantial computational cost, mostly related to the repeated evaluation of the magnetic vector potential. In this paper, in order to reduce this cost, we first consider a specific gauge transformation that allows to reduce significantly the number of vector potential evaluations. We then analyze the sensitivity of the numerical solution to the interpolation procedure required to compute magnetic vector potential data from gridded precomputed values at the locations required by high order time integration methods. Finally, we compare several high order integration techniques, in order to assess their accuracy and efficiency for these long term simulations. Explicit high order Lie methods are considered, along with implicit high order symplectic integrators and conventional explicit Runge Kutta methods. Among symplectic methods, high order Lie integrators yield optimal results in terms of cost/accuracy ratios, but non symplectic
Runge Kutta methods perform remarkably well even in very long term simulations. Furthermore, the accuracy of the field reconstruction and interpolation techniques are shown to be limiting factors for the accuracy of the particle tracking procedures. |
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14/2018 - 24/02/2018
Cuffaro, M.; Miglio, E.; Penati, M.;Viganò, M.
Mantle upwelling driven by asymmetric sea-floor spreading at northern Mid–Atlantic ridge | Abstract | | Numerical modeling at spreading centeres provides useful information on mantle upwelling and geodynamic processes beneath mid-ocean ridges. We computed mantle thermal structure at northern Mid-Atlantic ridge using numerical simulations with asymmetric spreading rates and ridge migration as initial conditions. We explored the use of different lateral boundary
conditions in numerical models such as velocity and velocity and stress to evaluate differences in mantle velocity field, temperature and depth of the thermal base of the lithosphere versus domain width. We propose additional boundary conditions (i.e., namely stress-only) choosing
a proper tangential stress at the bottom of the domain and on lateral boundaries, taking into account ridge migration. When stress-only conditions are imposed, we obtain lower differences with respect to the expected solution and errors are minimized in simulation domains
with intermediate width, also saving computational costs. Moreover, dimension analyses of governing equations result in that heat generation due to work of the viscous forces can not be neglected in the computations. Consequently, we provide an application to a geodynamic
realm (e.g., northern Mid-Atlantic ridge at the reference latitude of 43°N) of such an integrated numerical model that reveals a region of hot upwelling mantle beneath the ridge axis, and shows that the base of the lithosphere reaches the top of the domain. The use of asymmetric
spreading and ridge migration accounts for an asymmetric accretion of the oceanic lithosphere.
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