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 1239 products
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17/2018 - 02/24/2018
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 - 02/24/2018
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 - 02/24/2018
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 - 02/24/2018
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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13/2018 - 02/18/2018
Gandelli, E.; Penati, M.;Quaglini, V.;Lomiento, G.; Miglio, E.; Benzoni, G.M.
A novel OpenSees element for single curved surface sliding isolators | Abstract | | The increasing use of curved surface sliding bearings as seismic isolators benefits from the improvement of analytical models that can accurately capture their experimental performance and enhance the predictive capability of nonlinear response history analyses.
The mathematical formulation proposed in this paper aims at addressing the variability of the coefficient of friction based on experimental data that can be retrieved from prototype tests on curved surface sliders. The formulation accounts for variation in the coefficient of friction with the instantaneous change of axial load and sliding velocity at the contact
interface, and the accumulated heat due to cyclic motion; furthermore, it incorporates new features such as the static friction developed in the transition from the pre-sliding phase to the dynamic sliding condition. The proposed model has been coded in the object-oriented finite element software OpenSees by modifying the standard SingleFPSimple3d element
that describes the force – displacement relationship of a bearing comprising one concave sliding surface and a spherical articulation. The main novelties of the new CSSBearing_BVNC element are inclusion of the static friction before the breakaway and degradation of kinetic friction induced by the heat developed during the motion of the articulated slider. The primary assumptions in the development of the friction model and the
verification of the newly developed element are validated by agreement with available data.
A case study helps to demonstrate the improved prediction capability of the new bearing element over its standard counterpart when applied to real situations, such as estimating a +50% increase in isolator displacement, superstructure drift and base shear demand under high intensity earthquakes, and possible non-activation of the sliding isolators under weak or medium intensity earthquakes. |
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12/2018 - 02/14/2018
Dal Santo, N.; Deparis, S.; Manzoni, A.; Quarteroni, A.
Multi space reduced basis preconditioners for large-scale parametrized PDEs | Abstract | | In this work we introduce a new two-level preconditioner for the efficient solution of large scale linear systems arising from the discretization of parametrized PDEs. The proposed preconditioner combines in a multiplicative way a reduced basis solver, which plays the role of coarse component, and a "traditional" fine grid preconditioner, such as one-level Additive Schwarz, block Gauss-Seidel or block Jacobi preconditioners. The coarse component is built upon a new Multi Space Reduced Basis (MSRB) method that we introduce for the first time in this paper, where a reduced basis space is built through the proper orthogonal decomposition (POD) algorithm at each step of the iterative method at hand, like the flexible GMRES method. MSRB strategy consists in building reduced basis (RB) spaces that are well-suited to perform a single iteration, by addressing the error components which have not been treated yet. The Krylov iterations employed to solve the resulting preconditioned system targets small tolerances with a very small iteration count and in a very short time, showing good optimality and scalability properties. Simulations are carried out to evaluate the performance of the proposed preconditioner in different large scale computational settings related to parametrized advection diffusion equations and compared with the current state of the art algebraic multigrid preconditioners. |
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11/2018 - 02/14/2018
Delpopolo Carciopolo L.; Bonaventura L.; Scotti A.; Formaggia L.
A conservative implicit multirate method for hyperbolic problems | Abstract | | This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the spatial domain. We propose a novel mass conservative multirate approach, that can be generalized to various implicit time discretization methods. It is based on flux partitioning, so that flux exchanges between a cell and its neighbors are balanced.
A number of numerical experiments on both non-linear scalar problems and systems of hyperbolic
equations have been carried out to test the efficiency and accuracy of the proposed approach. |
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10/2018 - 02/02/2018
Menafoglio, A.; Gaetani, G.; Secchi, P.
Random Domain Decompositions for object-oriented Kriging over complex domains | Abstract | | We propose a new methodology for the analysis of spatial fields of object data distributed over complex domains. Our approach enables to jointly handle both data and domain complexities, through a divide et impera approach. As a key element of innovation, we propose to use a Random Domain Decomposition, whose realizations define sets of homogeneous sub-regions where to perform simple, independent, weak local analyses (divide), eventually aggregated into a final strong one (impera). In this broad framework, the complexity of the domain (e.g., strong concavities, holes or barriers) can be accounted for by defining its partitions on the basis of a suitable metric, which allows to properly represent the adjacency relationships among the complex data (such as scalar, functional or constrained data) over the domain. As an insightful illustration of the potential of the methodology, we consider the analysis and spatial prediction (Kriging) of the probability density function of dissolved oxygen in the Chesapeake Bay. |
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