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 1242 products
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21/2019 - 07/05/2019
Martino, A.; Guatteri, G.; Paganoni, A.M.
Hidden Markov Models for multivariate functional data | Abstract | | Hidden Markov Models (HMMs) are a very popular tool used in many fields to model time series data. In this paper we want to extend the usual HMM framework, where the observed objects are univariate or multivariate data, to the case of functional data. In particular, since we have a sequence of multivariate curves that evolves in time, we want to model the temporal structure of the system using HMMs. The functional observations, which rely on the statistical tools related to Functional Data Analysis (FDA), are linked to the state of the HMM according to a similarity function, which depends on some metric in Hilbert spaces. We first assess our results in a simulation setting and then we apply our model to a case study regarding the climate. |
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19/2019 - 06/17/2019
Torti, A.; Pini, A.; Vantini, S.
Modelling time-varying mobility flows using function-on-function regression: analysis of a bike sharing system in the city of Milan. | Abstract | | In today’s world bike sharing systems are becoming increasingly common in all main cities around the world. To understand the spatio-temporal patterns of how people move by bike through the city of Milan, we apply functional data analysis to study the flows of a bike sharing mobility network. We introduce a complete pipeline to properly analyse and model functional data through a concurrent functional-on-functional model taking into account the effects of weather conditions and calendar on the bike flows. |
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18/2019 - 06/17/2019
Delpopolo Carciopolo, L.; Cusini, M.; Formaggia, L.; Hajibeygi, H.
Algebraic dynamic multilevel method with local time-stepping (ADM-LTS) for sequentially coupled porous media flow simulation | Abstract | | This paper presents an algebraic dynamic multilevel method with local time-stepping (ADM-LTS) for transport equations of sequentially coupled flow in heterogeneous porous media. The method employs an adaptive multilevel space-time grid determined on the basis of two error estimators, one in time and one in space.
More precisely, at each time step, first a coarse time step on a coarsest space-grid resolution is taken. Then, based on the error estimators, the transport equation is solved by taking different time step sizes at different spatial resolutions within the computational domain.
In this way, the method is able to use a fine grid resolution, both in space and in time, only at the moving saturation fronts.
In order to ensure local mass conservation, two procedures are developed. First, finite-volume restriction operators and constant prolongation (interpolation) operators are developed to map the system across different space-grid resolutions. Second, the fluxes at the interfaces across two different time resolutions are approximated with an averaging scheme in time.
Several numerical experiments have been performed to analyze the efficiency and accuracy of the proposed ADM-LTS method for both homogeneous and heterogeneous permeability field. The results show that the method provides accurate solutions, at the same time it reduces the number of fine grid-cells both in space and in time. |
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17/2019 - 06/02/2019
Antonietti,P.F.; De Ponti, J.; Formaggia, L.; Scotti, A.
Preconditioning techniques for the numerical solution of flow in fractured porous media | Abstract | | This work deals with the efficient iterative solution of the system of equations stemming from mimetic finite difference discretization of a hybrid-dimensional mixed Darcy problem modeling flow in fractured porous media.
We investigate the spectral properties of a mixed discrete formulation based on mimetic finite differences for flow in the bulk matrix and finite volumes for the fractures, and propose of a class of preconditioning techniques to accelerate convergence of iterative solvers applied to the resulting discrete system.
Numerical tests on significant three dimensional cases have assessed the properties of the proposed procedures. |
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16/2019 - 05/31/2019
Antonietti, P.F.; Houston, P.; Pennesi, G.; Suli, E.
An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids | Abstract | | In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polytopic meshes. The preconditioner is based on a coarse space and a non-overlapping partition of the computational domain where local solvers are applied in parallel. In particular, the coarse space can potentially be chosen to be non-embedded with respect to the finer space; indeed it can be obtained from the fine grid by employing agglomeration and edge coarsening techniques. We investigate the dependence of the condition number of the preconditioned system with respect to the diffusion coefficient and the discretization parameters, i.e., the mesh size and the polynomial degree of the fine and coarse spaces. Numerical examples are presented which confirm the theoretical bounds.
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15/2019 - 05/31/2019
Brandes Costa Barbosa, Y. A.; Perotto, S.
Hierarchically reduced models for the Stokes problem in patient-specific artery segments | Abstract | | In this contribution we consider cardiovascular hemodynamic modeling in patient-specific artery branches. To this aim, we first propose a procedure based on non-uniform rational basis splines (NURBS) to parametrize the artery volume which identifies the computational domain. Then, we adopt an isogeometric hierarchically reduced model which suitably combines separation of variables with a different discretization of the principal and of the secondary blood dynamics. This ensures the trade-off desired in numerical modeling between efficiency and accuracy, as shown by the good performances obtained in the numerical assessment of the last section. |
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14/2019 - 05/31/2019
Antonietti, P.F.; Facciolà, C; Verani, M.
Mixed-primal Discontinuous Galerkin approximation of flows in fractured porous media on polygonal and polyhedral grids | Abstract | | We propose a formulation based on discontinuous Galerkin methods on polygonal/polyhedral grids for the simulation of flows in fractured porous media. We adopt a model for single-phase flows where the fracture is modelled as a (d - 1) - dimensional interface in a d - dimensional bulk domain and the flow is governed by the Darcy's law
in both the bulk and the fracture. The two problems are then coupled through physically consistent conditions. We focus on the numerical approximation of the coupled bulk-fracture problem, discretizing the bulk problem in mixed form and the fracture problem in primal form. We present an priori h- and p-version error estimate in a suitable (mesh-dependent) energy norm and numerical tests assessing it. |
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13/2019 - 03/26/2019
Manzoni, A; Quarteroni, A.; Salsa, S.
A saddle point approach to an optimal boundary control problem for steady Navier-Stokes equations | Abstract | | In this paper we propose a saddle point approach to solve boundary control problems for the steady Navier-Stokes equations with mixed Dirichlet-Neumann boundary conditions, both in two and three dimensions. We provide a comprehensive theoretical framework to address (i) the well posedness analysis for the optimal control problem related to this system and (ii) the derivation of a system of first-order optimality conditions. We take advantage of a suitable treatment of boundary Dirichlet controls (and data) realized by means of Lagrange multipliers. In spite of the fact that this approach is rather common, a detailed analysis is still missing for mixed boundary conditions. We consider the minimization of quadratic cost (e.g., tracking-type or vorticity) functionals of the velocity.
A descent method is then applied for numerical optimization, exploiting the Galerkin finite element method for the discretization of the state equations, the adjoint (Oseen) equations and the optimality equation. Numerical results are shown for simplified two-dimensional fluid flows in a tract of blood vessel where a bypass is inserted; to avoid to simulate the whole bypass configuration, we represent its action by a boundary velocity control. |
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