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 1287 products
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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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12/2019 - 03/26/2019
Capezza, C.; Lepore, A.; Menafoglio, A.; Palumbo, B.; Vantini, S.
Control charts for monitoring ship operating conditions and CO2 emissions based on scalar-on-function regression | Abstract | | To respond to the compelling air pollution programs, shipping companies are nowadays setting-up on their fleets modern multi-sensor systems that stream massive amounts of observational data, which can be considered as varying over a continuous domain. Motivated by this context, a novel procedure is proposed that extends classical multivariate techniques to the monitoring of multivariate functional data and a scalar quality characteristic related to them. The procedure is effectively applied to a real-case study on monitoring of operating conditions (i.e., the multivariate functional data) and total CO2 emissions (i.e., the scalar quality characteristic) at each voyage of a cruise ship. |
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11/2019 - 03/26/2019
Benacchio, T.; Klein, R.
A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics | Abstract | | We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in conservation form while relying on Exner pressure for the pressure gradient term. It discretises the rotating compressible equations by evolving full variables rather than perturbations around a background state, and operates with time steps constrained by the advection speed only. Perturbation variables are only used as auxiliary quantities in the formulation of the elliptic problem. Borrowing ideas on forward-in-time differencing, the algorithm reframes the authors' previously proposed schemes into a sequence of implicit midpoint, advection, and implicit trapezoidal steps that allows for a time integration unconstrained by the internal gravity wave speed. Compared with existing approaches, results on a range of benchmarks of nonhydrostatic- and hydrostatic-scale dynamics are competitive. The test suite includes a new planetary-scale inertia-gravity wave test highlighting the properties of the scheme and its large time step capabilities. In the hydrostatic-scale cases the model is run in pseudo-incompressible and hydrostatic mode with simple switching within a uniform discretization framework. The differences with the compressible runs return expected relative magnitudes. By providing seamless access to soundproof and hydrostatic dynamics, the developments represent a necessary step towards an all-scale blended multimodel solver. |
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10/2019 - 03/26/2019
Abramowicz, K.; Pini, A.; Schelin, L.; Sjostedt de Luna, S.; Stamm, A.; Vantini, S.
Domain selection and family-wise error rate for functional data: a unified framework | Abstract | | Functional data are smooth, often continuous, random curves, which can be seen as an extreme case of multivariate data with infinite dimensionality. Just as component-wise inference for multivariate data naturally performs feature selection, subset-wise inference for functional data performs domain selection. In this paper, we present a unified null-hypothesis testing framework for domain selection on populations of functional data. In detail, $p$-values of hypothesis tests performed on point-wise evaluations of functional data are suitably adjusted for providing a control of the family-wise error rate (FWER) over a family of subsets of the domain. We show that several state-of-the-art domain selection methods fit within this framework and differ from each other by the choice of the family over which the control of the FWER is provided. In the existing literature, these families are always defined a priori. In this work, we also propose a novel approach, coined threshold-wise testing, in which the family of subsets is instead built in a data-driven fashion. The method seamlessly generalizes to multidimensional domains in contrast to methods based on a-priori defined families. We provide theoretical results with respect to exactness, consistency, and strong and weak control of FWER for the methods within the unified framework. |
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