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 1249 prodotti
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03/2018 - 13/01/2018
Antonietti, P. F.; Houston, P.; Pennesi, G.
Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods | Abstract | | In this paper we present efficient quadrature rules for the numerical approximation of integrals of polynomial functions over general polygonal/polyhedral elements that do not require an explicit construction of a sub-tessellation into triangular/tetrahedral elements. The method is based on successive application of Stokes' theorem; thereby, the underlying integral may be evaluated using only the values of the integrand at the vertices of the polytopic domain, and hence leads to an exact cubature rule whose quadrature points are the vertices of the polytope. We demonstrate the capabilities of the proposed approach by efficiently computing the stiffness and mass matrices arising from $hp$-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations. |
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01/2018 - 03/01/2018
Berrone, S.; Bonito, A.; Stevenson, R.; Verani, M.
An optimal adaptive Fictitious Domain Method | Abstract | | We consider a Fictitious Domain formulation of an elliptic partial differential equation and approximate the resulting saddle-point system using an inexact preconditioned Uzawa iterative algorithm.
Each iteration entails the approximation of an elliptic problems performed using adaptive finite element methods. We prove that the overall method converges with the best possible rate and illustrate numerically our theoretical findings. |
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02/2018 - 03/01/2018
Canuto, C.; Nochetto, R. H.; Stevenson, R.; Verani, M.
A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square | Abstract | | Both practice and analysis of adaptive $p$-FEMs and $hp$-FEMs raise
the question what increment in the current polynomial degree $p$
guarantees a $p$-independent reduction of the Galerkin error. We
answer this question for the $p$-FEM in the simplified context of homogeneous
Dirichlet problems for the Poisson equation in the
two dimensional unit square with polynomial data of
degree $p$. We show that an increment proportional to $p$ yields a
$p$-robust error reduction and provide computational evidence that a
constant increment does not. |
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68/2017 - 16/12/2017
Paolucci, R.; Infantino, M.; Mazzieri, I.; Özcebe, A.G.; Smerzini, C.; Stupazzini, M.
3D physics-based numerical simulations: advantages and current limitations of a new frontier to earthquake ground motion prediction. The Istanbul case study. | Abstract | | In this paper, an overview is presented to motivate the use of 3D physics-based numerical simulations of seismic wave propagation to support enhanced Probabilistic Seismic Hazard Assessment. With reference to the case study of Istanbul, we introduce the activities required to construct a numerical model of the surface geology and topography and to determine the input conditions to trigger future earthquakes in a physically sound way. Owing to the intrinsic frequency limitations of the numerical simulations, a post-processing technique to produce realistic broadband waveforms is introduced, allowing to correlate short-period to long-period spectral ordinates from an Artificial Neural Network. Finally, the results obtained in Istanbul from numerous physics-based ground motion scenarios of M7+ earthquakes allow us to throw light on the potential added value to PSHA of the 3D numerical simulations. Namely, to provide locally constrained probabilistic distributions of ground motion intensity measures, matching the actual footprint of a large earthquake in the specific area under study. |
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67/2017 - 16/12/2017
Esterhazy, S.; Schneider, F.; Mazzieri, I; Bokelmann, G.
Insights into the modeling of seismic waves for the detection of underground cavities | Abstract | | Motivated by the need to detect an underground cavity within the procedure of an On-Site-Inspection (OSI), of the Comprehensive Nuclear Test Ban Treaty Organization, the aim of this paper is to present results on the comparison of our numerical simulations with an analytic solution. The accurate numerical modeling can facilitate the development of proper analysis techniques to detect the remnants of an underground nuclear test. The larger goal is to help set a rigorous scientific base of OSI and to contribute to bringing the Treaty into force. For our 3D numerical simulations, we use the discontinuous Galerkin Spectral Element Code SPEED jointly developed at MOX (The Laboratory for Modeling and Scientific
Computing, Department of Mathematics) and at DICA (Department of Civil and Environmental Engineering) of the Politecnico di Milano. |
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66/2017 - 13/12/2017
Tamellini, M.; Parolini, N.; Verani, M.
An optimal control problem of two-phase compressible-incompressible flows | Abstract | | In this work two-phase compressible-incompressible flows are studied. In particular, the possibility of driving the gas bubbles moving in a liquid towards a prescribed position is investigated. To this end, first a well-established mathematical model for two-phase compressible-incompressible fluids is briefly introduced, then an adjoint-based optimal control problem is defined. Finally numerical results on the controllability of the system are presented. |
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65/2017 - 01/12/2017
Regazzoni, F.;Parolini, N.;Verani M.
Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers | Abstract | | We propose a solution strategy for a multimaterial minimum compliance topology optimization problem, which consists in finding the optimal allocation of a finite number of candidate (possibly anisotropic) materials inside a reference domain, with the aim of maximizing the stiffness of the body. As a relevant and novel application we consider the optimization of self-assembled structures obtained by means of diblock copolymers. Such polymers are a class of self-assembling materials which spontaneously synthesize periodic microstructures at the nanoscale, whose anisotropic features can be exploited to build structures with optimal elastic response, resembling biological tissues exhibiting microstructures, such as bones and wood. For this purpose we present a new generalization of the classical Optimality Criteria algorithm to encompass a wider class of problems, where multiple candidate materials are considered, the orientation of the anisotropic materials is optimized, and the elastic properties of the materials are assumed to depend on a scalar parameter, which is optimized simultaneously to the material allocation and orientation. Well-posedness of the optimization problem and well-definition of the presented algorithm are narrowly treated and proved. The capabilities of the proposed method are assessed through several numerical tests. |
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64/2017 - 01/12/2017
Fumagalli, I.; Parolini, N.; Verani, M.
Optimal control in ink-jet printing via instantaneous control | Abstract | | This paper concerns the optimal control of a free surface flow with moving contact line, inspired by an application in ink-jet printing. Surface tension, contact angle and wall friction are taken into account by means of the generalized Navier boundary condition. The time-dependent differential system is discretized by an arbitrary Lagrangian-Eulerian finite element method, and a control problem is addressed by an instantaneous control approach, based on the time discretization of the flow equations. The resulting control procedure is computationally highly efficient and its assessment by numerical tests show its effectiveness in deadening the natural oscillations that occur inside the nozzle and reducing significantly the duration of the transient preceding the attainment of the equilibrium configuration. |
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