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 1308 prodotti
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16/2014 - 05/05/2014
Dede, L.; Jaggli, C.; Quarteroni, A.
Isogeometric numerical dispersion analysis for elastic wave propagation | Abstract | | In this paper, we carry out a numerical dispersion analysis for the linear elastodynamics equations approximated by means of NURBS-based Isogeometric Analysis in the framwork of the Galerkin method; specifically, we consider the analysis of harminic plane waves in an isotropic and homogeneous elastic medium. We compare and discuss the errors associated to the compressional and shear wave velocities and we provide the anisotropic curves for numerical approximations obtained by considerin B-splines and NURBS basis functions of different regularity, namely globally C^0- and C^(p-1)- continuous, being p the polynomial degree. We conclude our analysis by numerically simulating the seismic wave propagation in a sinusoidal shaped valley with discontinuous elastic parameters across an internal interface. |
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15/2014 - 02/05/2014
Esfandiar, B.; Porta, G.; Perotto, S.; Guadagnini, A;
Anisotropic mesh and time step adaptivity for solute transport modeling in porous media | Abstract | | We assess the impact of space-time mesh adaptivity on the modeling of solute transport in porous media. This approach allows an automatic selection of both the spatial mesh and the time step on the basis of a suitable recovery-based error estimator. In particular, we deal with an anisotropic control of the spatial mesh. The solver coupled with the adaptive module deals with an advection-dispersion equation to model the transport of dissolved species, which are assumed to be convected by a Darcy flow field. The whole solution-adaptation procedure is assessed through two-dimensional numerical tests. A numerical convergence analysis of the spatial mesh adaptivity is first performed by considering a test-case with analytical solution. Then, we validate the space-time adaptive procedure by reproducing a set of experimental observations associated with solute transport in a homogeneous sand pack. The accuracy and the efficiency of the methodology are discussed and numerical results are compared with those associated with fixed uniform space-time discretizations. This assessment shows that the proposed approach is robust and reliable. In particular, it allows us to obtain a significant improvement of the simulation quality of the early solute arrivals times at the outlet of the medium. |
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14/2014 - 23/04/2014
Dassi, F.; Formaggia, L.; Zonca, S.
Degenerate Tetrahedra Recovering | Abstract | | Many mesh generation or optimization algorithms could produce a low quality tetrahedral mesh, i.e. a mesh where the tetrahedra have very small solid or dihedral angles. In this paper, we propose a series of operations to recover these degenerate tetrahedra. In particular, we will focus on the standard shapes of these undesired mesh elements (sliver, cap, wedge and spade) and, for each of these configurations, we apply a suitable sequence of classical mesh modification procedures to get a higher quality mesh. The reliability of the proposed mesh optimization algorithm is numerically proved with some examples. |
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13/2014 - 21/04/2014
Ballarin, F.; Manzoni, A.; Quarteroni, A.; Rozza, G.
Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations | Abstract | | In this work we present a stable proper orthogonal decomposition (POD)-Galerkin approximation for parametrized steady Navier-Stokes equations. The stabilization is guaranteed by the use of supremizers solutions that enrich the reduced velocity space. Numerical results show that an equivalent inf-sup condition is fulfilled, yielding stability for both velocity and pressure. Our stability analysis is first carried out from a theoretical standpoint, then confirmed by numerical tests performed on a parametrized two-dimensional backward facing step flow. |
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12/2014 - 14/03/2014
Fumagalli, I; Parolini, N.; Verani, M.
Shape optimization for Stokes flow: a reference domain approach | Abstract | | In this paper we analyze a shape optimization problem, with Stokes equations as the state problem, defined on a domain with a part of the boundary that is described as the graph of the control function. The state problem formulation is mapped onto a reference domain, which is independent of the control function, and the analysis is mainly led on such domain. The existence of an optimal control function is proved, and optimality conditions are derived. After the analytical inspection of the problem, finite element discretization is considered for both the control function and the state variables, and a priori convergence error estimates are derived. Numerical experiments assess the validity of the theoretical results. |
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11/2014 - 28/02/2014
Taddei, T.; Quarteroni, A.; Salsa, S.
An offline-online Riemann solver for one-dimensional systems of conservation laws | Abstract | | In this paper we present a new technique based on two different phases, here called offline and online stages, for the solution of the Riemann problem for one-dimensional hyperbolic systems of conservation laws. After theoretically motivating our offline-online technique, we prove its effectiveness by means of two numerical examples. |
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10/2014 - 17/02/2014
Antonietti, P.F.; Dedner, A.; Madhavan, P.; Stangalino, S.; Stinner, B.; Verani, M.
High order discontinuous Galerkin methods on surfaces | Abstract | | We derive and analyze high order discontinuous Galerkin methods for
second-order elliptic problems on implicitely defined surfaces in R^3. This is done by carefully adapting the unified discontinuous Galerkin framework of [D.N. Arnold, F. Brezzi, B. Cockburn, and L.D. Marini, SIAM J. Numer. Anal., 2002] on a triangulated surface approximating the smooth surface. We prove optimal error estimates in both a (mesh dependent) energy and L^2 norms. |
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09/2014 - 12/02/2014
Chen, P.; Quarteroni, A.
A new algorithm for high-dimensional uncertainty quantification problems based on dimension-adaptive and reduced basis methods | Abstract | | In this work we develop an adaptive and reduced computational framework based on dimension-adaptive hierarchical approximation and reduced basis method for solving high-dimensional uncertainty quantification (UQ) problems. In order to tackle the computational challenge of curse-of-dimensionality commonly faced by these problems, we employ a dimension-adaptive tensor-product algorithm [29] and propose a verified version to enable effective removal of the stagnation phenomenon besides automatically detecting the importance and interaction of different dimensions. To reduce the heavy computational cost of UQ problems modelled by partial differential equations (PDEs), we adopt a weighted reduced basis method [18] and develop an adaptive greedy algorithm in combination of the previous verified algorithm for efficient construction of an accurate reduced basis approximation space. The effectivity, efficiency and accuracy of this computational framework are demonstrated and compared to several other existing techniques by a variety of classical numerical examples. Keywords: uncertainty quantification, curse-of-dimensionality, generalized sparse grid, hierarchical surpluses, reduced basis method, adaptive greedy algorithm, weighted a posteriori error bound
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