IRIS Pol. Torinohttps://iris.polito.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Thu, 24 Jun 2021 12:15:10 GMT2021-06-24T12:15:10Z10771A wavelet-based adaptive finite element method for advection-diffusion equationshttp://hdl.handle.net/11583/1398416Titolo: A wavelet-based adaptive finite element method for advection-diffusion equations
Abstract: MATH. MOD. METHS. APPL. SCI.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/11583/13984161997-01-01T00:00:00ZMultilevel stabilization of convection-diffusion problems by variable order inner productshttp://hdl.handle.net/11583/1398420Titolo: Multilevel stabilization of convection-diffusion problems by variable order inner products
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/11583/13984202001-01-01T00:00:00ZA hybrid model for the computationally-efficient simulation of the cerebellar granular layerhttp://hdl.handle.net/11583/2663139Titolo: A hybrid model for the computationally-efficient simulation of the cerebellar granular layer
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11583/26631392016-01-01T00:00:00ZBDDC preconditioners for continuous and discontinuous Galerkin methods using spectral/hp elements with variable local polynomial degreehttp://hdl.handle.net/11583/2522698Titolo: BDDC preconditioners for continuous and discontinuous Galerkin methods using spectral/hp elements with variable local polynomial degree
Abstract: Locally adapted meshes and polynomial degrees can greatly improve spectral element accuracy and applicability. A balancing domain decomposition by constraints (BDDC) preconditioner is constructed and analysed for both continuous (CG) and discontinuous (DG) Galerkin discretizations of scalar elliptic problems, built by nodal spectral elements with variable polynomial degrees. The DG case is reduced to the CG case via the auxiliary space method. The proposed BDDC preconditioner is proved to be scalable in the number of subdomains and quasi-optimal in both the ratio of local polynomial degrees and element sizes and the ratio of subdomain and element sizes. Several numerical experiments in the plane confirm the obtained theoretical convergence rate estimates, and illustrate the preconditioner performance for both CG and DG discretizations. Different configurations with locally adapted polynomial degrees are studied, as well as the preconditioner robustness with respect to discontinuities of the elliptic coefficients across subdomain boundaries. These results apply also to other dual–primal preconditioners defined by the same set of primal constraints, such as FETI-DP preconditioners.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11583/25226982014-01-01T00:00:00ZNumerical solution of partial differential equations in random domains: An application to wind engineering.http://hdl.handle.net/11583/1899323Titolo: Numerical solution of partial differential equations in random domains: An application to wind engineering.
Abstract: An application of recent uncertainty quantification techniques to Wind Engineering is presented. In particular, the study of the effects of small geometric changes in the Sunshine Skyway Bridge dock on its aerodynamic behavior is addressed. This results in the numerical solution of a proper PDE posed in a domain affected by randomness, which is handled through a mapping approach. A non-intrusive Polynomial Chaos expansion allows to transform the stochastic problem into a deterministic one, in which a commercial code is used as a black-box for the solution of a number of Reynolds-Averaged Navier-Stokes simulations. The use of proper Gauss-Patterson nested quadrature formulas with respect to a Truncated Weibull probability density function permits to limit the number of these computationally expensive simulations, though maintaining a sufficient accuracy. Polynomial Chaos approximations, statistical moments and probability density functions of time-independent quantities of interest for the engineering applications are obtained.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11583/18993232009-01-01T00:00:00ZFinite-Element Preconditioning of G-NI Spectral Methodshttp://hdl.handle.net/11583/2302863Titolo: Finite-Element Preconditioning of G-NI Spectral Methods
Abstract: Several old and new finite-element preconditioners for nodal-based spectral discretizations of -Delta u = f in the domain Omega = (-1, 1)(d) (d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of both condition number and computational efficiency. The computational domain covers the case of classical single-domain spectral approximations (see [C. Canuto et al., Spectral Methods. Fundamentals in Single Domains, Springer, Heidelberg, 2006]), as well as that of more general spectral-element methods in which the preconditioners are expressed in terms of local (upon every element) algebraic solvers. The primal spectral approximation is based on the Galerkin approach with numerical integration (G-NI) at the Legendre-Gauss-Lobatto (LGL) nodes in the domain. The preconditioning matrices rely on either P-1, Q(1), or Q(1), (NI) (i.e., with numerical integration) finite elements on meshes whose vertices coincide with the LGL nodes used for the spectral approximation. The analysis highlights certain preconditioners, which yield the solution at an overall cost proportional to Nd+1, where N denotes the polynomial degree in each direction.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11583/23028632010-01-01T00:00:00ZModelling and Subject-Specific Validation of the Heart-Arterial Tree Systemhttp://hdl.handle.net/11583/2584956Titolo: Modelling and Subject-Specific Validation of the Heart-Arterial Tree System
Abstract: A modeling approach integrated with a novel subject-specific characterization is here proposed for the assessment of hemodynamic values of the arterial tree. A 1D model is adopted to characterize large-to-medium arteries, while the left ventricle, aortic valve and distal micro-circulation sectors are described by lumped submodels. A new velocity profile and a new formulation of the non-linear viscoelastic constitutive relation suitable for the {Q, A} modeling are also proposed. The model is firstly verified semi-quantitatively against literature data. A simple but effective procedure for obtaining subject-specific model characterization from non-invasive measurements is then designed. A detailed subject-specific validation against in vivo measurements from a population of six healthy young men is also performed. Several key quantities of heart dynamics—mean ejected flow, ejection fraction, and left-ventricular end-diastolic, end-systolic and stroke volumes—and the pressure waveforms (at the central, radial, brachial, femoral, and posterior tibial sites) are compared with measured data. Mean errors around 5 and 8%, obtained for the heart and arterial quantities, respectively, testify the effectiveness of the model and its subject-specific characterization.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11583/25849562015-01-01T00:00:00ZAnalisi Matematica Ihttp://hdl.handle.net/11583/1851477Titolo: Analisi Matematica I
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11583/18514772008-01-01T00:00:00ZUncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategyhttp://hdl.handle.net/11583/2719883Titolo: Uncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategy
Abstract: A non-intrusive bifidelity strategy is applied to the computation of statistics of a quantity of interest (QoI) which depends in a non-smooth way upon the stochastic parameters. The procedure leverages the accuracy of a high-fidelity model and the efficiency of a low-fidelity model, obtained through the use of different levels of numerical resolution, to pursue a high quality approximation of the statistics with a moderate number of high-fidelity simulations. The method is applied first to synthetic test cases with outputs exhibiting either a continuous or a discontinuous behaviour, then to the realistic simulation of a flow in an underground network of fractures, whose stochastic geometry outputs a non-smooth QoI. In both applications, the results highlight the efficacy of the approach in terms of error decay versus the number of computed high-fidelity solutions, even when the QoI lacks smoothness. For the underground simulation problem, the observed gain in computational cost is at least of one order of magnitude.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11583/27198832019-01-01T00:00:00ZA multi-timestep Robin–Robin domain decomposition method for time dependent advection-diffusion problemshttp://hdl.handle.net/11583/2743311Titolo: A multi-timestep Robin–Robin domain decomposition method for time dependent advection-diffusion problems
Abstract: Many physical processes present separated evolution time scales in different regions, such as windblown sand in the desert. The evolution of bed-surface locally affects the sandy- wind flow, which erodes the sand in turns, while few meters higher from the ground the airflow is almost stationary. This and other applications suggest to improve the overall computational efficiency by locally adapting the time advancing step to the evolution in each region. We propose a multi-timestep Robin-Robin domain decomposition method, which uses mutually proportional time steps, based on a predictor-corrector strategy, cou- pled with linear interpolation in time. The resulting algorithm is completely segregated. Several numerical tests, obtained by the finite volume code OpenFOAM, are reported to show its stability and convergence properties.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11583/27433112019-01-01T00:00:00Z