00414nas a2200109 4500008004100000245010800041210006900149300001100218100002100229700001700250856003700267 2018 eng d00aAccelerating the iterative solution of convection-diffusion problems using singular value decomposition0 aAccelerating the iterative solution of convectiondiffusion probl a1–211 aPitton, Giuseppe1 aHeltai, Luca uhttps://arxiv.org/abs/1807.0946700730nas a2200109 4500008004100000245008900041210006900130520032300199100002900522700002100551856004800572 2018 en d00aNon-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis0 aNonlinear GrossPitaevskii dynamics of a 2D binary condensate a n3 aWe present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.1 aMichelangeli, Alessandro1 aPitton, Giuseppe uhttp://preprints.sissa.it/handle/1963/3532301177nas a2200145 4500008004100000245008600041210006900127300001300196490000800209520068400217100001800901700002100919700002100940856007000961 2018 eng d00aNumerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves0 aNumerical study of the KadomtsevPetviashvili equation and disper a201704580 v4743 a

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

1 aGrava, Tamara1 aKlein, Christian1 aPitton, Giuseppe uhttps://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.045800437nas a2200121 4500008004100000245010800041210006900149300001400218490000800232100002100240700001700261856003700278 2018 eng d00aNURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces0 aNURBSSEM A hybrid spectral element method on NURBS maps for the  a440–4620 v3381 aPitton, Giuseppe1 aHeltai, Luca uhttps://arxiv.org/abs/1804.0827101212nas a2200109 4500008004100000245010500041210006900146520071800215100002100933700002100954856012700975 2017 eng d00aOn the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics0 aApplication of Reduced Basis Methods to Bifurcation Problems in 3 a

In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

1 aPitton, Giuseppe1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/application-reduced-basis-methods-bifurcation-problems-incompressible-fluid-dynamics02413nas a2200205 4500008004100000245015800041210006900199260001200268300000800280490000800288520159500296653004301891653002501934653002301959653003401982100002102016700002102037700002102058856012802079 2017 eng d00aComputational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology0 aComputational reduction strategies for the detection of steady b c09/2017 a5570 v3443 a

We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

10aParametrized Navier–Stokes equations10aReduced basis method10aStability of flows10aSymmetry breaking bifurcation1 aPitton, Giuseppe1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/computational-reduction-strategies-detection-steady-bifurcations-incompressible-fluid01002nas a2200109 4500008004100000245009900041210007000140520058100210100002900791700002100820856005100841 2016 en d00aNon-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics0 aNonlinear Schrödinger system for the dynamics of a binary conden3 aWe present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.1 aMichelangeli, Alessandro1 aPitton, Giuseppe uhttp://urania.sissa.it/xmlui/handle/1963/35266