Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes
暂无分享,去创建一个
Luca Heltai | Gianluigi Rozza | Francesco Ballarin | Filippo Salmoiraghi | L. Heltai | G. Rozza | F. Ballarin | F. Salmoiraghi
[1] T. Hughes,et al. Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .
[2] Niels Leergaard Pedersen,et al. Discretizations in isogeometric analysis of Navier-Stokes flow , 2011 .
[3] Alfio Quarteroni,et al. A discontinuous Galerkin reduced basis element method for elliptic problems , 2016 .
[4] J. Hesthaven,et al. Certified Reduced Basis Methods for Parametrized Partial Differential Equations , 2015 .
[5] Adrien Leygue,et al. The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer , 2013 .
[6] Jens Nørkær Sørensen,et al. Evaluation of Proper Orthogonal Decomposition-Based Decomposition Techniques Applied to Parameter-Dependent Nonturbulent Flows , 1999, SIAM J. Sci. Comput..
[7] Numérisation de documents anciens mathématiques,et al. Mathematical modelling and numerical analysis : Modélisation mathématique et analyse numérique. , 1985 .
[8] Laura Iapichino. Reduced Basis Methods for the Solution of Parametrized PDEs in Repetitive and Complex Networks with Application to CFD , 2012 .
[9] F. Chinesta,et al. A Short Review in Model Order Reduction Based on Proper Generalized Decomposition , 2018 .
[10] Mihai Anitescu,et al. Proper orthogonal decompositions in multifidelity uncertainty quantification of complex simulation models , 2014, Int. J. Comput. Math..
[11] Gianluigi Rozza,et al. Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows , 2014, J. Sci. Comput..
[12] A. Fowler,et al. Acid polishing of lead glass , 2011 .
[13] A. Quarteroni,et al. Numerical solution of parametrized Navier–Stokes equations by reduced basis methods , 2007 .
[14] Thomas W. Sederberg,et al. Free-form deformation of solid geometric models , 1986, SIGGRAPH.
[15] A. Quarteroni,et al. Shape optimization for viscous flows by reduced basis methods and free‐form deformation , 2012 .
[16] Luca Heltai,et al. Isogeometric analysis based reduced order modelling for incompressible viscous flows in parametrized shapes: applications to underwater shape design , 2015 .
[17] David J. Benson,et al. A multi-patch nonsingular isogeometric boundary element method using trimmed elements , 2015, Computational Mechanics.
[18] Zhendong Luo,et al. A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems , 2013, Math. Comput. Simul..
[19] Nadine Aubry,et al. On The Hidden Beauty of the Proper Orthogonal Decomposition , 1991 .
[20] A. Patera,et al. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations , 2007 .
[21] Thomas J. R. Hughes,et al. Trivariate solid T-spline construction from boundary triangulations with arbitrary genus topology , 2012, Comput. Aided Des..
[22] Ionel M. Navon,et al. An optimizing reduced order FDS for the tropical Pacific Ocean reduced gravity model , 2007 .
[23] Gianluigi Rozza,et al. A Reduced Basis Method for Evolution Schemes with Parameter-Dependent Explicit Operators , 2008 .
[24] Patrick Laborde,et al. A Reduced Basis Enrichment for the eXtended Finite Element Method , 2009 .
[25] G. Rozza,et al. Parametric free-form shape design with PDE models and reduced basis method , 2010 .
[26] D. Rovas,et al. Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods , 2002 .
[27] S. Ravindran. A reduced-order approach for optimal control of fluids using proper orthogonal decomposition , 2000 .
[28] S Niroomandi,et al. Real‐time simulation of surgery by reduced‐order modeling and X‐FEM techniques , 2012, International journal for numerical methods in biomedical engineering.
[29] Alfio Quarteroni,et al. Isogeometric analysis and proper orthogonal decomposition for parabolic problems , 2017, Numerische Mathematik.
[30] Gianluigi Rozza,et al. Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations , 2015 .
[31] Gianluigi Rozza,et al. Certified reduced basis approximation for parametrized partial differential equations and applications , 2011 .
[32] Thomas J. R. Hughes,et al. Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .
[33] Simona Perotto,et al. Space–time adaptive hierarchical model reduction for parabolic equations , 2015, Advanced Modeling and Simulation in Engineering Sciences.
[34] Thomas J. R. Hughes,et al. Patient-Specific Vascular NURBS Modeling for Isogeometric Analysis of Blood Flow , 2007, IMR.
[35] O. Anwar Bég,et al. Modeling and simulation in engineering sciences , 2016 .
[36] Gianluigi Rozza,et al. Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization , 2016, J. Comput. Phys..
[37] Zhendong Luo,et al. Reduced-Order Modeling of the Upper Tropical Pacific Ocean Model using Proper Orthogonal Decomposition , 2006, Comput. Math. Appl..
[38] B. Haasdonk,et al. REDUCED BASIS METHOD FOR FINITE VOLUME APPROXIMATIONS OF PARAMETRIZED LINEAR EVOLUTION EQUATIONS , 2008 .
[39] Alfio Quarteroni,et al. Spectral based Discontinuous Galerkin Reduced Basis Element method for parametrized Stokes problems , 2016, Comput. Math. Appl..
[40] Gianluigi Rozza,et al. Reduced basis methods for Stokes equations in domains with non-affine parameter dependence , 2009 .
[41] L. Heltai,et al. Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils , 2015 .
[42] A. Patera,et al. Certified real‐time solution of the parametrized steady incompressible Navier–Stokes equations: rigorous reduced‐basis a posteriori error bounds , 2005 .
[43] Bernard Haasdonk,et al. Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation , 2012, SIAM J. Sci. Comput..
[44] Simona Perotto,et al. Hierarchical Model Reduction for Advection-Diffusion-Reaction Problems , 2008 .
[45] G. Rozza,et al. On the stability of the reduced basis method for Stokes equations in parametrized domains , 2007 .
[46] Giancarlo Sangalli,et al. IsoGeometric Analysis: Stable elements for the 2D Stokes equation , 2011 .
[47] L. Heltai,et al. Nonsingular isogeometric boundary element method for Stokes flows in 3D , 2014 .
[48] Gianluigi Rozza,et al. Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants , 2013, Numerische Mathematik.
[49] Simona Perotto,et al. Hierarchical Local Model Reduction for Elliptic Problems: A Domain Decomposition Approach , 2010, Multiscale Model. Simul..
[50] B. Haasdonk,et al. A new local reduced basis discontinuous Galerkin approach for heterogeneous multiscale problems , 2011 .
[51] Gianluigi Rozza,et al. A Reduced Basis Model with Parametric Coupling for Fluid-Structure Interaction Problems , 2012, SIAM J. Sci. Comput..
[52] Stefan Volkwein,et al. Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics , 2002, SIAM J. Numer. Anal..
[53] John A. Evans,et al. ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE STEADY NAVIER–STOKES EQUATIONS , 2013 .
[54] Marina Rinaldi,et al. Reduced Basis method for Isogeometric Analysis: application to structural problems , 2015 .
[55] A. Patera,et al. A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations , 2005 .
[56] Henry J. Lamousin,et al. NURBS-based free-form deformations , 1994, IEEE Computer Graphics and Applications.
[57] Gianluigi Rozza,et al. Reduced Order Methods for Modeling and Computational Reduction , 2013 .
[58] Ionel Michael Navon,et al. An optimizing finite difference scheme based on proper orthogonal decomposition for CVD equations , 2011 .
[59] N. Nguyen,et al. An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .
[60] Thomas J. R. Hughes,et al. Isogeometric divergence-conforming B-splines for the unsteady Navier-Stokes equations , 2013, J. Comput. Phys..
[61] Stefan Turek,et al. Isogeometric Analysis of the Navier-Stokes equations with Taylor-Hood B-spline elements , 2015, Appl. Math. Comput..