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Applied Mathematics: numerical analysis and scientific computing

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Reduced Order Methods for Computational Mechanics

The course aims to provide the basic aspects of numerical approximation and efficient solution of parametrized; PDEs for computational mechanics problem (heat and mass transfer, linear elasticity, viscous and potential flows) using reduced order methods.

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Topics in Computational Fluid Dynamics

Introduction to Fluid Mechanics, examples.
Constitutive laws
Incompressible flows. Navier-Stokes equations
Numerical methods for potential and thermal flows
Boundary layer theory
Thermodynamics effects, energy equation, enthalpy and entropy
Vorticity equations
Introduction to turbulence
Numerical methods for viscous flows: steady Stokes equations
Stabilization (SUPG) and inf-sup condition

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Entrance examination 2018 - Spring session

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Topics in Continuum Mechanics

Reminders on Linear Algebra and Tensor Calculus
Kinematics of deformable bodies
Eulerian and Lagrangian descriptions of motion
Balance laws of continuum mechanics: conservation of mass, balance of linear and angular momentum, energy balance and dissipation inequality
Constitutive equations
Fluid dynamics: the Navier Stokes equations
Solid mechanics: nonlinear and linearized elasticity
Selected topics from the mechanics of biological systems

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Magneto-active polymers: challenges in fabrication, testing, modelling and simulation

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On a certified smagorinsky reduced basis turbulence model

Rebollo TC, Ávila ED, Marmol MG, Ballarin F, Rozza G. On a certified smagorinsky reduced basis turbulence model. SIAM Journal on Numerical Analysis [Internet]. 2017 ;55:3047-3067. Available from: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c

A reduced order model for investigating the dynamics of the Gen-IV LFR coolant pool

Lorenzi S, Cammi A, Luzzi L, Rozza G. A reduced order model for investigating the dynamics of the Gen-IV LFR coolant pool. Applied Mathematical Modelling [Internet]. 2017 ;46:263-284. Available from: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85020006623&doi=10.1016%2fj.apm.2017.01.066&partnerID=40&md5=f6e5715037eb0ef2ecb9ae03f373294f

Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts

Ballarin F, Faggiano E, Manzoni A, Quarteroni A, Rozza G, Ippolito S, Scrofani R. Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts. Biomechanics and Modeling in Mechanobiology [Internet]. 2017 ;16:1373-1399. Available from: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd0

Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models

Martini I, Haasdonk B, Rozza G. Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models. Journal of Scientific Computing [Internet]. 2018 ;74:197-219. Available from: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a964

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