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Numerical Analysis

Introduction to Mechanics of Solids, Fluids, and Biological Systems

  • Kinematics of deformable continua
  • Eulerian and Lagrangian descriptions of motion
  • The balance laws of continuum mechanics
  • Conservation of mass
  • Balance of linear and angular momentum
  • Constitutive Equations
  • Fluid dynamics: the Navier Stokes equations
  • Solid mechanics: nonlinear and linear elasticity
  • Selected topics from the mechanics of biological systems

Introduction to numerical analysis

The foundations of Numerical analysis

  • Resolution of linear systems with direct methods
  • Resolution of linear systems with iterative methods
  • Polynomial interpolation and projection
  • Numerical Integration
  • Numerical solutions of ODEs

Numerical Methods for PDEs

  • Finite Elements
  • Elliptic Problems
  • Parabolic Problems
  • Hyperbolic Problems

Numerical Analysis and Scientific Computing

The research deals with the analysis, development, application of mathematical models for the integration of complex systems. The analysis is conducted using mathematical methods in several fields such as linear algebra, approximation theory, partial differential equations, optimization and control. Solution methods are developed and applied to domains as diverse as (potential and viscous) flow dynamics, (linear and nonlinear) structural analysis, mass transport, heat transfer and in general to multiscale and multiphysics applications.

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