Advances in Numerical Simulation in Physics and Engineering

1. Front Matter

   Pages i-xi

   PDF

2. Courses

   1. Front Matter

      Pages 1-1

      PDF

   2. Fundamental Aspects in Modelling the Constitutive Behaviour of Fibered Soft Tissues

      • Begoña Calvo, Estefanía Peña

      Pages 3-49

   3. Some Remarks on Avalanches Modelling: An Introduction to Shallow Flows Models

      • Enrique D. Fernández-Nieto, Paul Vigneaux

      Pages 51-106

   4. Introduction to Stochastic Calculus and to the Resolution of PDEs Using Monte Carlo Simulations

      • Emmanuel Gobet

      Pages 107-178

   5. Structure-Preserving Shock-Capturing Methods: Late-Time Asymptotics, Curved Geometry, Small-Scale Dissipation, and Nonconservative Products

      • Philippe G. LeFloch

      Pages 179-222

3. Talks

   1. Front Matter

      Pages 223-223

      PDF

   2. Gradient Calculus for a Class of Optimal Design Problems in Engineering

      • Carlos Castro

      Pages 225-243

   3. Medical Image Processing: Mathematical Modelling and Numerical Resolution

      • Emanuele Schiavi, Juan Francisco Garamendi, Adrián Martín

      Pages 245-265

   4. On Probabilistic Analytical and Numerical Approaches for Divergence Form Operators with Discontinuous Coefficients

      • Denis Talay

      Pages 267-296

The book is mainly addressed to young graduate students in engineering and natural sciences who start to face numerical simulation, either at a research level or in the field of industrial applications. The main subjects covered are: Biomechanics, Stochastic Calculus, Geophysical flow simulation and Shock-Capturing numerical methods for Hyperbolic Systems of Partial Differential Equations. The book can also be useful to researchers or even technicians working at an industrial environment, who are interested in the state-of-the-art numerical techniques in these fields. Moreover, it gives an overview of the research developed at the French and Spanish universities and in some European scientific institutions. This book can be also useful as a textbook at master courses in Mathematics, Physics or Engineering.

• avalanche and Tsunami modeling
• mathematical modeling in biosciences
• numerical methods for PDEs
• schock-capturing and structure preserving numerical methods
• stochastics PDE
• partial differential equations

• Facultad de Ciencias, Universidad de Málaga, Málaga, Spain

  Carlos Parés

• Facultad de Informática, Universidade da Coruña, A Coruña, Spain

  Carlos Vázquez

• Centre de Mathématiques Appliquées, CNRS and Ecole Polytechnique, Paris, France

  Frédéric Coquel

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