Separated Representations and PGD-Based Model Reduction

1. Front Matter

   Pages i-vii

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2. Model Order Reduction based on Proper Orthogonal Decomposition

   • Elías Cueto, Francisco Chinesta, Antonio Huerta

   Pages 1-26

3. PGD for solving multidimensional and parametric models

   • Francisco Chinesta, Elías Cueto, Antonio Huerta

   Pages 27-89

4. PGD in linear and nonlinear Computational Solid Mechanics

   • Pierre Ladevèze

   Pages 91-152

5. Fundamentals of reduced basis method for problems governed by parametrized PDEs and applications

   • Gianluigi Rozza

   Pages 153-227

The papers in this volume start with a description of the construction of reduced models through a review of Proper Orthogonal Decomposition (POD) and reduced basis models, including their mathematical foundations and some challenging applications, then followed by a description of a new generation of simulation strategies based on the use of separated representations (space-parameters, space-time, space-time-parameters, space-space,…), which have led to what is known as Proper Generalized Decomposition (PGD) techniques. The models can be enriched by treating parameters as additional coordinates, leading to fast and inexpensive online calculations based on richer offline parametric solutions. Separated representations are analyzed in detail in the course, from their mathematical foundations to their most spectacular applications. It is also shown how such an approximation could evolve into a new paradigm in computational science, enabling one to circumvent various computational issues in a vast array of applications in engineering science.

• Computational Solid Mechanics
• Orthogonal Decomposition
• Proper Generalized Decomposition
• Simulation Techniques

• Ecole Centrale de Nantes, Nantes, France

  Francisco Chinesta

• Ecole Normale Supérieure de Cachan, Cachan, France

  Pierre Ladevèze

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