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PGD in computational mechanics

PGD in computational mechanics. F. Chinesta, A. Leygue EADS Chair, Ecole Centrale of Nantes Reduced Bases Workshop. Computational mechanics. The past. The dream. PGD & …. 1 – Models defined in high dimensional spaces; 2 – Separating the physical space;

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PGD in computational mechanics

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  1. PGD in computational mechanics F. Chinesta, A. Leygue EADS Chair, Ecole Centrale of Nantes Reduced Bases Workshop

  2. Computational mechanics • The past • The dream

  3. PGD & … 1 – Models defined in high dimensional spaces; 2 – Separating the physical space; 3 – Parametric models: optimization, inverse methods and simulation in real time; 4 – Miscellaneous.

  4. 1 - Multidimensional models

  5. JNNFM, 2006

  6. Successive enrichment: R S S R

  7. Variants: - Newton linearization; - Residual minimization in the case of non-symmetric operators; - Other more efficient and optimal constructors are in progress.

  8. Transient: INNFM 2007 Extension of the radial approximation, Ladeveze 1985 Non linear models: AR 2007 Non linear models: CMS 2010 Newton and advanced fixed point

  9. BCF descriptions: MSMSE 2007 Quantum chemistry & Master Equation: IJMCE 2008, EJCM 2010 Complex flows: ACME 2009, MCS 2010

  10. 2 - Separating the space … CMAME 2008 Boundary conditions and separating non hexahedral domains IJNME 2010

  11. 3D modeling in plate domains 3D solution with 2D complexity CMAME, In press

  12. Shells FEM solution: times steps, implicit PGD solution y x using matlab z

  13. 3 - Parametric modeling

  14. allows the solution of a single problem instead the many solutions required by usual strategies in: Optimization & Inverse identification is explicitly available

  15. accounting for variability

  16. Parametric solution computed off-line with all the sources of variability considered as extra-coordinates On-line processing of such solution in real time and using light computing platforms: e.g. smartphones, …

  17. Parametric modeling: MCS 2010, ACME 2010, JNNFM 2010 Process optimization: Composites Part A, 2011 Shape optimization: ACME 2010 Inverse identification: JNNFM 2011 Control & DDDAS: CMAME, MCS - Submitted Accounting for variability: CMAME In press Using smarthphones: CMAME In press, CMAME Submitted

  18. 4 – Miscellaneous Error estimator: CMAME 2010 Coupling PGD & FEM: IJMCE 2011 Coupled models & multi-scale: IJNME 2010, IJMF 2010

  19. Time multi-scale & parallel time integration: IJNME 2011, In press

  20. PGD based transient boundary element discretizations: EABE 2011 Convective stabilization: - Separating and then stabilizing - Stabilizing and then separating Computational Mechanics, Submitted

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