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Model Order Reduction and Computational Homogenisation of Magnetorheological Elastomers

Explore model order reduction techniques for MREs, replacing expensive FEM with cheaper models for computational efficiency. Includes numerical studies & conclusions.

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Model Order Reduction and Computational Homogenisation of Magnetorheological Elastomers

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  1. Model Order Reduction and Computational Homogenisation of Magnetorheological Elastomers Benjamin Brands, Julia Mergheim, Denis Davydov and Paul Steinmann Chair of Applied Mechanics Friedrich-Alexander Universität Erlangen-Nürnberg 6th deal.II Users and Developers Workshop 2018, Trieste, 23rd - 27thJuly

  2. Model Order Reduction Replacing expensive numericalmodel (e.g FEM) bycheaperreducedmodelofacceptableaccuracy Online Stage employingthereducedmodel Offline Stage settingupthereducedmodel Meggy Computing Cluster at RRZE Erlangen Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  3. 1. Multiscale Modelling of MREs: Homogenisation 2. Model Order Reduction for Magnetomechanics 2.1 Reduced Basis Construction 2.2 GalerkinReduced Model 2.3 DEIM Reduced Model 2.4 GappyPOD Reduced Model 2.5 EC Reduced Model 3. Numerical Studies 4. Conclusion Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  4. 1. Multiscale Modelling of MREs: Homogenisation replace FEM microscalemodel withreducedmodel  reducingcomputationalcost Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  5. 1. Multiscale Modelling of MREs: Homogenisation Micro-scale problem Micro to macro transition: homogenised quantities Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  6. 2. Model Order Reduction for Magnetomechanics Fundamental assumption: Solution oftheproblem (e.gpPDE) resides in manifoldofsmalldimension Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  7. 2.1 Reduced Basis Construction Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  8. 2.1 Reduced Basis Construction: SVD and POD Singular Value Decomposition (SVD) Proper Orthogonal Decomposition (POD) Usingdeal.II‘sScaLAPACKwrappersfor fast computationof SVD/POD Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  9. 2.2 GalerkinReduced Model FEM model Galerkin ROM computationofresiduum and tangentmatrix and subsequent projectionrenderstheGalerkin ROM inefficient Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  10. 2.3 DEIM Reduced Model Chaturantabut & Sorensen 2010 DEIM ROM Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  11. 2.4 GappyPODReduced Model Emerson & Sirovich2007 GappyPOD ROM Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  12. 2.5 EmpiricalCubatureReduced Model Farhat et al. 2014, Hernández et al. 2016 Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | ESMC 2018, Bologna, 2nd - 6th July

  13. 2.5 EC Reduced Model EC ROM Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  14. 3. Numerical Studies: Problem Setting Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  15. 3. Numerical Studies: Problem Setting Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  16. 3.1 Numerical Studies: DEIM Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  17. 3.1 Numerical Studies: DEIM Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  18. 3.2 Numerical Studies: GappyPOD Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  19. 3.3 Numerical Studies: EC Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  20. 4. Conclusion Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  21. Acknowledgement: DAAD-UGC DIP Program Thank you for your patience! Questions? Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

  22. Benjamin Brands, Julia Mergheim, Denis Davydov & Paul Steinmann | deal.II workshop 2018, Trieste, 23rd - 27th July

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