Numerical Homogenization Based Fast Solver for Multiscale PDEs

Numerical Homogenization Based Fast Solver for Multiscale PDEs

Hausdorff Center for Mathematics via YouTube Direct link

Intro

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1 of 17

Intro

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Numerical Homogenization Based Fast Solver for Multiscale PDEs

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  1. 1 Intro
  2. 2 Model Problem
  3. 3 Numerical Resolution of Elliptic Operator
  4. 4 Low dimensionality of Solution Space
  5. 5 Bayesian Framework for Numerical Homogenization
  6. 6 Variational Formulation for the Basis Elements
  7. 7 Two Scale Decomposition and Optimality
  8. 8 Accuracy of Localization
  9. 9 RPS: An exponential decaying basis
  10. 10 A Hierachy of Exponential Decay Basis
  11. 11 Interpolation and restriction matrices/operators
  12. 12 Algorithm for Exact Gamblet transformation
  13. 13 Algorithm for Fast (Localized) Gamblet Transform
  14. 14 Gamblet: A Multiresolution Decomposition
  15. 15 Property of Exponential Decaying Basis
  16. 16 Properties of Gamblet Decomposition
  17. 17 Convergence of Gamblet based Multigrid

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