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