Jun 11, 7:30 am
|
First Day Info Text Books MS & DD
|
Jun 11, 5:02 pm
|
Sunday, June 7 class by Prof. Y. Efendiev
|
Jun 12, 8:00 am
|
Office Hours in Office 4105, Building 1.
|
Jun 14, 1:00 pm
|
Lecture 3 files: Review of Jun12 class, Review of FEM 1D
|
Jun 18, 8:00 am
|
Lecture 4 files: Intro Analysis, Review FEM2D
|
Jun 22, 11:11am
|
Jun 19, Jun 21 class:
- Finished FEM2D
- Weak Formulations Revised: First order
formulation, several weak formulations (at least 4,
including weak boundary conditions),
- Review Chapter 1 of E.H.
|
Jun 28
|
Jun 25, Jun 26 and Jun 28 class:
- Multiscale basis function construction
- Boundary condition: Linear, 1D aux. along edge, oversampling
- Global coupling: Galerkin, Petrov Galerkin
- Computations involved: basis functions, Global coarse matrix
- Computations in the case of RV
- Downscaling and upscaling operations
- Linear algebra computation of Global matrix and local problems solutions
- Performance
- Chapter 2 E.H. (notes here)
|
July 3
|
July 2 and 3 classes (Chapter 1 of TW, 1.1, 1.2, 1.4, 1.5):
- Intro DD: Alternating Schwarz 2D, 1D examples
- Matrix form of the Alternating Schwarz
- One level multiplicative method and preconditioner
- One level additive method and preconditioner
- Two level preconditioner
- Presentation here
|
July 12
|
July 5 class (Appendix B of TW+Class Notes):
- Review of Iterative methods: Richardson and CG
- Convergence of CG (Back to this later)
- Schur complement idea (General concept)
- Application of Schur complement (non-overlapping two subdomains decomposition)
July 9 class (Chapter 1 of TW, 1.3)
- Application of Schur complement (non-overlapping two subdomains decomposition)
- Subdomain matrix form, global matrix form
- Local Schur complement
- Subassembly of global Schur complement
- Schur complement operator (Dirichlet-to-Neumann operator, Steklov-Poincaré operator)
- An equation for the Dirichlet value on the interface (or trace on the interface). ==> primal formulation
- Equation ===> Schur complement
- Preconditioners===> Dirichlet-Neumann iteration, Neumann-Neumann method
- Partition of Identity matrix
- An equation for the Neumann value on the interface (or flux on the interface)===> Dual formulation
- Equation==> a FETI formulation
- Preconditioners===> Neumann-Dirichlet iteration, Dirichlet-Dirichlet method
- Partition of Identity matrix
- Introduction to the multi-subdomain case (Back to this later)
- Added July 12:
- Optimality, Scalability
- General comments on convergence rates. quasi-optimality.
- Robustness
|
|
===>PART I ENDS HERE ||||||| HERE STARTS PART II====>
|
July 12
|
July 10 class by Y. Efendiev:
- Non-linear equations. Examples: Linear, Richards, Forchheimer
- Non-linear
Homogenization/Upscaling: Expansion, cell problem, look-up table.
Examples: Linear, Richards non-separable, Richards separable, comments.
- Numerical non-linear homogenization
- Non-linear miltiscale finite element method
- Comments
- Other topics:
- Homogenization of ordinary differential equations
- Homogenization of Stokes equation in perforated domains==>Darcy equation
- Comments
|
July 14
|
July 12 class:
- Conservation properties of solutions in subdomains
- Finite Volume Discretization review.
- Multiscale Finite Elements with a Finite Volume global coupling
- Conservation only in coarse blocks. Comments on getting conservation in the fine scale.
|
|
July 16 class Part I:
- Review of Mixed Finite Element Methods. Raviart-Thomas Elements
- Multiscale Mixed Finite Element Methods.
------------------------------
July 16 class Part II:
- Condition number of the additive method
- Convergence of Richarson Iteration and relaxation parameter
- Convergence of CG
- Condition number of the Schur complement
|
|
July 17 class (by Antti Niemi):
|
|
July 19 class:
|