Lecturer: Jed Brown, PhD student, VAW, ETH Zurich

PDF version. Updates will be posted here.

Update 2009-01-27: slides available for lecture 2

Update 2009-01-29: slides available for lecture 3

Update 2009-01-29: References

Update 2009-02-05: slides available for lecture 5

Time and place

  • Five lectures: Tuesday and Thursday, 13:00 to 14:00
  • Chapman building, room 106

What is a scalable solver?

Stokes Scaling
  • A scalable solver can solve N equations in N unknowns with O(N) work.
  • Newton-Krylov methods offer:
    • Quadratic convergence on the nonlinearity
    • Parallel scalability and mesh-independence for the linear solve

Is it time to look at your solver?

  • Is your solver using significantly more time or memory than the physics?
  • Is your time stepping limited by stability?
  • Are you putting loops around the analysis?

Proposed schedule

  • Jan 22: Nonlinear systems
    • Motivation for coupled implicit methods
    • Scalability
    • Newton's method for large systems
    • Globalization
  • Jan 27: Linear solvers slides (pdf)
    • Limitations of direct methods
    • Krylov methods
    • Representation of matrices and Jacobian-free methods
    • Preconditioners for simple definite problems
    • Parallel scalability
  • Jan 29: Constraints and coupling slides (pdf)
    • Preconditioners for indefinite problems
    • Preconditioners for multi-physics
  • Feb 3: Parallel software day: PETSc
    • Generic solver components
    • Physics-based preconditioners
    • Working with legacy code
  • Feb 5: Higher order finite elements slides (pdf)
    • High-order elements at the cost of low-order elements
    • Exploiting the memory hierarchy and tensor-product operations

Schedule and content are flexible, let me know if you have requests.

Have a look at my AGU poster for a bit of a preview.


The Knoll and Keyes paper is especially recommended. Please email me if you need a copy of these or anything else.