Preconditioners

• The why and how
  • Cost trade-off
  • Left and right preconditioning
• Jacobi Preconditioning
  • Block Jacobi Methods
  • Discussion
• SSOR preconditioning
• Incomplete Factorization Preconditioners
  • Creating an incomplete factorization
    • Solving a system with an incomplete factorization preconditioner
  • Point incomplete factorizations
    • Fill-in strategies
    • Simple cases: and -
    • Special cases: central differences
    • Modified incomplete factorizations
    • Vectorization of the preconditioner solve
    • Parallelizing the preconditioner solve
  • Block factorization methods
    • The idea behind block factorizations
    • Approximate inverses
    • The special case of block tridiagonality
    • Two types of incomplete block factorizations
  • Blocking over systems of partial differential equations
  • Incomplete LQ factorizations
• Polynomial preconditioners
• Preconditioners from properties of the differential equation
  • Preconditioning by the symmetric part
  • The use of fast solvers
  • Alternating Direction Implicit methods