1. Introduction to Scientific Computing II
Preconditioned Conjugate Gradient Method
&
Iterative Solvers Overview
Dr. Miriam Mehl

2. PCG – Idea convergence rate cg: Solve system M-1Ax=M-1b
better condition number k
M-1 easy to apply

3. PCG – Algorithm

4. PCG – Algorithm

5. PCG – Preconditioner (Jacobi) SSOR incomplete Cholesky decomposition
incomplete LU decomposition
(algebraic) multigrid

6. Iterative Solvers – Parallelisation
Jacobi
inherently parallel

7. Iterative Solvers – Parallelisation
Gauss-Seidel/SOR
domain decomposition
no equivalent solver!!!

8. Iterative Solvers – Parallelisation
multigrid
domain decomposition
idle times!!!

9. Iterative Solvers – Parallelisationcg
inherently parallel

10. Iterative Solvers – Overview
efficiency
ease of use
parallelisation
Jacobi - +
Gauss-Seidel o
SOR
multigrid cg