Smoother Basic Principles Jacobi ← LOW MODES→}<一 HIGH MODES 000 02 0000 14161820 mode k v(modek-2) n=19 15(mode k=15) Is Jacobi a smoother? →NO SMA-HPC⊙2003MT Iterative Methods: Multigrid Techniques 5
Smoother Basic Principles Under-Relaxed Jacobi 05 1/2 R=R3+(1-)0 ①=23 -5 (UNSTABLE) =1 mode k 入(a)=u(R)+(1-a)=1-c(1-入(E)), 1=1 SMA-HPC⊙2003MT Iterative Methods: Multigrid Techniques 6
Smoother Basic Principles Under-Relaxed Jacob Iterations required to reduce an error mode by a factor of 100 n=19 0=1 500 -0=23 8101214161820 mode k SMA-HPC⊙2003MT Iterative Methods: Multigrid Techniques 7
Smoother Basic Principles Gauss-Seidel Recall -06 mode k =19 Is Gauss-Seidel a good smoother? SMA-HPC⊙2003MT Iterative Methods: Multigrid Techniques 8
Smoother Basic Principles Gauss-Seidel Iterations required to reduce an a error mode by a factor of 100 n=19 gEz 0246810121416182 node k GS is a good smoother SMA-HPC⊙2003MT Iterative Methods: Multigrid Techniques 9