Оглавление секции
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- Lecture 10. Discretization of PDE: overview of FEM. Direct and iterative methods for sparse linear systems: comparison. General formulation of iterative methods and convergence criterion
- Lecture 11. Classical iterative methods. Simple iteration, Jacobi, Gauss-Seidel, Successive Over Relaxation (SOR), Symmetric Successive Over Relaxation (SSOR) and their variations
- Lecture 12. Projection methods. 1D projection methods: Steepest Descent Method (SDM), Minimal Residual Iteration Method (MRIM), Residual Norm Steepest Descent Method (RNSD)
- Lecture 13. Krylov subspace methods based on Arnoldi’s orthogonalization. Full Orthogonalization method (FOM)
- Lecture 14. Krylov subspace methods based on Arnoldi’s orthogonalization. Generalized Minimal Residual method (GMRES)
- Lecture 15. Comparison of FOM and GMRES. Methods based on Lacnzoc orthogonalization for symmetric (Hermitian) matrices: Lanczos method for symmetric systems, Direct Lanczos, Conjugate Gradient (CG), Generalized Conjugate Residual (GCR) and biorthogonalization. Methods based on Lacnzoc orthogonalization for nonsymmetric (non-Hermitian) matrices: Lanzos method for nonsymmetric systems, Biconjugate Gradient (BiCG).Preconditioning techniques. Examples of preconditioners. Examples of preconditioned methods: Preconditioned conjugate gradient method (PCG), Split Preconditioned Conjugate Gradient method (Split PCG), Left preconditioned Generalized Minimal Residual method (LP GMRES), Right preconditioned Generalized Minimal Residual method (RP GMRES)