Domain Descomposition and Large Scale Scientific Computing (250970) – Course 2024/25 PDF
Contents
Course Introduction 1.1 Matrix factorizations and inverses 1.2 QR & SVD 1.3 Eigenvalues of a matrix 1.4 Condition number 1.5 Ill-conditioning 1.6 Conditioning of the mass matrix 1.7 Conditioning of the Laplacian matrix 1.6 Gaussian elimination 1.7 Richardson and Steepest Descent Method 1.8 Conjugate Gradient Method 1.9 Combining Preconditioners 1.10 Krylov methods for indefinite and nonsymmetric matrices 1.1 Penalty Method 1.2 Lagrange Multipliers 1.3 Multi Point Constraints 1.1 Conjugate Gradient 1.2 GMRES 1.3 Others 1.4 Matrix Free Methods 1.5 Newton-Krylov approaches 1.1 - Diagonal Preconditioning 1.2 - ILU type preconditioning 1.3 - AMG
Dedication
14h Large group + 19h 36m Self Study4.1 Parallel architectures (shared vs distributed memory) 4.2 Parallel eficiency 4.3 Programming paradigms (OpenMP vs MPI) 4.4 Data structures in numerical linear algebra 4.5 Implementation of simple operations in MPI 4.6 HPC Assignements
Dedication
16h Laboratory classes + 22h 24m Self Study2.1 Motivation of DDM 2.1.1 Overlapping approach 2.1.2 Nonoverlapping approach 2.2 Overlapping subdomain algorithms 2.2.1 Additive Schwarz algorithms 2.2.2 Multiplicative Schwarz algorithms 2.3 Nonoverlapping subdomain algorithms 2.3.1 Dirichlet-Neumann 2.3.2 Neumann-Neumann 2.3.3 The case of many subdomains 3.1 Coarse level algorithms 3.2 Balancing Neumann-Neumann 3.3 BDDC 3.4 Implementation aspects 3.5 Numerical experimentation 3.6 Further topics FINAL ASSIGNMENT
Dedication
9h Large group + 6h Medium group + 21h Self Study