Parallel Numerical Libraries

1. Introduction to FORTRAN Programming Language
2. Set of Tools for Numerical Computing
o Trilinos, Eigen, Armadillo, MKL
o PETSc a nadstavby (SLEPc, TAO, libMesh, Deal.II, FEniCS)
3. BLAS Specification (Basic linear algebra subroutines)
o Existing Implementations (ATLAS, GotoBLAS, MKL, CUBLAS)
4. Methods for Solving Dense Systems of Linear Equations
o Storage of Dense Matrices
o Blocking for Efficient Utilization of Processor Cache Memory
o Indefinite or Singular Matrix Systems of Linear Equations and Their Solution
o Stabilization through Pivotization and RBT (Random Butterfly Transformation) method
o Existing Implementations (LINPACK, LAPACK, ScaLAPACK, MKL, CULA, PLASMA, MAGMA)
5. Methods for Solving Sparse Systems of Linear Equations
o Storage of Sparse Matrices (CSR, CSC, …)
o Recasting for Retaining Sparsity
o Graph Methods (METIS and other)
o Multi-frontal Method
o Super-nodal Method
o Existing Implementations (MUMPS, SuperLU, PaStiX, PARDISO)
6. Methods for Solving Large-scale Eigenvalue Problems
o QR decomposition, Connection with Cholesky Decomposition
o Spectral and Singular Value Decomposition
o Iterative Methods
o Existing Implementations (e.g. ARPACK, BLOPEX, FEAST, MKL)
7. Preconditioning, Domain Decomposition, and Multigrid Methods
o Existing Implementations (Hypre, Trilinos, PETSc)
8. Methods of Discretization in HPC Context
o FDM, FEM
o Existing Implementations (libMesh, Deal.II, FEniCS)