Parallel algorithms in Computational Mathematics
| Lecture: |
Dr. Sven Beuchler, Room KG 502, Tel. 9164 Thursday, 13.45 – 15.15, HS 11 |
| Tutorials: |
Dipl.-Ing. Clemens Pechstein, Room KG 503, Tel. 9169 Thursday, 15.30 – 17.00, HF 136 (about every 2 weeks) |
| Target audience: | Students of mathematics ≥ 5 semester, further interested students |
| ECTS: | Lecture: 3.00 ECTS credits, Tutorials: 1.50 ECTS credits |
| Required knowledge: | Linear Algebra, programming (C/C++ or Fortran), Numerical methods for partial differential equations |
| The lecture and the tutorials will be held in English if necessary. |
Lecture
- Introduction
- Why parallel computers?
- Classification of parallel computers due to Flynn
- Classification of parallel computers due to memory access
- Network topologies
- Performance measurement of parallel algorithms: Slide for Speed-Up
- Message passing
- Introduction
- Initialization programs in Fortran, programs in C
- Data exchange, routine for the computation of ln 2 in Fortran und C
- Parallelization of methods from Linear Algebra
- BLAS-routines, e.g., Adding two vectors, Multiplication by a scalar, scalar product, Storage of a matrix,...
- LU-Decomposition/Gauss-algorithm
- Iterative methods for the solution of systems of linear equations
- Parallel methods for the solution of systems of nonlinear equations
- Parallel methods for the solution of ordinary differential equations
- Domain decomposition for finite element methods
- Sequential algorithm
- Parallel FEM
- The parallele conjugate gradient method with Jacobi preconditioner
- Primal domain decomposition preconditioners
- The additive Schwarz method with applications
- FETI-preconditioners (if there is time)
Additional lecture: Thursday, April 10, 15.30 – 17.00, HS 11
Tutorials
| Nr. | Time | Room | Topic | Assignment |
|---|---|---|---|---|
| 1 | Th, April 03, 13.45–15.15 | HF 136 | Introduction to MPI | |
| 2 | Th, April 17, 15.30–17.00 | KG 519 | Parallelization of simple problems | |
| 3 | Mo, April 21, 12.45–14.15 | HF 136 | Graph partitioning (presentation by the PhD students) | |
| 4 | Th, May 15, 15.30–17.00 | HF 136 | Parallelization of FEM | |
| 5 | Th, June 5, 15.30–17.00 | HF 136 | Preconditioning I | |
| 6 | Th, June 12, 15.30–17.00 | HF 136 | Preconditioning II | |
| 7 | Th, June 26, 15.30–17.00 | HF 136 | Domain Decomposition |
Generation of a parallel cluster in NuMa pool in room KG 519:
- login with ssh to pool2-01.numa.uni-linz.ac.at
- login to pool2-0x with ssh
- lamboot -b -v hostfile
- The file hostfile contains the names of the computers
Further information
- To get an account at the NuMa pool contact Clemens Pechstein or directly Oliver Koch
- Official homepage of the MPI standard
- MPI-Tutorial of P. Jimack
last change:
2013-12-05
