Parallel and Distributed Numerical Algorithms and Tools

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Not Required

Course Contents

Message passing computing (MPI): Communicators and groups, derived data types, virtual topologies, parallel I / O, remote memory access and dynamic memory management. Graph theory. Area parsing and graphic segmentation algorithms. Numerical Algorithms: Canon, Fox, DNS Algorithms. Direct Methods: Gauss Elimination, LU Decomposition, QR factoring. Recursive methods: Jacobi, Gauss-Seidel, SOR. Red-Black ranking. Thomas algorithm. Parallel algorithms for Ordinary and Partial Differential Equations: Multiple-staining algorithms. Hybrid programming: OpenMP + MPI. Non-stationary iterative methods: CG and GMRES.

Weekly Schedule

1) Message Passing Computing: Communicators and Groups, Derived Data Types.
2) Virtual Topologies
3) Parallel I/O, Remote Memory Access and Dynamic Memory Management
4) Graph Theory
5) Domain Decomposition and Graph Partitioning Algorithms
6) Numerical Algorithms: Matrix Multiplications Canon, Fox, DNS Algorithms
7) Dense Matrix Operations: Direct Methods Gauss Elimination, LU Decomposition, Factorizations
8) Midterm Exam
9) Iterative Methods and Sparse Matrices: Jacobi, Gauss-Seidel, SOR, Red-Black Ordering, Thomas Algorithm
10) Algorithms for ODE’s and PDE’s based on Finite Difference: Multi-coloring Algorithms
11) Algorithms for ODE’s and PDE’s based on Finite Difference: Multi-coloring Algorithms II
12) Multi-level Programming: OpenMP+MPI and OpenMPI
13) Non-Stationary Matrix Methods: CG and GMRES
14) Performance İssues and Parallel Profiling
15) Performance İssues and Parallel Profiling II

Recommended or Required Reading

1- Parallel Programming in C with MPI and OpenMP, Michael J. Quinn, Mc Graw Hill, 2003.
2- Using OpenMP, Barbara Chapman et al., MIT press, 2008.
3- Parallel Algorithms, Casanova H., Legrand A. and Robert Y., CRC Press, 2009.
4- Parallel Algorithms for Matrix Computations, K. A. Gallivan at al., SIAM, 1990
5- Principles of Parallel Programming, Calvin Lin and Lawrence Snyder, Pearson International, 2009.

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
5) Modelling
6) Group Study
7) Simulation
8) Case Study
9) Lab / Workshop
10) Self Study
11) Problem Solving
12) Project Based Learning

Assessment Methods and Criteria

Contribution of Semester Studies to Course Grade	50%
Number Percentage Semester Studies Quiz 1 50% Project 1 50%
Contribution of Final Examination to Course Grade	50%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Required