MATH 453: High-Performance Numerical Computing

Instructor: Shahriar Afkhami
Email: shahriar.afkhami@njit.edu
Phone: (973) 596-5719
Office: 623 Cullimore Hall
Office Hours: TR:1-2 PM, and by appointment





Some useful resources:

1- Numerical Linear Algebra by L. N. Trefethen and D. Bau, SIAM.
2- Parallel Programming in OpenMP by Chandra et al.,

Course Description: 

Week 1: Finite difference numerical methods; Iterative methods, Jacobi, Gauss-Seidel.

Week 2: Introduction to parallel computing.

Week 3: Introduction to Open MP; Parallel matrix and vector operations.

Week 4: Introduction to Open MP; Parallelizing iterative methods with Open MP.

Week 5: Introduction to Open MP; Performance metrics.

Week 6: Finite difference numerical methods - 2D Poisson equation; Multigrid methods.

Week 8-9: Cojugate Gradient method. Iterative method for eigenvalues. Solving non-linear system of equations.

Week 9-10: Introduction to Open MPI; Parallelizing iterative methods with Open MPI.




Announcements:

 -- Welcome to Math 453!
  * Information about NJIT AFS:

https://ist.njit.edu/accessing-afs/

  * NJIT HPC resources:

https://wiki.hpc.arcs.njit.edu/index.php/Main_Page

  * Shell Basics: PDF

  * Intro to HPC: LINK

  * NJIT-HPC: PDF


Homework:
Week 1:
  Write programs to solve a system, Ax=b, by the Jacobi and Guass-Seidel iterative methods.
  Compare the above methods with the relaxation method.

Lecture Notes:
Week 1:
  Algorithms for Jacobi and Gauss-Seidel methods. Relaxation method.
  1-D heat equation. Explicit, implicit, and Crank-Nicolson finite difference methods. Notes.pdf

Codes:
Week 1:
  Gauss-Seidel Code in C: G-S.c


Homework:
Week 3: HW3

Lecture Notes:
Week 3:
  Introduction to Open MP; Parallelizing iterative methods with Open MP. Notes.pdf
  Lawrence Livermore National Laboratory Intro to OpenMP

Codes:
Week 3:
  OpenMP Code in C: Codes


Lecture Notes:
Week 5:
  Introduction to Open MP; Parallelizing iterative methods with Open MP. Notes.pdf

Codes:
Week 5:
  OpenMP Code Matrix Multiplication: mm.c
  Code Jacobi Iterative Method: jacobi.c

Homework:
Week 5: HW5


Lecture Notes:
Week 8:
  Finite difference numerical methods - 2D Poisson equation; Multigrid methods. Notes.pdf

Codes:
Week 8:
  Code Multigrid Iterative Method: multigrid.c


Lecture Notes:
Week 9:
  Cojugate Gradient method Notes.pdf


Lecture Notes:
Week 9:
  Iterative method for eigenvalues Notes.pdf


Lecture Notes:
Week 10-11:
  Introduction to Open MPI Notes.pdf
  Lawrence Livermore National Laboratory Intro to Open MPI


Codes:
Week 10-11:
  Parallelizing iterative methods with Open MPI: jacobi_mpi.c