Corso di Metodi Numerici per EDP 3 (ex Calcolo Scientifico (Parallelo)), A.A. 2013/14

Il corso verte sulle architetture ed algoritmi paralleli nel calcolo scientifico contemporaneo. Verranno studiati sia la costruzione ed analisi di algoritmi paralleli per problemi di calcolo scientifico, che la loro implementazione su macchine parallele del nostro Dipartimento e di centri di calcolo nazionali.

Modalita` d'esame: compitino a fine corso + prova orale (con eventuale progetto)

Materiale del corso: slides disponibili online (vedi sotto), tratte da diversi corsi online di calcolo parallelo.

Possibili libri di testo:
- A. Grama, A. Gupta, G. Karypis, V. Kumar, Introduction to Parallel Computing, Addison Wesley, 2003
- L. R. Scott, T. Clark, B. Bagheri, Scientific Parallel Computing, Princeton University Press, 2005


Tutorial for cluster ulisse.mat.unimi.it (file pdf), MPI timing subroutines in C (file pdf),


1. Introduction (file ppt)

2. Architectures (file ppt)

3. Networks (file ppt)

4. Interprocessor communications: point-to-point, collective, new version (from p. 27)

4bis. Interprocessor communications: more detailed algorithms

5. Parallel algorithm design

6. Parallel programming, MPI: message passing interface (more on send/receive , file ppt)

MPI homepage, tutorials, a set of exercises

7. Parallel performance

8. Vector and matrix products (Cannon and DNS algorithms + pipelined LU , file ppt)

9. LU factorization (dettagli LU con overlap)

10. Cholesky factorization

11.1 Triangular systems, 11.2 Tridiagonal systems

12.1 PETSc homepage, 12.2 PETSc introductions (tutorials) , (12.3 PETSc introduction) .

13. Iterative methods for linear systems

14. QR factorization

15. Eigenvalues

16. Nonlinear equations and ODEs

17.1 Partial Differential Equations

17.2 Domain Decomposition methods,

17.3 Abstract Schwarz theory (Ch. 2 in Toselli and Widlund DD book), condition number bound for overlapping Schwarz (Ch. 3 in Toselli and Widlund DD book),


Topics for final projects:

parallel Mat-Mat algorithms
Parallel LU
Parallel QR
eigenvalues: preconditioned Krylov methods
eigenvalues: parallel divide and conquer
eigenvalues: parallel Jacobi
parareal algorithms for ODEs and PDEs
GPUs in PETSc
Parmetis and graph partitioning algorithms