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Credits Dept.
7.5 (6.0 ECTS) AC


Person in charge:  (-)

General goals

The main goal of this course is to provide a general view of the basic parallelization schemes used in numerical simulations. We present a review of the algorithmic structure of relevant computational science problems, like solving PDEs, ab-initio molecular dynamics or wave inversion problems. We review also the common numerical kernels in these applications. The parallelization approach using MPI and openMP for each kind of algorithm is presented.

Specific goals


  1. To learn the basic data partitioning schemes used in numerical simulations.
  2. To know different computational science applications.
  3. To understand the trade-offs from different numerical schemes.
  4. To know the practical problems associated with and hybrid MPI+openMP parallelization scheme.


  1. To identify application problems where parallel numerical simulation is critical.
  2. To use tools/algorithms/techniques from different computational science areas.
  3. To identify the potential problems associated with a numerical simulation.
  4. To have a common language with both scientists and computer scientists.


  1. To give computational support to user groups in industry and science.
  2. To work integrated in teams with different backgrounds.


Estimated time (hours):

T P L Alt Ext. L Stu A. time
Theory Problems Laboratory Other activities External Laboratory Study Additional time

1. Overview of numerical simulations: PDEs, ab-inito molecular dynamics, particle simulations.
T      P      L      Alt    Ext. L Stu    A. time Total 
6,0 0 0 0 0 4,0 0 10,0

2. Discretization techniques and FFT.
T      P      L      Alt    Ext. L Stu    A. time Total 
8,0 0 4,0 0 0 7,0 0 19,0

3. Numerical kernels I: Dense matrices operations.
T      P      L      Alt    Ext. L Stu    A. time Total 
8,0 0 4,0 0 0 7,0 0 19,0

4. Numerical kernels II: Sparse matrices operations.
T      P      L      Alt    Ext. L Stu    A. time Total 
10,0 0 6,0 0 0 8,0 0 24,0

5. Optimization problems and sensibility analysis.
T      P      L      Alt    Ext. L Stu    A. time Total 
8,0 0 4,0 0 0 6,0 0 18,0

Total per kind T      P      L      Alt    Ext. L Stu    A. time Total 
40,0 0 18,0 0 0 32,0 0 90,0
Avaluation additional hours 0
Total work hours for student 90,0

Docent Methodolgy

Theory classes building up concepts in a structured fashion and setting out the commitment required for their practical application. The classes will give a perspective of the future trends. Laboratory classes focusing on co-operative work in order to consolidate concepts, skills and competencies.

Evaluation Methodgy

The evaluation of the course will be based on a set of practical works. Each work must be presented as a technical report, including an introduction on the subject and a set of bibliographical references.

Basic Bibliography

  • Burnett, David Finite Element Analysis: From Concepts to Applications, Addison-Wesley, 1987.
  • Golub, G. and Van Loan, C. Matrix Computations, Academic Press, 1981.
  • Dongara, J.J., Duff, I.S., Sorensen, D., Van der Vost, H.A. Solving linear systems on Vector and Shared Memory Computers, SIAM, 1991.
  • Saad. Y. Iterative Methods for Sparse Linear Systems, PWS, 1996.
  • Kumar, V., Grama, A., Gupta, A., Kapyris, G. Parallel Computing, Benjamin Cummings, 1994.

Complementary Bibliography

(no available informacion)

Web links

(no available informacion)

Previous capacities

-  Undergraduate courses in linear algebra, mathematical analysis, numerical methods, optimization.
-  Undergraduate courses in structured programming.
-  Knowledge of C or Fortran90.
-  Notions of MPI, OpenMP, Pthreads.
-  Notions of computer architecture.


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