Numerical Methods for Partial Differential Equations 3
A.Y. 2019/2020
Learning objectives
The course aims at providing the basic techniques concerning parallel computing for the numerical treatment of problems arising from the approximation of PDEs, and, more generally, from numerical linear algebra.
Expected learning outcomes
At the end of the course students wil have acquired the basic ideas of parallel programming, as well as the ability to implement some parallel algorithms for the solution of partial differential equations, and, more genearlly, for linear algebra problems.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
- Parallel architectures
- Communications: point-to-point, collective.
- Design of parallel algorithms.
- Parallel programming: MPI.
- Parallel performance.
- Parallel vector and matrix products.
- Parallel LU and Cholesky factorization.
- PETSc library.
- Iterative methods for linear systems.
- QR factorization and parallel numerical methods for eigenvalues.
- Domain decomposition methods for Partial Differential Equations.
- Communications: point-to-point, collective.
- Design of parallel algorithms.
- Parallel programming: MPI.
- Parallel performance.
- Parallel vector and matrix products.
- Parallel LU and Cholesky factorization.
- PETSc library.
- Iterative methods for linear systems.
- QR factorization and parallel numerical methods for eigenvalues.
- Domain decomposition methods for Partial Differential Equations.
Prerequisites for admission
Calcolo numerico 1
Teaching methods
Lectures and lab exercises.
Teaching Resources
- A. Grama, A. Gupta, G. Karipys, V. Kumar, Introduction to parallel computing, 2nd ed., Addison Wesley, 2003.
- L. R. Scott, T. Clark, B. Bagheri, Scientific Parallel Computing, Princeton University Press, 2005.
- A. Toselli and O. B. Widlund. Domain Decomposition Methods - Algorithms and Theory, Springer, 2004.
- B. Smith, P. Bjorstad and W. Gropp. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations.
- L. R. Scott, T. Clark, B. Bagheri, Scientific Parallel Computing, Princeton University Press, 2005.
- A. Toselli and O. B. Widlund. Domain Decomposition Methods - Algorithms and Theory, Springer, 2004.
- B. Smith, P. Bjorstad and W. Gropp. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations.
Assessment methods and Criteria
The final examination consists of two parts: a lab exam and an oral exam.
-The lab exam consists in developing a project, which will be assigned in advance by the professor. The project consists of designing a parallel code for the solution of a system of partial differential equations (PDEs). The project will be presented by the student during the oral exam. The lab portion of the final examination serves to assess the capability of the student to put a problem of numerical approximation of PDEs by parallel computing into context, find a solution and to give a report on the results obtained.
- The oral exam can be taken only if the lab component has been successfully passed. In the oral exam, the student will be required to illustrate results presented during the course and will be required to solve problems regarding parallel computing in order to evaluate her/his knowledge and comprehension of the arguments covered as well as the capacity to apply them.
The complete final examination is passed if all two parts (lab and oral) are successfully passed. Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.
-The lab exam consists in developing a project, which will be assigned in advance by the professor. The project consists of designing a parallel code for the solution of a system of partial differential equations (PDEs). The project will be presented by the student during the oral exam. The lab portion of the final examination serves to assess the capability of the student to put a problem of numerical approximation of PDEs by parallel computing into context, find a solution and to give a report on the results obtained.
- The oral exam can be taken only if the lab component has been successfully passed. In the oral exam, the student will be required to illustrate results presented during the course and will be required to solve problems regarding parallel computing in order to evaluate her/his knowledge and comprehension of the arguments covered as well as the capacity to apply them.
The complete final examination is passed if all two parts (lab and oral) are successfully passed. Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.
MAT/08 - NUMERICAL ANALYSIS - University credits: 9
Laboratories: 36 hours
Lessons: 42 hours
Lessons: 42 hours
Professor:
Scacchi Simone
Shifts:
-
Professor:
Scacchi SimoneProfessor(s)