Numerical Methods for Partial Differential Equations 3
A.Y. 2021/2022
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
Based on the evolution of the pandemic situation, information will be given on any distance learning methods.
Course syllabus
- Introduction to parallel computing, examples, top500.org. Parallel architectures.
- Parallel architectures, Interconnection networks, Interprocessor communications: point-to-point, collective.
- Parallel algorithm design, Parallel programming, MPI.
- Parallel performance, Vector products.
- Matrix-vector and matrix-matrix products.
- Parallel LU factorization.
- Parallel Cholesky factorization, solution of triangular and tridiagonal systems.
- Parallel iterative methods for linear systems.
- Parallel QR factorization. Parallel eigensolvers: power, inverse power, QR, Arnoldi methods.
- PETSc library: VEC, MAT and DM objects.
- Overlapping Domain Decomposition methods: Additive Schwarz, Multiplicative Schwarz methods.
- Non-overlapping Domain Decomposition methods: Schurm complement system, Dirichlet-Neumann, Neumann-Neumann Methods.
- Abstract Schwarz theory.
- Parallel architectures, Interconnection networks, Interprocessor communications: point-to-point, collective.
- Parallel algorithm design, Parallel programming, MPI.
- Parallel performance, Vector products.
- Matrix-vector and matrix-matrix products.
- Parallel LU factorization.
- Parallel Cholesky factorization, solution of triangular and tridiagonal systems.
- Parallel iterative methods for linear systems.
- Parallel QR factorization. Parallel eigensolvers: power, inverse power, QR, Arnoldi methods.
- PETSc library: VEC, MAT and DM objects.
- Overlapping Domain Decomposition methods: Additive Schwarz, Multiplicative Schwarz methods.
- Non-overlapping Domain Decomposition methods: Schurm complement system, Dirichlet-Neumann, Neumann-Neumann Methods.
- Abstract Schwarz theory.
Prerequisites for admission
Basic notions of numerical analysis
Teaching methods
Lectures and lab sessions.
Teaching Resources
- A. Grama, A. Gupta, G. Karipys, V. Kumar. Introduction to parallel computing. Addison Wesley, 2003.
- L. R. Scott, T. Clark, B. Bagheri. Scientific parallel computing. Princeton University Press, 2005.
- Lecture notes.
- L. R. Scott, T. Clark, B. Bagheri. Scientific parallel computing. Princeton University Press, 2005.
- Lecture notes.
Assessment methods and Criteria
The exam consists of a project and an oral exam.
- The project consists in the development of a code for the solution of a model described by partial differential equations assigned by the teacher.
- During the oral exam you will be asked to illustrate the project and some results of the teaching program, in order to evaluate the knowledge and understanding of the topics covered, as well as the ability to know how to apply them.
The exam is passed if the project is carried out and the oral exam is passed. The mark is expressed out of thirty and will be communicated immediately at the end of the oral exam.
- The project consists in the development of a code for the solution of a model described by partial differential equations assigned by the teacher.
- During the oral exam you will be asked to illustrate the project and some results of the teaching program, in order to evaluate the knowledge and understanding of the topics covered, as well as the ability to know how to apply them.
The exam is passed if the project is carried out and the oral exam is passed. The mark is expressed out of thirty and will be communicated immediately at the end of the oral exam.
MAT/08 - NUMERICAL ANALYSIS - University credits: 9
Laboratories: 36 hours
Lessons: 42 hours
Lessons: 42 hours
Professor:
Scacchi Simone
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