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Intensive Computation - Calcolo Intensivo

Annalisa Massini

Office Hours: appointment by email
News

  • Monday's lectures will start at 10:15.

  • 22 March 2020 I created a personal folder for each student for delivering homeworks, in the Google Drive folder of Classroom. Each folder has the name of the student and is shared only with the teacher.

  • From Monday 9 March, lessons will be delivered in real-time using platform Google Meet, according to the official class schedule.

Aim of the course

The aim of the course is to provide students with methodologies for the solution of problems requiring intensive computation, in particular scientific problems.

Topics covered in this course include:

  • Introduction to Matlab
  • Concepts and methods: sparse matrices, eigenvalues and eigenvectors, linear algebras methods, etc.
  • Errors and simulations
  • Problems like Molecular Dynamics, Graph connectivity, Global search algorithms, etc.
  • Advanced topics on architectures and arithmetic operations
  • Introduction to GPU architecture and programming
  • Performance measures

Lectures 2019-2020

Lecture 1, February 24th, 2020 Introduction to the course - Lecture 1 - Introduction

Lecture 2, February 26th, 2020 Introduction to Matlab - Part 1 - Lecture 2 - Matlab
Laboratory, February 26th, 2020 Laboratory: Introductory exercises - Part 1

Lecture 3, March 2ndth, 2020 Introduction to Matlab - Part 2 - Lecture 3 - Matlab
Laboratory, March 2ndth, 2020 Laboratory: Introductory exercises - Part 2

Lecture 4, March 4th, 2020 Sparse matrices: definitions and motivation of compact formats. Compact storage methods for sparse matrix: Coordinate, Skyline, Compact Sparse Row CSR, Compact Sparse Column CSC, Modified Sparse Row MSR. Lecture 4 - Sparse Matrices - Slide 1-44

  • Appendix of book Solving Numerical PDEs: Problems, Applications, Exercises - Formaggia, Saleri, Veneziani - 2012 - read pp. 395-409

Lecture 5, March 9th, 2020 Compact storage methods for sparse matrix: Block Sparse Row, , Diagonal, Ellpack-Itpack. Lecture 5 - Sparse Matrices - Slide 45-62

Lecture 6, March 11th, 2020 Lecture by Dr. Viviana Arrigoni. Linear systems. Gaussian elimination for solving systems of linear equations. Pivoting. Methods to avoid pivoting. Random Butterfly Transformations and Transpose methods Lecture 6 - Linear Systems Part 1

Lecture 7, March 16th, 2020 Lecture by Dr. Viviana Arrigoni. Linear systems. Cholesky factorization. Jacobi iterative method. Gauss-Seidel iterative method. Lecture 7 - Linear Systems Part 2

Lecture 8, March 18th, 2020 Errors: Computational errors, Data errors, Truncation errors, Rounding errors. Forward error and backward error. Sensitivity and condition number. Stability and accuracy. Errors in floating point representation. Lecture 8 - Errors -Slide 1-55

Lecture 9, March 23th, 2020 Errors in floating point arithmetic. Uncertainty in measurements. Lecture 9 - Errors - Slide 56-84
Laboratory Discussion on Homework 1: solutions of students.

Lecture 10, March 25th, 2020 Eigenvalues and eigenvectors. The Power method. The Deflation methods. Lecture 10 - Eigenvalues, Eigenvectors - Slide 1-30


Some papers proposed for past exam projects - Articoli proposti per esami passati

Past year lectures

Exam

The exam consists of two parts:

  • Written exam. Students attending the lessons can take a mid-term exam and a final exam (or a whole exam). Mid-term and final exam (or whole exam) consist in a written test and exercises.
  • One of the following, at the choice of the student: oral exam/presentation of one-two papers/project.

There will also be homework assignments. Homeworks will contribute to the final grade.


Text of exams


Grades


Textbooks - Testi di riferimento

  • Introduction to High-Performance Scientific Computing, Lloyd D. Fosdick, Elizabeth R. Jessup, Carolyn J. C. Schauble and Gitta Domik, The MIT Press, 1996, ISBN 0-262-06181-3
  • Programming Massively Parallel Processors: A Hands-on Approach, David B. Kirk and Wen-mei W. Hwu, Morgan Kaufmann, 2010
  • Introduction to scientific computing: A Matrix-Vector Approach Using MATLAB, Charles F. Van Loan, Prentice Hall , 1997
  • Manuale di MATLAB. Consultare il sito: http://www.mathworks.com/help/techdoc/learn_matlab/bqr_2pl.html
  • Matlab. Concetti e progetti, Giovanni Naldi e Lorenzo Pareschi, Apogeo, 2007
  • Calcolo Scientifico: Esercizi e Problemi Risolti Con MATLAB e Octave, Alfio Quarteroni, Fausto Saleri, 2008

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-- AnnalisaMassini

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