Nicola Guglielmi

Professor

Area: Numerical analysis

Georgia Tech (visiting from University of L'Aquila)

e-mail nguglielmi3(at)math.gatech.edu

Tel. +1-404-894-6536 - Fax +1-404-894-4409

Curriculum vitae and publications CV

Index

Syllabus

Fall 2009, Tu, Th 4:35 PM - 5:55 PM, Skiles 246

Homework 1: for those who are interested to discuss the exercises I will be in my office on August 31 in the afternoon (starting from 3pm).
I plan to collect the exercises on September 1. You are invited (but not obliged) to give me the solutions.
Homework will not be graded.

Homework 2: do exercises 1,4,8,9, 13, 15, 16, 18 at pages 41--43 of the textbook. Due date: September 17.
I plan to collect the exercises on September 20. You are invited (but not obliged) to give me the solutions.

I will be abroad for the next two weeks; Professor Luca Dieci will replace me and give the lectures. His office is Skiles 215. His office hours are the same as mine.

Since today I am moving to office Skiles 216.

The midterm will take place at 16.35 in room 246.
On the 29 I will be out of my office.
The midterm will include the topics in the first two chapters of the textbook, the first part of chapter 4, till page 112 and the first part of chapter 7, till page 179.
Professor Luca Dieci will assist you during the exam.

The midterm will take place on October 29th at 16.35 in room 246.
I will be at a conference from October 26th to 29th.
You are invited to come to my office to discuss about exercises and/or theory every day in the week from October 19th to October 24th. From October 26th to 29th you can send me questions by email. I will answer as soon as possible.
The midterm will include the following topics: LU decomposition (Gauss method). Iterative methods. Conjugate directions and conjugate gradient method. Cholesky factorization. Gershgorin's theorem for eigenvalues localization. Power method.
Professor Luca Dieci will assist you during the exam.

The lecture of October 27th will be given by Professor Lew Lefton who will introsduce you to the use of the cluster in the laboratory (the topics will include - how to access the cluster - how to copy files back and forth - how to compile and run a simple MPI program - how to submit and monitor a batch job)
You are recommended to bring your laptops with you when possible.

I will be travelling on the 29th. For any question or clarification before the midterm write me within the evening of the 28th.

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October 29

Midterm 2

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Pdf file with exercises

Solutions of Midterm 2

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Pdf file with solutions

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November 24th

Fortran code for adaptive integration (sequential)

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Fortran code

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November 25th

Homework 6

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Pdf file with exercises

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December 6

Solutions of Homework 6

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Pdf file with solutions

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December 7

All projects (for those students who have chosen to do them) have to be submitted by Wednesday December 9-th afternoon. They should consist of a short description of the problem and of the used algorithms (3 to 5 pages), the written codes and an experimental measure of the speed up.


The final exam will take place on Friday December 11-th at 14.50 in room 246.
Everybody is allowed to to bring with you a calculator and a one page cheat sheet 8.5 x 11 inches with anything you want written on it, both sides.
The final examination will include all the topics treated in the course. One of the exercises will be concerned with the coding of an algorithm.

1. Stability of numerical methods for delay differential equations.
2. Computation of the joint spectral radius of a family of matrices.
3. Regularization of forward backward parabolic partial differential equations.
4. Stiff delay equations Scholarpedia introduction .

Main collaborations

• Group of computational mathematics
• Ernst Hairer

• RETARD Extension of the code DOPRI5 to delay differential equations y'(t)=f(t,y(t),y(t-a),...)
• DR_RETARD Driver for RETARD

• the tar file radar5-v2.1.tar contains a directory with the Fortran 90 code RADAR5, the necessary linear algebra routines, and subdirectories for the following eleven examples. For unfolding the directory use the command tar xvf radar5-v2.1.tar
• ENZYME kinetics with an inhibitor molecule, dimension 4, one constant delay;
• HAYASHI an almost singular state dependent neutral problem, dimension 2 as differential-algebraic problem, one vanishing delay;
• HEPATITIS acute hepatitis B virus infection, dimension 10, 5 constant delays;
• OREGONATOR chemical kinetics, dimension 2, one constant delay;
• ROBERTSON chemical reaction with steady state solution, dimension 3, one constant delay, very large time interval (step sizes larger than the delay);
• SDISC, non smooth artificial problem, dimension 1, 1 constant delay;
• WALTMAN, threshold model for antibody production, dimension 6, 2 state-dependent delays tending to zero, discontinuities in the right-hand side of the equations;
• PAUL, state-dependent artificial problem, various order discontinuities;
• ELSNOR, problem with solution termination;
• MODCEG, neutral problem with state dependent delays and termination
• NEUTLOG, predator-pray neutral Gause-model.

Where to find me (in 2009 I am on leave)