wisL602, Spring 2017
Lecturer:
Dr. P.A. Zegeling, room 513, Math. Building (= HF-Building), Budapestlaan 6, Utrecht (030-2533720).
Venue:
Universiteit Utrecht , Budapestlaan 6, Utrecht, HF-Building : room 611AB (weeks 6-16) and in ISRAELS room KELDER1.07 (weeks 17-21)
Time:
10:00-12:45 (2 hours with theory: "hoorcollege" and 1 hour with exercises: "werkcollege").
Grade:
the final grade (FG) will be based on: 20% computerexercise C1, 60% on the midtermtest MTT and 20% on computerexercise C2, i.e. FG = 0.2*C1+0.6*MTT+0.2*C2
Literature:
the book "Finite Difference Methods for Ordinary and Partial Differential Equations" Randall J. LeVeque, 2007 (RL) and
lecture notes and articles (see below). In this overview you can find an additional list of references.
Official schedule in Osiris.
| DATE | LECTURE | LECTURE NOTES & EXERCISES | LITERATURE | EXTRA INFO | DEADLINES | |
| February 8 | Lecture 1: intro PDEs + basic tools | Lecture notes 1 + extra info & Exercises 1-6 Solutions | RL: Appendix E and Chapter 1 | Exercises (most recent update: => Monday April 10) | ||
| February 15 | Lecture 2: the method of lines: heat equation | Lecture notes 2 & Exercises 7-8 Solutions (exercise 7), Solutions (exercises 8 and 9) | RL: Chapters 9.1-9.4 and a summary of Chapters 5-8 (NumODE theory) | |||
| February 22 | Lecture 3: the heat equation: consistency, stability and convergence of FDs | Lecture notes 3 & Heat equation in 2d & Exercises 10-14 Solutions | RL: Chapters 9.5-9.9 | |||
| March 1 | Lecture 4: hyperbolic PDEs (1): the advection equation (the linear case) | Lecture notes 4 & Exercises 14-20 Solutions (exercise 15; ignore in this file the others; see =>) & Solutions (exercises 16-20) | RL: Chapters 10.1-10.4 | computer exercise C1 * updated version (one question in Part B deleted and the footnote changed in Part C * hand in individually * additional information on Part C) can be found here * restrict your report please to a maximum of 15-20 pages: only include the most relevant formulas, figures and tables! *** grades have been sent by email on Monday May 2 |
==> a hard copy of the report on April 5 (13:00), i.e. right after the midterm test! Please not by email (only in special situations possible; notify me in time) ==> On Monday April 3 and Tuesday April 4, I am in room 513 HF-building, alternative: contact by telephone 030-2533720 |
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| March 8 | Lecture 5: hyperbolic PDEs (2): the advection equation (the nonlinear case) | Lecture notes 5 & Exercises 21-23 Solutions | RL: Chapters 10.5-10.13 | |||
| March 15 | Lecture 6: hyperbolic PDEs (3): finite volumes, method of characteristics, the wave equation | Lecture notes 6 & Exercises 24-28 Solutions | ||||
| March 22 | Lecture 7: finite elements for parabolic equations | Lecture notes 7 & Exercises 29-31 (solutions for exercises 29 and 31 can be found in the lecture notes on pages 8/9 and 16, respectively; more information on finite elements and the solution for exercise 30 can be found here and here as well) | ||||
| March 29 | No lecture today! | |||||
| April 5 | MIDTERM TEST (on Lectures 1-7, all exercises are of importance, except exercises 2, 3, 8 and 9); the midtermtest & the solutions; The grades have been sent by email on Monday April 24. | LOCATION: Ruppert Wit | TIME: 10:00-12:45 (doors open at 9:45) | A map of the Ruppert Building; A map of De Uithof; A picture of the Ruppert Building | ||
| April 12 | Lecture 8: Adaptive grid methods | Lecture notes 8 (part 1), part 2, part 3, part 4 & exercises 32-37 | syllabus (7.5Mb) | some extra notes on MFE and the deformation method (see sections 3.2 and 3.3.1) | ||
| April 19 | Lecture 9: Numerics for inverse problems in time-dependent PDEs (guest lecturer: Tristan van Leeuwen) | Lecture notes 9 | ||||
| April 26 | Lecture 10: Fractional PDEs & boundary-value methods; note the change in location (see the official schedule)! | Lecture notes 10 (updated on May 17!) | * Extra information on fractional finite differences * Extra information on boundary value methods, paper 2 and paper 3 * two hints for Part A: 1) check the derivation of the representation of the second derivative in polar coordinates, 2) apply Taylor series for the function x(xi) at the i-th gridpoint. * Here is some information about the numerical treatment of the integral in Part B. |
computer exercise C2 (first part: update May 10!; second part: May 10) * hand in individually * matlab file for computer exercise C in C2 * information on eigenvalues in computer exercise C in C2 * Questions on Part C: please ask Tristan van Leeuwen (T dot vanLeeuwen at uu dot nl). * Questions on Part D: please ask Jason Frank (J dot E dot Frank at uu dot nl). * hint for the boundary conditions in Part B: check matrix D3 on page 33 in the lecture notes of April 26 and adjust the first two (or three) lines) and the last two (or three) lines in the matrix. * please check the minus signs in Part D 1. (see the email that was sent on Saturday May 20). |
May 24 | |
| May 3 | Lecture 11: Higher-order methods, nonstandard FDs & operator splitting methods | lecture notes on higher-order methods, lecture notes on nonstandard finite differences & Lecture notes on operator splitting | ||||
| May 10 | Lecture 12: Hamiltonian ODEs and conservative time-integration (guest lecturer: Jason Frank): 10:00-10:45 hints will be given for exercise C2 (parts A and B); 11:00-12:45 guest lecture on Hamiltonian models | computer exercise C2 (part D; updated version: May 20) * please check the minus signs in Part D 1. (see the email that was sent on Saturday May 20). |
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| May 17 | Lecture 13: Hamiltonian PDEs (guest lecturer: Jason Frank): 11:00-12:45!!! | Lecture notes 12 & 13 | ||||
| May 24 | check extra info (most recent update: May 17) => |
* regularly check this webpage for updates! * between June 2 and June 13: NOT in office (NO email!) * => questions about Retake: BEFORE June 2 * results for C2 and final grades: I send an email to each student (Thursday June 1) * Mastermath administrates and sends the final grades to the universities * contact Mastermath if there are any problems with the administration of the grades * Rules and Guidelines: on webpage Mastermath |
* Note that pages 34 and 43 of the lecture notes of April 26 have been modfied! ==> The Euler Forward step has been left out, the index of the MP-method goes until N-1 instead of N and the matrix C is added in the EB step. |
Hand in computer exercise C2 * deadline = May 24 * option 1: in room 513 between 10:00 and 13:00, HF-building (one floor below lecture room 611) * option 2: send your report by email (only pdf file and only ONE file) |
* Note that pages 34 and 43 of the lecture notes of April 26 have been modfied! ==> The Euler Forward step has been left out, the index of the MP-method goes until N-1 instead of N and the matrix C is added in the EB step. |
June 14 | RETAKE EXAM (on Lectures 1-7) | LOCATION: Ruppert Rood | TIME: 10:00-12:45 (doors open at 9:45) | A map of the Ruppert Building; A map of De Uithof; A picture of the Ruppert Building |
