4301Intro20081022

4301Intro20081022 - Lecture #8 (Part A) 22 October 2008...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Applied Mathematics 4301: Numerical Methods for PDEs Introduction, Lecture #8 Wed aft. 4:10-6:40 S. W. Mudd Bldg. 1024 Prof. David Keyes, instructor S. W. Mudd Bldg. 215 [email protected] Yan Yan, teaching assistant [email protected] Lecture #8 (Part A) 22 October 2008
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Plan for 22 Oct meeting • Special announcement: CSGF applications open • Questions • Review topic “Introduction to PDEs” (esp. classification) • Main topic “Dominant first-order terms and adaptivity”
Background image of page 2
Special Announcement - CSGF • DOE Computational Science Graduate Fellowship applications open ( http://www.krellinst.org/csgf/ ) • Premier computational science fellowship program in the world (in 19 th year) • For illustrative projects, see Deixis ( http://www.krellinst.org/csgf/deixis/ ) • Columbia’s APAM has had four of these as graduate students; Columbia Physics has grown one from UG program •S e e Deixis articles on APAM’s Richard Katz, Ethan Coon
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Homework pipeline • PS #5 posted 10/1 – Richardson extrapolation and defect correction – due 10/24 (2-day extension) • PS #6 posted 10/8 – Green’s functions for ODE BVPs – questions welcome – due 10/29
Background image of page 4
Action items for this week • Obtain new electronic handouts – two slide sets for Lecture #8 – two supplementary articles – reading for Lectures #9-10: An introduction to the conjugate gradient method without the agonizing pain • By a graduate student for graduate students • Loved by most faculty members
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Midterm Exam • 31 students took it • Not yet graded / – expected to be returned next week – solution sets will be posted – means and medians, by problem and overall, will be reported
Background image of page 6
Review of 8 Oct lecture • Reviewed basic theory of second-order linear scalar PDEs – Eigenfunction expansions – Green’s functions – Similarity solutions • Looked at Green’s functions in various domains (mainly – Derived without using δ -function, then interpreted in terms of δ – Focused on understanding “domain of dependence”: how a solution at ( x,t ) is forced by an initial condition at y (for transient problems) or a source at y (for steady problems) and what is the magnitude of the influence as a function of distance in space and time • Looked at what makes a second-order linear PDE well posed, in terms of BCs and ICs
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Canonical parabolic •D o m a i n • Unknown – field • Governing equation – linear – constant coefficient – homogeneous • Initial condition – inhomogeneous • Boundary conditions – homogeneous –D i r ich le t 2 2 x u t u = α ) , ( t x u ) , 0 [ ], 1 , 0 [ t x ) ( ) 0 , ( 0 x u x u = 0 ) , 1 ( ) , 0 ( = = t u t
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/30/2011 for the course APMA 4301 taught by Professor Keyes during the Fall '08 term at Columbia.

Page1 / 33

4301Intro20081022 - Lecture #8 (Part A) 22 October 2008...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online