4301Intro20080917

4301Intro20080917 - Lecture#3(Part A 17 September 2008 Applied Mathematics 4301 Numerical Methods for PDEs Introduction Lecture#3 Wed aft 4:10-6:40

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Applied Mathematics 4301: Numerical Methods for PDEs Introduction, Lecture #3 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 #3 (Part A) 17 September 2008
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Plan for Sep 17 meeting • Report survey results (“who you are”) • Review of Sep 10 lecture • Questions • Main lecture: “Parabolic equations in 2 or more space variables” (chapter 3 of Morton & Mayers)
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Survey results • We are now stable (?) at 41, 32 on campus and 9 CVN – 3 Juniors –9 S e n i o r s – 28 Graduate students – 1 Non-degree candidate • We have 19 replies to the survey • Survey respondents by class:
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Survey results • Regarding foundational courses and MATLAB 0 2 4 6 8 10 12 14 16 18 20 LA (3101) PDE (3102, 4200) NA (4300) MATLAB None Rudi. Comf.
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Survey results • Regarding “adult” software for the numerical analysis of PDEs 0 2 4 6 8 10 12 14 16 18 Linux C/C++ F77/F90 PETSc None Rudi. Comf.
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Survey results: your objectives are… • “to gain a good understanding of finite difference method. My profession is in financial engineering and this method is widely used in valuing derivative instruments.” • “acquiring useful knowledge to become an expert in advanced modeling of environmental systems” • “to do some CFD for two-phase flow (drop/bubble breakup) for my PhD thesis” • “improve my understanding about the advantages and disadvantages of different numerical schemes for general circulation models in atmospheric and climate research. I also hope to construct by myself a simple general circulation model, which can be used for demonstration or theoretical research.”
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Survey results: your objectives are… • “to learn the machinery to tackle and model complicated PDEs” • “to become comfortable enough with solving PDEs numerically that I can use them in my own research” • “to learn some more math that could be potentially useful in applications to medicine” • “to prepare to attend graduate school in applied math” • “to gain more understanding of the finite element method, since part of my PhD project involves FE modeling of the electrical field induced by brain simulation” • “to enjoy a solid programming component. I am really into computers.”
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Survey results: your applications are… • Molecular simulations of continuum mechanics • Elastic models of flexible organs • Fluid mechanics • Structural analysis of materials • Plasma physics applications • Arterial blood flow through stenosed vessels • Quantum mechanics (besides those implicitly stated on previous pages)
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Comments: my objectives are… To create community among computational researchers To create a trained user group for Columbia’s present and coming high-end computational facilities
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This note was uploaded on 08/30/2011 for the course APMA 4301 taught by Professor Keyes during the Fall '08 term at Columbia.

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4301Intro20080917 - Lecture#3(Part A 17 September 2008 Applied Mathematics 4301 Numerical Methods for PDEs Introduction Lecture#3 Wed aft 4:10-6:40

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