EGM 6352 - ADVANCED FINITE ELEMENT METHODS - Fall 2004

• Instructor : Dr. L. Vu-Quoc, Tel: 392-6227, E-mail: vu-quoc AT ufl.edu.
• Office: 135 NEB (New Engineering Building)
• Classroom: 102 NEB (FEEDS, videotaping classroom)
  Outreach Engineering Education Program: Handouts, streaming videos, etc.
• Class time:
  Tue, period 7 (1:55pm - 2:45pm)
  Thu, periods 7 + 8 (1:55pm - 3:50pm)
• Office hours:
  Tue, period 2 (8:30am - 9:20am)
  Thu, periods 2 + 3 (8:30am - 10:25am)

Course objectives:

• To provide a solid mechanics and mathematical foundations of the finite-element formulation for various engineering applications (heat, fluids, solids, electromagnetics).
• Beyond the basic material for the finite element methods (FEM), a theme for this year will be multiscale finite-element methods, homogenization methods, spectral element methods (as time permits). Other topics will be covered depending on mutual interests of students and instructor.
• Ultimately, a goal of the course is to introduce students to some of the recent research interests related to the FEM (as exemplified in the list of articles below), and to help provide the necessary (mechanics and mathematics) background for students to read the recent literature in the field. Strategy:
  • Select a representative paper for each field of application (heat, fluids, solids, electromagnetics).
  • Identify the "obscure" mathematical expressions (i.e., "Greek", "Latin", "Sanskrit", etc. :-)) in these papers.
  • Go back to the basics to develop an understanding of these expressions.
  • Read and survey some more of the recent papers in each field; additional suggestions from students are welcomed.
• The course will be taught as a seminar; here, (moderate) "Russian-style seminar" is preferred and highly encouraged.
  NOTE on the "Russian-style seminar": "It encourages listeners to aggressively ask questions right from the start of a talk. At times the main speaker is pushed aside, and things can get downright abrasive." (for more details, see Settling In on Campus, Yudhijit Bhattacharjee, Science, Vol 304, Issue 5675, 1282-1284 , 28 May 2004). The speaker could be the instructor, and the listeners could be the students (but we can do away with being abrasive; in other words, be moderate).
• Students will do assigned homework in teams and on a voluntary basis; there will be no exams. At the end of the semester, it is possible to have in-class team presentations of papers selected by students.
• This course should be of interest to engineering students in all areas of engineering (computer science, chemical, civil, electrical, mechanical and aerospace, nuclear, etc.).

Prerequisites: Having had a course on FEM would be an advantage, but not necessary, since this course is intended for a wider audience and will be taught from the basics with a bend toward a more rigorous presentation of the FEM and its general applications, and particularly to develop skills in FE formulation.

Textbook: None required.

References:

Books:
addall.com, bestbookbuys.com, bookfinder.com.
• Malvern, L.E. [1969], Introduction to the Mechanics of a Continuous Medium , Prentice-Hall. New = $110.67; Used = $60. Library call No. 531 M 262i. A good reference for continuum mechanics, which is a basic foundation for the finite element method. See also the course EGM 6611 Continuum Mechanics, Fall 2003. Thu, 23 Sep 2004.
• T.J.R. Hughes [2000], The Finite Element Method: Linear Static and Dynamic Finite Element Analysis.
  Format: Paperback ISBN: 0486411818 List Price: $ 26.95 Publisher: Dover Publications; (September 1, 2000).
  Written by an engineer for engineers with a more mathematical bend than the average. Thu, 01 Jul 2004.
• K. Eriksson, D. Estep, P. Hansbo, C. Johnson, K. Eriksson [1996], Computational Differential Equation.
  Format: Paperback ISBN: 0521567386 List Price: $ 49.95 Publisher: Cambridge University Press; 2nd Ed edition (September 5, 1996).
  Highly self contained book, written by mathematicians, but with a gentle introduction to the finite element method, starting from basic calculus! There are a lot of historical remarks and interesting quotes; the book start with the Vision of Leibniz in Chapter 1, and ends with the abstract formulation of the FEM in the final Chapter 21 of the book on the Power of Abstraction. Error estimates are introduced using 1-D cases first, before generalizing to 2-D and 3-D. Wed, 14 Jul 2004.
• B. Daya Reddy [1998], Introductory Functional Analysis: With applications to boundary value problems and finite elements.
  Format: Hardcover ISBN: 0387983074 List Price: $ 59.95 Publisher: Springer-Verlag; (November 1, 1997).
  Excellent book for engineers since there are solutions to problems for self study, and since the author was an engineer, receiving all of his degrees in civil engineering. The book was therefore written with an awareness of the needs of engineering students in terms of math background and concrete examples to explain abstract concepts. Wed, 14 Jul 2004.
• G. Allaire [2001], Shape Optimization by the Homogenization Method.
  Format: Hardcover ISBN: 0387952985 List Price: $ 79.95 Publisher: Springer-Verlag; 1st edition (October 19, 2001).
  Mathematical aspects of the homogenization theory; application to composite materials, shape optimization for conductivity and elasticity problems; numerical algorithms. The homogenization theory part provides background materials for several multiscale methods. Wed, 14 Jul 2004.

Articles: Tentative suggested articles on multiscale methods---with application in heat conduction, solid mechanics, fluid mechanics, and electromagnetics---to be discussed in class.
Motivation for multiscale methods
• Complex Systems and Multi-scale Methodology, Chemical Engineering Science Volume 59, Issues 8-9 , April-May 2004. Thu, 01 Jul 2004.
• Design and integration of multi-scale structures, James Wei, Pages 1641-1651. Wed, 21 Jul 2004.
• Managing complex systems: some trends for the future of chemical and process engineering, J. C. Charpentier and T. F. McKenna, Pages 1617-1640. Thu, 01 Jul 2004.
• Beyond transport phenomena and reaction engineering, Pages 1613-1616. Wed, 14 Jul 2004.

Multiscale methods and homogenization theory: Heat, solid mechanics, electromagnetics.
• A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media, Thomas Y. Hou and Xiao-Hui Wu, Journal of Computational Physics, Volume 134, Issue 1 , June 1997, Pages 169-189. Thu, 01 Jul 2004.
• G. Allaire, R. Brizzi, A multiscale finite element method for numerical homogenization, submitted, Internal report, n. 545, CMAP, Ecole Polytechnique (July 2004).
• Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. Part II: a computational environment for adaptive modeling of heterogeneous elastic solids, Kumar S. Vemaganti and J. Tinsley Oden, Computer Methods in Applied Mechanics and Engineering Volume 190, Issues 46-47 , 14 September 2001, Pages 6089-6124. Wed, 14 Jul 2004.
• Concurrent multi-scale analysis of elastic composites by a multi-level computational model, P. Raghavan and S. Ghosh, Computer Methods in Applied Mechanics and Engineering Volume 193, Issues 6-8 , 13 February 2004, Pages 497-538. Thu, 01 Jul 2004.
• Adaptive modeling of wave propagation in heterogeneous elastic solids, Albert Romkes and J. T. Oden, Computer Methods in Applied Mechanics and Engineering Volume 193, Issues 6-8 , 13 February 2004, Pages 539-559. Thu, 01 Jul 2004.
• Microstructure-based deep-drawing simulation of knitted fabric reinforced thermoplastics by homogenization theory, N. Takano, Y. Ohnishia, M. Zakoa and K. Nishiyabu, International Journal of Solids and Structures Volume 38, Issues 36-37 , September 2001, Pages 6333-6356, Thu, 15 Jul 2004.
• Computational electromagnetics and the rational design of new dielectric heterostructures, C. Brosseau and A. Beroual, Progress in Materials Science Volume 48, Issue 5 , 2003, Pages 373-456. Contain an excellent list of annotated references. Wed, 14 Jul 2004.

Variational multiscale methods, stabilized finite element: Fluid mechanics.
• Advances in Stabilized Methods in Computational Mechanics, Computer Methods in Applied Mechanics and Engineering Volume 166, Issues 1-2 , 13 November 1998.
• The variational multiscale method: a paradigm for computational mechanics, Thomas J. R. Hughes, Gonzalo R. Feijóo, Luca Mazzei and Jean-Baptiste Quincy, Pages 3-24. Wed, 14 Jul 2004.
• Recent Advances in Stabilized and Multiscale Finite Element Methods, Computer Methods in Applied Mechanics and Engineering Volume 193, Issues 15-16, Pages 1323-1528 (16 April 2004) Thu, 01 Jul 2004.
• A three-level finite element method for the instationary incompressible NavierStokes equations, Volker Gravemeier, Wolfgang A. Wall, and Ekkehard Ramm, Pages 1323-1366. Thu, 09 Sep 2004.
• A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes: Application to vortex shedding, Bruno Koobus and Charbel Farhat, Pages 1367-1383. Wed, 14 Jul 2004.
• Complex Systems and Multi-scale Methodology, Chemical Engineering Science Volume 59, Issues 8-9 , April-May 2004. Thu, 01 Jul 2004.
• Multi-scale methodology for complex systems, Jinghai Li, Jiayuan Zhang, Wei Ge and Xinhua Liu, Pages 1687-1700. Wed, 21 Jul 2004.

Spectral methods
• New Perspectives for Spectral and High-Order Methods, SIAM News, Volume 37, Number 1, January/February 2004. Thu, 08 Jul 2004.
• Spectral element methods on triangles and quadrilaterals: comparisons and applications, Richard Pasquetti and Francesca Rapetti, Journal of Computational Physics Volume 198, Issue 1 , 20 July 2004, Pages 349-362. Thu, 08 Jul 2004.
• The Spectral Grid Method: A Novel Fast SchrÖdinger-Equation Solver for Semiconductor Nanodevice Simulation, Liu, Q.H.; Cheng, C.; Massoud, H.Z., IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol.23, No.8, Aug. 2004, pp.1200-1208. (toc) Tue, 10 Aug 2004.

Additional background materials: Tue, 31 Aug 2004.

• Journals:
  • Multiscale Modeling & Simulation, SIAM publication. Our library has access to papers in this journal that are 1 year old from current date. Tue, 31 Aug 2004.
  • International Journal of Multiscale Computational Engineering, Begel House Inc. Our library has access to papers up to current date. Tue, 31 Aug 2004.
• Conferences, workshops:
  • Third DOE Workshop on Multiscale Mathematics, September 21-23, 2004, Marriott Portland Downtown Portland, Oregon. Mon, 30 Aug 2004.
  • Second DOE Workshop on Multiscale Mathematics, July 20-22, 2004, Broomfield, Colorado.
    Presentation slides Mon, 30 Aug 2004.
  • DOE Workshop on Multiscale Mathematics, May 3-5, 2004, The Sheraton Pentagon South Hotel, Alexandria, VA.
    Presentations, report. Tue, 31 Aug 2004.
  • Computational Methods in Multiscale Analysis and Applications, 29 Feb - 2 Mar 2004, University of Florida. Wed, 01 Sep 2004.
• Papers:
  • Numerical investigation for stress, strain and energy homogenization of orthotropic composite with periodic microstructure and non-symmetric inclusions, Qing-Sheng Yang and Wilfried Becker, Computational Materials Science Volume 31, Issues 1-2 , September 2004, Pages 169-180 Homogenization and finite-element computation of effective properties of composites. Tue, 31 Aug 2004.
  • Verification and validation in computational engineering and science: basic concepts, Ivo Babuska and J. Tinsley Oden, Computer Methods in Applied Mechanics and Engineering Volume 193, Issues 36-38 , 10 September 2004, Pages 4057-4066 Tue, 31 Aug 2004.
• Reverse Hall-Petch effects:
• Reverse Hall-Petch effects: Google search Thu, 26 Aug 2004.
• Nanocrystals: The strongest size, Sidney Yip, Nature 391, 532 - 533 (05 February 1998). See Fig.1 in this paper. Thu, 26 Aug 2004.
• The reverse Hall-Petch effect,
  Figure on reverse Hall-Petch effect, definition of maximal flow stress and yield stress. Thu, 26 Aug 2004.

Other interesting links:

• See also my teaching schedule for more info on this course as taught in previous years.
• The hunger site: Click to donate food with no cost to you. Mon, 26 Jul 2004.
• The Dead Grandmother/Exam Syndrome and the Potential Downfall Of American Society. (:-)) Fri, 06 Aug 2004.

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Home page: Loc Vu-Quoc E-mail: vu-quoc AT ufl.edu MAE Department