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Chad Westphal


Research
Teaching
Personal
westphac@wabash.edu

P.O. Box 352
Dept. of Math and CS
Wabash College
Crawfordsville, IN 47933

(765) 361 6101
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Research Overview :

I am a numerical analyst with broad interests in applied mathematics. Most of the work that I am currently involved with is within the context of least-squares finite element methods for partial differential equations (PDEs) in one form or another. I also dabble in multilevel iterative solvers for linear systems. Depending on your viewpoint, I'm either an analyst who does computations to confirm my theory, or I'm a computational guy who analytically justifies my numerical methods. You decide, I've quit trying.

I'm working with a group of undergraduates in the summer of 2008 in the Wabash Summer Institute in Mathematics, an 8 week REU program funded by the NSF.

Undergrads looking for a friendly forum to present recent research may be interested in the 2008 Illiana Conference on October 25. Our funding includes support for student travel, so check it out.

If you're interested, have a look at my CV (pdf). Or perhaps you'd be more interested in a more detailed description of some of my current and past projects?

Projects:
  • Least-squares methods for viscoelastic fluids
  • Weighted-norm least-squares methods for PDEs with boundary singularities
  • Least-squares finite element methods for nonlinear elasticity
  • Efficient nested iteration schemes

    Slides from a few talks:
  • An undergraduate level overview of computational modeling with PDEs.
  • On a least-squares formulation for nonlinear elasticity.
  • On a weighted-norm least squares method for problems with singularities.
  • Overview of a mixed least-squares approach to viscoelasticity.

    Papers/Manuscripts/Publications etc.:

     Research Articles:

  • Z. Cai and C.R. Westphal, "An Adaptive Mixed Least-Squares Finite Element Method for Viscoelastic Fluids of Oldroyd Type," (submitted).

  • Z. Cai and C.R. Westphal, "A Weighted H(div) Least-Squares Method for Second-Order Elliptic Problems," SIAM J. Numer. Anal., 46 (2008), pp 1640-1651.

  • C. Westphal, "A Least-Squares Finite-Element Method for Viscoelastic Fluids," Proc. Appl. Math. Mech. (PAMM), 7(1), 1025101-2, 2008.

  • E. Lee, T. Manteuffel and C.R. Westphal, "Weighted-Norm First-Order System Least Squares for Problems with Three Dimensional Edge Singularities." SIAM J. Numer. Anal., 46 (2008), pp 1619-1639.

  • E. Lee, T. Manteuffel and C.R. Westphal, "Weighted-Norm First-Order System Least Squares for Problems with Corner Singularities." SIAM J. Numer. Anal. 44 (2006), pp. 1974-1996.

  • T. Manteuffel, S.F. McCormick, J.G. Schmidt and C.R. Westphal, "First-Order System Least Squares (FOSLS) for Geometrically Nonlinear Elasticity." SIAM J. Numer. Anal. 44 (2006), pp. 2057-2081.

     Expository Articles:

  • C. Westphal, "Teaching Time Savers: Encouraging Contact Early in the Semester," FOCUS, 27(6), 2007.

     Theses:

  • C. Westphal, "First-Order System Least Squares (FOSLS) for Geometrically Nonlinear Elasticity in Nonsmooth Domains." Ph.D. Thesis, University of Colorado, 2004.

  • S. Nuchia and C. Westphal, "Energy Statistics in Filament Model of 3-D Vorticity." M.S. Group Report, University of Tulsa, 2000.


    • Teaching Overview :

    I am an Assistant Professor in the Department of Mathematics and Computer Science at Wabash College. Smaller than many high schools and admitting only males, Wabash is truly a unique place. I have a passion for excellent teaching that isn't confined to the classroom.

    Fall 2008 Courses:
    CSC 271         Special Topics: Stochastic Simulation
    MAT 337         Numerical Analysis
    C&T 201         Cultures and Traditions

    Past Courses:
    CSC 111         Intro to Programming
    MAT 003 PreCalculus
    MAT 111 Calculus I
    MAT 112 Calculus II
    MAT 223 Linear Algebra
    MAT 224 Differential Equations
    MAT 324 Advanced Differential Equations: PDEs
    MAT 337 Numerical Analysis
    APPM 1350     Calculus I for Engineers (University of Colorado)
    APPM 2350 Calculus III for Engineers (University of Colorado)
    PHY 1114 General Physics I (Tulsa Community College)
    PHY 1214 General Physics II (Tulsa Community College)

    Like to solve problems? Check out the problem of the fortnight.



    Personal :
    The Westphal family consists of Chad and Amy, our two kids, Henry and Adah, and our dogs. Have a look at our photos page if you're interested.

    We live in Crawfordsville, Indiana, a nice small town an hour from Indianapolis. Before moving here in the summer of 2004, we lived in Lafayette, Colorado, just outside the People's Republic of Boulder. Before that we lived in Tulsa, Oklahoma.

    I spend most of my time either working or with my family, as I should. Theoretically, if I had lots of free time I'd spend it woodworking, snowboarding, mountain biking, skateboarding and playing disc golf. In what seems like another lifetime, I was an avid skateboarder. Now-a-days I enjoy getting outdoors in any way I can. I'm a bit of a presidential history buff, but only enough to be annoying. I sometimes pretend I can play the banjo, but I'm really much better at listening to bluegrass and classic country music.


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