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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 computation to confirm my theory, or I'm a computational guy who analytically justifies my numerical methods. You decide, I've quit trying.

For the past few years I've been privileged to work with young brilliance in the Wabash Summer Institute in Mathematics, an 8 week REU program funded by the NSF. I'm looking forward to another good group in the summer of 2010.

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? (Warning: outdated!)

Current and Recent Projects:
  • Analysis of numerical methods for Navier-Stokes equations.
  • Adaptive methods for convection dominated diffusion problems.
  • Least-squares for capillarity phenomenon.
  • Least-squares methods for viscoelastic and biological fluids.
  • Weighted-norm least-squares methods for PDEs with boundary singularities.
  • Least-squares finite element methods for nonlinear elasticity.
  • Efficient nested iteration schemes.


    Papers/Publications:

     Research Articles (having appeared):

  • Z. Cai and C.R. Westphal, "An Adaptive Mixed Least-Squares Finite Element Method for Viscoelastic Fluids of Oldroyd Type," J. Non-Newt. Fluid Mech., 159 (2009), pp 72-80.

  • 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.

  • 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.

     Other Publications:

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

  • 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, Wabash is truly a unique place. I have a passion for excellent teaching that isn't confined to the classroom.

    Fall 2009 Courses:
    CSC 112         Advanced Programming
    MAT 223 Linear Algebra
    MAT 324 Advanced Differential Equations: PDEs

    Past Courses:
    MAT 337 Numerical Analysis
    MAT 324 Advanced Differential Equations: PDEs
    MAT 224 Differential Equations
    MAT 223 Linear Algebra
    MAT 112 Calculus II
    MAT 111 Calculus I
    MAT 003 PreCalculus
    CSC 271         Special Topics: Stochastic Simulation
    CSC 111         Intro to Programming (seriously cool class photos)
    C&T 201         Cultures and Traditions
    APPM 2350 Calculus III for Engineers (University of Colorado)
    APPM 1350     Calculus I for Engineers (University of Colorado)
    PHY 1214 General Physics II (Tulsa Community College)
    PHY 1114 General Physics I (Tulsa Community College)


    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 I just 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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