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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 and computational mathematics and am interested in applications ranging from non-Newtonian fluids to infectious disease dynamics on complex networks. Most of my work relates to developing efficient numerical methods for systems of differential equations in one form or another. Some of my favorite projects lie in the intersection of deterministic and stochastic modeling, where we can make good use of computational and analytical tools from both frameworks.

Doing research with undergrads? Check out Ethics for Undergraduate Researchers in Mathematics, a side-project developed with Mike Axtell.

I spent the 2018-2019 academic year as Distinguished Visiting Professor in the Department of Mathematical Sciences at the U.S. Air Force Academy.

Since 2023 I've had the privilege of being The Eugene N. and Marian C. Beesley Professor at Wabash College. This is an endowed chair at Wabash College, named in honor of Eugene Beesley.

If you're interested, have a look at my CV, but it's probably outdated.

Infectious Disease Modeling on Complex Networks

Adaptively weighted finite element methods

First-order system LL* methods

Finite element methods for fully nonlinear problems

Stochastic simulation of game theoretic models

Papers/Publications:

C.R. Westphal, "A Newton Div-Curl Least-Squares Finite Element Method for the Elliptic Monge-Ampere Equation," Comp. Meth. Appl. Math., 19-3, pp. 631-643, 2019.

T. Nguyen and C.R. Westphal "Soccer Penalty Kicks and the Mixed-Strategy Nash Equilibrium: An Evolutionary Approach," submitted.

B. Hayhurst, M. Keller, C. Rai, X. Sun and C.R. Westphal, "Adaptively Weighted Least Squares Finite Element Methods For Partial Differential Equations with Singularities," 13-1, pp. 1-25, 2018.

E. Lee, T.A. Manteuffel and C.R. Westphal, "FOSLL* for Nonlinear Partial Differential Equations," Siam. J. Sci. Comput., 37-5, pp. S503-S525, 2015.

Y. Sun and C.R. Westphal, "An Adaptively Weighted Galerkin Finite Element Method for Boundary Value Problems," CAMCoS, 10-1, pp27-41, 2015.

S. Bidwell, M.E Hassell and C.R. Westphal, "A Weighted Least Squares Finite Element Method For Elliptic Problems with Degenerate and Singular Coefficients," Math. Comp., 82, 672-688, 2013.

B. Kraynik, Y. Sun and C. Westphal, "Multiscale Adaptively Weighted Least Squares Finite Element Methods for Convection Dominated PDEs," Involve, 5-1, 39-49, 2012.

M. Axtell and C. Westphal, "Ethics for Undergraduate Researchers", Notices of the AMS, 59(3), 2012.

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, pp 72-80, 2009.

Z. Cai and C.R. Westphal, "A Weighted H(div) Least-Squares Method for Second-Order Elliptic Problems," SIAM J. Numer. Anal., 46, pp 1640-1651, 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, pp 1619-1639, 2008.

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.

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, pp. 1974-1996, 2006.

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, pp. 2057-2081, 2006.

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

Teaching Overview :

Since 2004, I've been in the Department of Mathematics and Computer Science at Wabash College. I've taught a lot of courses here and a few elsewhere.

Past Courses:

MAT 337	(=CSC 337) Numerical Analysis
MAT 344	Complex Analysis
MAT 324	Partial Differential Equations
MAT 224	Differential Equations
MAT 223	Linear Algebra
MAT 112	Calculus II
MAT 111	Calculus I
MAT 108	Discrete Mathematics
MAT 103	Probability
MAT 100	Math Modeling and Precalculus
CSC 271	Intro to Data Science
CSC 235	(=MAT 235=PHY 235) Stochastic Simulation
CSC 211	Data Structures
CSC 112	Advanced Programming
CSC 111	Intro to Programming (seriously cool class photos)
C&T 201	Cultures and Traditions
FRC	Freshman Colloquium, Enduring Questions
MATH 141	Calculus I (USAFA)
MATH 245	Differential Equations (USAFA)
MATH 469	Partial Differential Equations (USAFA)
APPM 4660	Numerical Analysis II (University of Colorado)
APPM 4650	Numerical Analysis I (University of Colorado)
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 two dogs. Amy and I are dangerously close to being empty nesters. We live just outside Crawfordsville, Indiana, a nice small town an hour from Indianapolis. We've lived in Colorado three separate times -- 2000-2004 (grad school), 2011-2012 (sabbatical #1), and 2018-2019 (sabbatical #2).

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 or skiing, 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.

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