
 Professor David Stewart
Office: McLean Hall 325B
 Email: davidestewart (at) uiowa.edu
 Paper Mail
Department of Mathematics
Room 14, McLean Hall
The University of Iowa
Iowa City, IA 522421419 USA
 Phone: voice: 3193353832
 Fax: 3193350627

Email: davidestewart@uiowa.edu
Office hours: MTuW 10:3011:30am
Research Areas: Numerical
Analysis, Mathematical Modeling, Scientific Computing,
Optimization, Optimal Control
Books:
Other
Publications here.
Other activities:
More Details on Research:

Mechanical impact & measure differential
inclusions
I have worked on mathematical and
computational models of rigid body mechanics (including friction
and collisions). This involves pure mathematics (measure differential inclusions,
J.J. Moreau, 1983) as well as numerical analysis and more classical
applied mathematics. This relates to my PhD work (1990) on
discontinuous ODE's and differential inclusions. One of the major outstanding
issues in the area is the resolution of Painlevé's paradoxes. In
1998 I proved rigorously in terms of measure differential inclusions
& equations, that these problems do indeed have solutions,
provided the maximal dissipation form of Coulomb's law is used with
the post impact velocity  at least for 1dimensional
frictional forces and one contact. This includes Painlevé's
examples, and was the first general result on rigid body dynamics to
do so. This work led me to investigations and results about measure
differential inclusions and equations. More details here. Going beyond rigid
body models, I worked on elastic body mechanics with impact. I
studied a number of different models of elastic and viscoelastic
bodies in impact over 20052009; some of this work was done with my
former students T. Wendt and Jeongho Ahn. The most recent results
published in 2014 were on nonuniqueness of solutions of a family of
viscoelastic bodies in impact.

Differential Variational Inequalities
Differential
Variational Inequalities (DVIs) are a means of modeling
dynamical systems which have hard constraints or limits. These
extend the idea of differential equation, are closely related to differential
inclusions, and are useful for modeling a wide variety of
systems arising in mechanics, biology, economics, and engineering. I
have explored questions of when solutions exist (with J.S. Pang),
and when solutions are also unique.

Mathematics of Machine Learning & Data Mining
Machine learning and data mining are important topics with the
vast amount of data that is being collected through many many
means. I am interested in efficient and useful algorithms for data
mining and machine learning. In 2018, with S. Oliveira
and J. Hajewski I have developed an algorithm for
efficiently solving Support Vector Machine optimization problems
with an l^{1} penalty term. We are designing
parallel algorithms for this type of classification. I have
also worked with P. Jorgensen on the approximation theory of sums
of ridge functions.

Continuous and Discrete Optimization
Other interests include optimization and optimal control. This
includes some work on solving optimal control problems with discrete
control values (e.g., {on, off}, or {1, 0, +1}) with switching
costs. (Without switching costs, the optimal solutions typically
``chatter'' rapidly between the allowed control values, which
``convexifies'' the problems and makes into standard optimal control
problems.) These problems can be NPhard, but there are ways of
developing good, efficient, suboptimal algorithms. In 2006 I
have worked on optimal control problems where the dynamics are discontinuous with
M. Anitescu. In these systems the adjoint variables
(essentially Lagrange multipliers) satisfy the usual differential
equations, except that at times they have jumps.
In 2017, I developed an algorithm with C. Stiegler for minimizing
quadratic functions over permutations. This was used to improve an
algorithm ELMVIS+ which used Extreme Learning Machines for
visualizing complex data sets.
I am interested in good computational/numerical methods for dealing
with dynamical systems, fractals and related objects. One area of
interest is the (numerically stable) calculation of Lyapunov
exponents, which has led me to investigate singular value
decompositions of products of matrices and the notion of stable
products: small perturbations to the factor matrices
should not lead to large relative changes in the singular values. I
have also worked on algorithms that can distinguish between the fractal
and HausdorffBesicovitch dimensions.

Scientific Computing & Interdisciplinary Research
I have worked on a variety of problems in scientific computing
including: done some work on using quadtrees and octrees to improve
the asymptotic behavior of some algorithms for meshfree
methods. Meshfree methods are Galerkin methods for solving
PDE's which don't rely on a mesh like standard Finite Element
Methods do. However, this means that there are more geometric tasks
that have to be performed in the basic meshfree methods. I developed
some computational geometry algorithms using quadtrees for these
tasks with S. Oliveira and students. In 2013 I also worked on the
stability of the numerical solution of the LaplaceBeltrami
operation using meshless methods on curved manifolds with A. Paiva
Neto, L.G. Nonato and others.
In 2014, I analyzed the stability of a numerical method for finite
difference problems arising from timedependent diffusion problems
with C. Oishi and J. Cuminato. During 2017 I consulted with a
biomedical lab to help understand the mechanical behavior of mucus.
I have a passion for mathematical modeling of biological and medical
phenomena, and plan to continue this work in the future.
Current PhD students
 Michael Kratochvil.
 Violet Tiema.
Former PhD students (reverse chronological order):
 Cole Stiegler, obtained PhD in 2018, University of
Iowa; currently at Target Corp.
 Mario Barela, obtained PhD in 2016, University of Iowa;
currently at BAE Systems.
 Benjamin Dill, obtained PhD in 2016, University of
Iowa; currently at Westminster College, Utah.
 Brian Gillispie;
obtained PhD in 2009, University of Iowa; currently at Mt Mercy
College, Cedar Rapids, Iowa.
 Ted Wendt; obtained
PhD in 2008, University of Iowa; currently at Carroll College,
Montana.
 Ricardo Ortiz;
obtained PhD in 2007, University of Iowa; currently at KitWare,
Inc.
 KoungHee Leem;
obtained PhD in 2003, University of Iowa; currently at Southern
Illinois U, Edwardsville.
 Jeongho Ahn; obtained
PhD in 2003, University of Iowa; currently at Arkansas State U.
 Christopher Cartright;
obtained PhD in 2002, University of Iowa; currently at Lawrence
Tech U
Places I have worked
1998present Mathematics Dept., University of Iowa
 19961997 Mathematics Dept., Virginia Polytechnic Institute and
State University
19951996 Mathematics Dept., Texas
A&M University
19911994 Australian National University, School of Mathematical
Sciences and advanced
computation group
 19901991 Mathematics
Department, University of
Queensland,Australia
Some Pictures and Trips:
Here
is a picture from the DaVinci/SICONOS meeting at Grenoble in 2005
showing the DaVinci group.
Here
is a picture of some of us relaxing after the International
Conference on Complementarity Problems (ICCP) in Berlin in 2014.
(Thanks to Uday Shanbhag  not shown  for the picture.)
Here is a
picture from the January 1993 SCADE meeting in Auckland, New
Zealand.
If you can identify anybody not already identified, let me
know...
Or better yet, if you know xfig, then update the xfig file in the
zip here: auckland93.zip.
Here is the list
of the attendees.
My Erdös
number is less or equal to 3. Here
is the proof.
To the Department of
Mathematics