Computational
and Applied Mathematics (CAM) Seminar
Fall, 2016
– Spring, 2017
CAM seminar
talks are held on Wednesday from 2:003:00PM in Snow Hall 306, unless otherwise
noted.
Previous CAM
talks: Fall, 2006;
Spring, 2007; Fall, 2007; Spring, 2008; Fall, 2008; Spring, 2009;
20092010; 20102011; 20112012 20122013 20132014 20142015 20152016
KU Numerical
Analysis Group Webpage
Date 
Speaker/Institution 
Title
and Abstract 
Aug
31 
Organizational
meeting 

Sept
7 
Xiang
Wang (Jilin University, China) 
Title:
L2 error estimates for high order finite volume methods on triangular meshes Abstract:
Due to the local conservation property, the finite volume method (FVM) has
enjoyed great popularity among scientific and engineering computation.
However, compared to its wide applications, the development of FVM theory
lags far behind, especially for high order schemes on triangular meshes. We
establish a unified framework for L2 error analysis for high order Lagrange
finite volume methods on triangular meshes. Orthogonal conditions are
proposed to construct dual partitions on triangular meshes so that the
corresponding FVMs hold optimal L2 norm convergence order. 
Sept
14 
Ashish Pandey (UIUC) 
Title:
Modulational instability in nonlinear dispersive
equations. Abstract:
Slow modulations in wave characteristics of a nonlinear, periodic traveling
wave in a dispersive medium may develop nontrivial structures
which evolve as it propagates. This phenomenon is called modulational instability. In context of water waves, this
phenomenon was observed by Benjamin and Feir and,
independently, by Whitham in Stokes' waves. I will
discuss a general mechanism to study modulational
instability of periodic traveling waves which can be
applied to several classes of nonlinear dispersive equations including KdV, BBM and regularized Boussinesq
type equations. 
Sept
21 
Geng Chen 
Title: Large solutions of compressible Euler equations Abstract: Compressible Euler equations (introduced by Euler in 1757)
model the motion of compressible inviscid fluids
such as gases. It is wellknown that solutions of
compressible Euler equations often develop discontinuities, i.e. shock waves.
Successful theories have been established in the past 150+ years for small
solutions in one space dimension. The theory on large solutions is widely
open for a long time, even in one space dimension. In this talk, I will discuss some recent exciting progresses in this
direction. In the first part of this talk, I will discuss our complete
resolution of shock formation problem, which extends the celebrated work of
Peter Lax in 1964. Our result relies on the discovery of a sharp
timedependent lower bound on density, when solutions approach vacuum in
infinite time. In the second part, I will show our recent negative example
concerning the failure of current available frameworks on approximate
solutions in order to establish large BV (bounded total variation)
theory. The talk is based on my joint works with A. Bressan,
H.K. Jenssen, R. Pan, R. Young, Q. Zhang, and S.
Zhu. This
talk is accessible for graduate students. The connection between our results
and RiemannÕs original paper in 1859 will also be mentioned. 
Sept
28 
Weizhang Huang 
Title: Conditioning of finite element
equations with arbitrary nonuniform meshes Abstract: Mesh adaptation has become
an indispensable tool for use in the numerical solution of partial
differential equations to improve computational accuracy and efficiency.
However, mesh adaptation often leads to nonuniform
meshes and their nonuniformity can have significant
impacts on the conditioning and the efficient solution of the underlying
algebraic systems. In this talk we will present some new results in the
studies of those impacts for the finite element approximation of boundary
value and initialboundary value problems of linear diffusion equations. 
Oct
5 
Hang
Si (WIAS, Berlin) 
Title: An Introduction to Delaunaybased Mesh
Generation and Adaptation Abstract: Mesh generation and
adaptation are key steps in many applications such as numerical methods like
finite element and finite volume methods. It is itself a research topic with
background in mathematics, computer science, and engineering. Delaunay triangulation has many nice
properties and is popularly used in many mesh generation methods. In this
talk, we will begin with triangle mesh generation in the plane. This problem
has been very well studied. Efficient algorithms are developed. We will then move to tetrahedral mesh
generation in 3d, which is still challenged by many theoretical and practical
issues. We will introduce classical and recent algorithms that are both
theoretically correct and efficient in practice. Various examples are
illustrated using open source software Triangle and TetGen. 
Oct
12 
Andrew
Roberts (Cerner Corporation) 
Title: Mathematics in Healthcare and
The Challenges of RealWorld Data Abstract: You may be familiar with methods like
regression, decision trees, survival analysis, and timeseries analysis. In academia, I was accustomed to
implementing methods with nice data.
What do you do when you have missing or mislabeled data? How do you analyze a timeseries where
the time between observations could range from 30 minutes to multiple
hours? This presentation will
highlight some of the challenges that the Cerner Math team faces and the
nuances of using familiar methods in realworld examples. 
Oct
19 
German
LozadaCruz (Sao
Paulo State University UNESP, Brazil) 
Title:
Continuity of the set of equilibria Abstract:
In this talk we will treat about the continuity of the set of equilibria of a parabolic PDE with homogeneous Dirichlet boundary conditions via the discretization of
finite element method. 
Oct
26 
Mat
Johnson 
Title: Stability and Long
Time Modulational Dynamics of Periodic Waves in
Dissipative Systems Abstract: The capability of
spatially periodic waves to cary modulation signals
makes their dynamics under perturbation rich in multiscale phenomena and
essentially infinite dimensional. Here, I will discuss recent progress in the
understanding of the stability and local dynamics of periodic waves capable
of carrying multiple modulation signals in dissipative models, and in
particular how (locally) the long time dynamics are approximately governed by
an averaged system of equations obtained through a nonlinear WKB process. 
Nov
2 
Junbo Cheng
(Institute of Applied Physics and Computational Mathematics, Beijing, China) 
Title:
Approximate Riemann solvers and the highorder cellcentered Lagrangian schemes for elasticplastic flows Abstract:
For elasticplastic flows with the hypoelastic constitutive model and vonMises' yielding condition, the nonconservative character
of the hypoelastic constitutive model and the vonMises'
yielding condition make the construction of the solution to the Riemann
problem a challenging task. In this talk, I will first present analysis for
the wave structure of the Riemann problem and develop accordingly a
tworarefaction Riemann solver with elastic waves for 1D elasticplastic
flows (TRRSE) and a fourrarefaction wave approximate Riemann solver with
elastic waves (FRRSE) for 2D elasticplastic flows. Because of the
complexities of the equation of state and the discontinuities around the
elastic limit, we have to use Gaussian quadrature method to evaluate the
integral term of Riemann invariant variables. Moreover, it is impossible to
get the exact solution of Riemann solvers, it is
necessary to use Newton Iteration method to obtain the convergent Riemann
solvers. Besides, for the 2D elasticplastic flows, in the construction of
FRRSE one needs to use a nested iterative method. A direct iteration
procedure for four variables is complex and computationally expensive. In
order to simplify the solution procedure we develop an iteration based on two
nested iterations upon two variables, and our iteration method is simple in
implement and efficient. Because the iteration is used during constructing
TRRSE, it is expensive in CPU time. So, we build a HLLC approximate Riemann solver
with elastic waves (HLLCE) for onedimensional elasticplastic flows. Based on TRRSE and HLLCE, we build the
thirdorder cellcentered Lagrangian numerical
schemes; Based on FRRSE as a building block, we therefore propose a 2ndorder
cellcentered Lagrangian numerical scheme. A
numerical result with smooth solutions shows our scheme achieves the desired
convergent order. Moreover, a number of numerical experiments with shock and
rarefaction waves demonstrate the scheme is essentially nonoscillatory and
appears to be convergent. Moreover, for shock waves the present scheme has
comparable accuracy to that of the scheme developed by Maire
et al, while it is more accurate in resolving rarefaction waves. 
Nov
9 
Fola Agosto (KU Ecology and Evolutionary Biology) 
Title:
Mathematical Model for Zika Virus Dynamics with
Sexual Transmission Pathway 
Nov
16 
Lam
Mountaga (Cheikh Anta Diop University, Senegal) 
Title:
Optimal intervention strategies of a SIHIV models with rdifferential
infectivity and two time delays Abstract:
Retarded optimal control theory is applied to a system of delays ordinary
differential equations modeling a HIV model with differential infectivity.
Seeking to reduce the infective individuals with high viral load, we use
control representing the fraction of infective individuals that is identified
and will be put under treatment. The optimal controls are characterized in
terms of the optimality system, which is solved numerically. 
Nov
23 
Thanksgiving


Nov
30 
Weishi Liu 
Title:
Nonlocal nature of excess potentials and
boundary value problems of PoissonNernstPlanck systems 
Dec
7 
Hongguo Xu 
Title:
Sign characteristics of Hermitian matrix
polynomials Abstract:
Sign characteristic is a concept that is essential for the stability analysis
in Hamiltonian
systems and the perturbation behavior of eigenvalues under structured perturbations. In this
talk, we define sign characteristic for infinite eigenvalues. We
show the behavior of sign characteristics under changes of variables and also
a signature constraint
theorem. This
is a joint work with Volker Merman, Vanni Noferini, and Francois Tisseur. 
Jan
18 
Organizational
meeting 

Jan
25 
Tao
Huang (NYUECNU Institute of Mathematical Sciences at NYU Shanghai) 
Title:
Singularities and nonuniqueness of nematic liquid crystal flows Abstract:
In this talk, we will discuss two examples of finite time blowups for the
simplified nematic liquid crystal flows in
dimension three. The first example is constructed within the class of
axisymmetric solutions, while the second one is constructed for initial data
with small energy but large topology. We will also construct infinitely many
weak solutions to the system with suitable initial and boundary data. These
weak solutions have bounded energy and Ôbackward bubblingÕ at a large time. 
Feb
1 


Feb
8 


Feb
15 
Paul
Cazeaux (University of Minnesota) 
Title:
C* Algebras, Modeling and Simulations for Incommensurate Van Der Waals 2D Heterostructures Abstract:
The recently discovered family of twodimensional materials has generated
enormous interest as highlighted by the 2010 Nobel Prize for the discovery of
graphene. These atomicallythin
crystals include insulators (boron nitride), semiconductors (transition metal
dichalcogenides), and conductors (graphene). Vertical stacks of a few such layers,
interacting through van der Waals forces, create a venue to explore and tune
desired electronic properties: new emergent orders and physical phenomena are
expected, leading to novel functionalities. However, the lack of periodicity
(incommensurability) of these systems represents a significant hurdle for
theoretical understanding and in particular for numerical simulations. In
this talk, we discuss a mathematical framework and multiscale calculations
aimed at predicting macroscopic properties of Van der Waals 2D heterostructures. We present an original methodology lying
at the intersection between computational mathematics, powerful algebraic
concepts such as C*algebras and noncommutative geometry, and modern physics
applications. With a onedimensional example, we illustrate the various rich
phenomena arising in such structures and their possible connections to
nontrivial topological behavior in materials. 
Feb
22 
Agnieszka Miedlar 
Title:
On matrix nearness problems: distance to delocalization. Abstract:
Numerous problems in mechanics, mathematical physics, and engineering can be
formulated as eigenvalue problems where the focus is to determine whether the
eigenvalues are inside a specific desirable domain, and later on to detect an
admissible size of a perturbation which will not move the eigenvalues away
from that domain. The most frequent of such domains in use are connected to
the stability of dynamical systems: the open left halfplane of the complex
plane (continuous dynamical systems) and the open unit disk (discrete dynamical systems). In this
talk we introduce two new matrix nearness problems, i.e., distance to
delocalization and the distance to localization, to analyze the robustness of
eigenvalues with respect to arbitrary localization sets (domains) in the
complex plane. Following the theoretical framework of Hermitian
functions and the Lyapunovtype localization
approach, we present a new Newtontype algorithm for the distance to
delocalization (D2D). Since our investigations are motivated by several
practical applications, we will illustrate our approach on some of them. 
Mar
1 
Chenchen Mou (UCLA) 
Title: Uniqueness and
existence of viscosity solutions for a class of integrodifferential
equations. Abstract: We present
comparison theorems and existence of viscosity solutions for a class of
nonlocal equations. This class of equations includes BellmanIsaacs equations
containing operators of Levy type with measures depending on the state
variable and control parameters. 
Mar
8 
Geng Chen 
Title:
Global wellposedness for scalar integrable systems with cusp singularity Abstract:
The cusp singularity is a common type of singularity for nonlinear waves. In
this talk, we discuss the global wellposedenss
for CamassaHolm and HunterSaxton equations. We
will focus on the existence and uniqueness. We will also discuss the
regularity of solutions for this type of equations and other type of
equations such as hyperbolic conservation laws and shortpulse equation. 
Mar
15 
Cuong Ngo 
Title:
A Moving Mesh Method for the Porous Medium Equation with Compactly Supported
Solutions. Abstract:
A moving mesh finite element method is considered for solving the porous
medium equation (PME), where the original equation is reformulated in terms
of its pressure. Such reformulation is a common strategy in mathematical
analysis of PME, since the pressure solution has a higher regularity than the
original solution. The method is based on the moving mesh partial
differential equation (MMPDE) method, and is applicable to solutions with
compact supports and/or having free boundaries. The method discretizes only
on the support of such a solution and employs DarcyÕs law for moving the free
boundary. Numerical results in 2D are presented. 
Mar
22 
Spring
break 

Mar
29 
Xuemin Tu 
Title:
BDDC methods for Darcy flows Abstract:
In this talk, BDDC algorithms will be developed for the saddle point
problems arising from mixed formulations of Darcy flow in porous media. In addition
to the standard nonetflux constraints on each edge/face, adaptive primal
constraints obtained from the solutions of local generalized eigenvalue
problems are included to control the condition number. Special deluxe scaling and local
generalized eigenvalue problems are designed in order to make sure that these
additional primal variables lie in a benign subspace in which the
preconditioned operator is positive definite. Condition number estimates will be
discussed and some numerical experiments will provide to confirm the
theoretical estimates. 
Apr
5 
JiCong (Jack) Shi
(KU Department of Physics & Astronomy) 
Title:
StrainEnergy Model for the Configuration of SelfAssembled Nanostructures in
Nanocomposite Films Abstract:
Selfassembled nanostructures in epitaxial films provide a unique approach to
design and tailor physical properties of nanocomposite
films by controlling the configuration of the nanostructures. Hightemperature superconducting films with secondary phase
nanostructures is an excellent example and the formation of
verticallyaligned secondary phase nanorods has
been extensively studied experimentally for the enhancement of magnetic
pinning properties of the films. To achieve an optimal pinning efficiency for
superconducting film applications, it is important to control nanostructure
configuration with a desired nanostructure density through selecting
compatible dopant materials or film fabrication conditions. Such a control
requires an understanding of the underlying physics of the formation of the
nanostructures. In the formation of secondary phase nanostructures in
epitaxial films, the lattice strain due to the lattice mismatch between the
film matrix and dopant has been recognized as a primary driving force
determining the configuration of the nanostructures. In this talk, I will
discuss how to model the elastic energy of the coherently strained lattice
and the noncoherent interfacial energy on the nanostructure surface for
studying the configuration of nanostructures in epitaxial nanocomposite
films. Especially, the mathematical difficulties of this problem will be
discussed. 
Apr
12 
Avary Kolasinski 
Title: A new functional for
variational mesh generation and adaptation based on
equidistribution and alignment for bulk meshes Abstract: We will introduce
a new meshing functional for variational mesh
generation and adaptation with minimal parameters based on the equidistribution and alignment conditions. We will
discuss the theoretical properties of this functional including its coercivity and the nonsingularity
and existence of limiting meshes. We will then present a comparative
numerical study of this new functional with one well known functional, which
is also based on the equidistribution and alignment
conditions. Finally, we will introduce the theory of variational
mesh generation and adaptation on surface meshes. 
Apr
19 
Hongguo Xu 
Title:
Transforming an LTI passive system to a portHamiltonian system Abstract:
PortHamiltonian system arises naturally from various modeling problems. A
portHamiltonian system is a passive system but with a special structure. In
this talk, we try to answer the following questions. Can a passive system be
transformed to a portHamiltonian system? If the answer is yes, how to
construct a portHamiltonian system? This
is a joint work with Christopher Beattie and Volker Merman. 
Apr
26 
Bob
Eisenberg (Rush University Medical Center) 
Title:
Electricity is different Abstract:
here 
May
3 
Weishi Liu 
Title: Flux ratios and channel structures Abstract: We investigate UssingÕs
unidirectional fluxes and flux ratios of charged tracers motivated
particularly by the insightful proposal of Hodgkin and Keynes on a relation
between flux ratios and channel structure. The study is based on analysis of
quasionedimensional PoissonNernstPlanck type models for ionic flows
through membrane channels. This class of models includes the Poisson equation
that determines the electrical potential from the charges present and is in
that sense consistent. UssingÕs flux ratios
generally depend on all physical parameters involved in ionic flows,
particularly, on bulk conditions and channel structures. Certain setups of
ion channel experiments result in flux ratios that are universal in the
sense that their values depend on bulk conditions but not on channel
structures; other setups lead to flux ratios that are specific in the
sense that their values depend on channel structures too. Universal flux
ratios could serve some purposes better than specific flux ratios in some
circumstances and worse in other circumstances. We focus on two treatments of
tracer flux measurements that serve as estimators of important properties of
ion channels. The first estimator determines the flux of the main ion species
from measurements of the flux of its tracer. Our analysis suggests a better
experimental design so that the flux ratio of the tracer flux and the main
ion flux is universal. The second treatment of tracer fluxes concerns ratios
of fluxes and experimental setups that try to determine some properties of
channel structure. We analyze the two widely used experimental designs of
estimating flux ratios and show that the most widely used method depends on
the spatial distribution of permanent charge so this flux ratio is specific
and thus allows estimation of (some of) the properties of that permanent
charge, even with ideal ionic solutions. The talk is based on a joint work with Shuguan Ji from Jilin
University and Bob Eisenberg from Rush Medical School at Chicago. 
May
10 
Brendan
Gavin (University of Massachusetts Amherst) 
Title: The FEAST Algorithm:
Using Complex Contour Integration for Solving Large Eigenvalue Problems Abstract: One of the most
challenging tasks in contemporary numerical linear algebra is the efficient
solution of large eigenvalue problems. FEAST is an algorithm that uses a
Cauchy integral representation of the indicator function in order to
selectively obtain the eigenvalues in userspecified
regions of the complex plane, making it possible to rapidly solve for the
eigenvalues of interest in a naturally parallel fashion. We describe the
theory and application of the FEAST eigenvalue solver, with an emphasis on
recent developments that make it possible to implement FEAST by using only
matrixvector multiplication. 