(Link to CAM seminar talks in Fall, 2007)
(Link to CAM seminar talks in Spring, 2007)
(Link to CAM seminar talks in Fall, 2006)
(Link to CAM seminar talks in other years.)
(Link to Numerical Analysis Group Webpage)
| January 30 | Organizational Meeting
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| February 6 |
Jeffrey Humpherys
Brigham Young University Evans Function Computation and the Stability of Viscous Shock Layers in Compressible Fluid Flow Abstract An important analytical and computational tool used in the study of traveling wave stability is the Evans function. In this talk, we review the Evans function and discuss the two classes of numerical methods used to compute it. Specifically, we discuss the compound-matrix method and the polar-coordinate method. The former (linear) method is well-behaved numerically but is of factorial complexity and thus is infeasible for large systems. The latter (non-linear) method has nice complexity properties but sometimes suffers from other numerical problems such as stiffness and ill-conditioning. In the second portion of this talk, we briefly discuss the use of these numerical methods to study the stability of viscous shock layers in compressible fluid flow. We are able to show that large-amplitude viscous shocks layers are stable in the one-dimensional ideal gas Navier-Stokes equations. Finally, we discuss related open problems. | ||||||||||||||||||||||||||||||||
| February 13 |
no speaker
University of XYZ title Abstract |
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February 20 |
Weizhang Huang
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University of Kansas MMPDE moving mesh methods for numerical simulation of problems with blowup solution Abstract
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February 27 |
Alin Pogan
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University of Missouri-Columbia The Dichotomy Theorem for ill-posed equations and applications to infinite dimensional Evans function Abstract We prove that the operator $G$, the closure of the first-order differential operator $-d/dt + D(t)$ on $L_2(R,X)$, is Fredholm if and only if the ill-posed equation $u'(t)=D(t)u(t)$, $t\in\RR$, has exponential dichotomies on $\RR_+$ and $\RR-$ and the ranges of the dichotomy projections form a Fredholm pair; moreover, the index of this pair is equal to the Fredholm index of $G$. Here $X$ is a Hilbert space, $D(t) = A + B(t)$, $A$ is the generator of a bi-semigroup, $B(\cdot)$ is a bounded piecewise strongly continuous operator valued function. Also, we prove some perturbations results and consider various examples of ill-posed problems. The applications to the study of the infinite dimensional Evans function are discussed.
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March 6 | Jens Lang
| Darmstadt University of Technology Will give the colloquium talk at 4PM, THURSDAY, March 6 in 306 Snow. Abstract
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March 12 |
Erik Van Vleck
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University of Kansas Orthosymplectic Integration, Schrodinger Operators, and Lattice Differential Equations Abstract
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March 26 |
Weishi Liu
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University of Kansas On Dafermos regularization of Burger's equation Abstract
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April 2 |
Lennard Kamenski
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Darmstadt University of Technology
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April 9 |
Hongguo Xu
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University of Kansas Perturbation of Purely Imaginary Eigenvalues of Hamiltonian Matrices Abstract We discuss the perturbation theory for purely imaginary eigenvalues of Hamiltonian matrices under Hamiltonian and non-Hamiltonian perturbations. We show that there is a substantial difference in the behavior under these perturbations. We also discuss the perturbation of real eigenvalues of real skew-Hamiltonian matrices under structured perturbations and use these results to analyze the properties of the URV method of computing the eigenvalues of Hamiltonian matrices.
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April 16 |
Myunghyun Oh
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University of Kansas The Evans function in infinite dimensions Abstract We consider an elliptic equation with periodic boundary conditions and define a stability index with Evans function. The key for defining the index is exponential dichotomies for the system. This system has infinite dimensional stable and unstable spaces. We use Galerkin approximation to reduce down these dimensions to finite and show persistence of dichotomies.
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April 23 |
Nicole Abaid
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University of Kansas Steady-State Poisson-Nernst-Planck Systems: Asymptotic expansions and applications to ion channels (MSc defense)
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April 30 |
Yinnian He
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University of Kansas and Xian Jiaotong University The Implicit/Explicit Scheme for the Time-Dependent Navier-Stokes Equations
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May 7 |
Haijun Wu
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Nanjing University Adaptive finite element methods for diffraction gratings Abstract Adaptive finite element strategies with error control are developed for wave scattering by periodic and biperiodic structures. The unbounded computational domain is truncated to a bounded one by a perfectly matched layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. Numerical experiments are presented to illustrate the competitive behavior of the proposed adaptive method.
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