Math/ICES Center of Numerical Analysis Seminar (Spring 2013)

Time and Location: Friday, 3:00-4:00PM, ACE 6.304. Special time and locations are indicated in color.

If you are interested in meeting a speaker, please contact Kui Ren (

Here are the links to the past seminars: Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009



Title and Abstract




Alessandro Munafo

(Von Karman Institute, Belgium)

Multiscale Models and Computational Methods for Nonequilibrium Aerothermodynamics

Understanding nonequilibrium phenomena occurring in aerothermodynamic flows is of fundamental importance for many applications. Typical examples, taken from the aerospace domain, are the design of heat shields for space vehicles and interpretation of experiments carried out in high enthalpy wind tunnels. Progresses made in the development physical models and computational methods for aerospace applications could also be used in other areas (such as plasma enhanced combustion and electric propulsion) where the occurrence of nonequilibrium must be taken into account as well. Di fferent regimes can be distinguished in the frame of nonequilibrium flows. When the local Knudsen number does not exceed values of the order 0:01, a hydrodynamic (or continuum) description of the  flow can be used. For higher values of the local Knudsen number, rarefied gas eff ects start to occur. The former can be correctly described only by adopting a kinetic description of the flow. The seminar will be divided into two parts. Thefirst will focus on the development of macroscopic physical models for molecular dissociation and internal energy excitation within the context of a continuum flow description. The second will be devoted to the development of computational methods for the solution of kinetic equations for rarefied flows.




Thierry E. Magin

(Von Karman Institute, Belgium)

Multicomponent transport algorithms for plasmadynamics models

A new formalism for the transport properties of partially ionized plasmas is investigated from a computational point of view. Well-posedness of the transport properties is established, provided that some conditions on the kinetic data are met. The mathematical structure of the transport matrices is readily used to build transport algorithms that rely either on a direct linear solver or on convergent iterative Krylov projection methods, such as the conjugate gradient. Air and carbon dioxide mixtures in local thermodynamic equilibrium at atmospheric pressure serve as benchmark to assess the physical model and numerical methods. Superiority of the conjugate gradient method with respect to the direct solver and approximate mixture rules found in the literature is demonstrated in terms of accuracy and computational cost.




RLM 11.176

Fons ten Kroode

(Shell Global Solutions International BV, The Netherlands)

A Wave-Equation-Based Kirchhoff Operator

In this talk, I will study a Kirchhoff-type integral, which can be seen as a linear operator mapping angle–azimuth-dependent reflection coefficients along a reflector into reflection data for the acoustic wave equation. I will show that a minor adaptation of a construction of angle–azimuth-dependent images as proposed by Sava and Fomel leads to a left inverse of this operator, which maps primary reflection data to angle–azimuth-dependent reflection coefficients. The new construction naturally leads to a reformulation of the Kirchhoff operator, acting on space-shift-extended images, which can be implemented completely in terms of the fundamental solutions of the wave equation. I will study the composition of this new wave-equation-based Kirchhoff operator with an operator forming space-shift-extended images from data. I will show that these operators are partial inverses of each other, with their compositions being pseudo-differential operators that reconstruct suitably microlocalized versions of primary reflection data and extended images focused at space-shift zero.



Jose Rodriguez

(UC Berkeley)

Numerical Algebraic Geometry in Statistics

Maximum likelihood estimation is a fundamental computational task in statistics and involves beautiful geometry. We discuss this task for determinantal varieties (matrices with rank constraints) and show how numerical algebraic geometry can be used to maximize the likelihood function. Our computational results with the software Bertini led to surprising conjectures and duality theorems. This is joint work with Jan Draisma, Jon Hauenstein, and Bernd Sturmfels.



Yuri Kuznetsov

(University of Houston)

Mixed Finite Element Method with Piecewise Constant Fluxes

In this presentation, we consider a new mixed finite element method for diffusion equations on general polygonal/polyhedral meshes. Originally the method was invented in 2007.Then it was used in a number of projects supported by ExxonMobil URC. The main idea of the method is based on the approximation of the fluxes by piecewise constant vector functions (PWCF).The normal components of the approximate vector functions are continuous on the interfaces between polyhedral mesh sells. In the interior of mesh cells these vector functions are discontinuous. The error estimates for the special type of meshes are derived. We discuss applications of the PWCF-method in geosciences as well as numerical results.



Ammar Hakim

Princeton Plasma Physics Laboratory

Aspects of Discontinuous Galerkin Schemes for Fluid and Kinetic Simulations of Plasmas

A large class of kinetic and fluid problems in plasma physics can be expressed using a Hamiltonian approach. Such systems consist of an advection equation coupled to field equations. The advection speeds are determined from the Hamiltonian and a Poisson bracket, and, in many instances, the fields are computed using elliptic equations. One feature of such systems are the existence of quadratic invariants, like energy and, in context of incompressible fluid flow, enstrophy. In this talk we present extensions of discontinuous Galerkin algorithms to solve such equations. We show that with a proper choice of basis functions for the advection and elliptic equations the DG schemes can conserve energy exactly. Further, with a choice of central fluxes the enstrophy (the L2 norm of the solution) can also be conserved exactly. Extension to the scheme to handle discontinuous Hamiltonians are developed. Application of these schemes to incompressible flow problems, drift wave turbulence and Vlasov-Poisson equations are presented.