NEW ! (login requested)
Photo Gallery
Slides of Invited Speakers
Abstracts of Posters
HOME
Registration / Payment
closed
Poster Abstract Submission
closed
Important dates/deadlines
Participants
Program
Venue and Accommodation
Contact / Committees
Print Media
Sponsors

Program
FRIDAY 18 February  Room: HG G3 
08:30 
Registration  Location: In room no. HG G19.1 
09:0009:45

Björn Engquist,
University of Texas Convergence rates for numerical approximations of hyperbolic equations
Abstract (click to expand)
The literature for convergence analysis of numerical approximations of hyperbolic equations is vast and contain
many highly elegant results. Still most of today's simulations of nonlinear problems lack a rigorous foundation.
We will discuss the history and focus on some inherent difficulties with a view to the future.

09:4510:30

Manuel Torrilhon, RWTH Aachen
On Entropy for Moment Equations in Kinetic Gas Theory
Abstract (click to expand/collapse)
Moment Equations are used as nonlinear approximations
for the solution of Boltzmann's equation in kinetic gas
theory. As a continuum model of gas flows they can
successfully replace classical gas dynamical equations
when the thermal nonequilibrium is too strong. The approximation theory must be build on accuracy with respect to the Boltzmann equation but also need
to satisfy structural requirements like the existence
of an entropy law. We will discuss recent developments how to establish
moment equations with entropy law.

10:3011:00 
Coffee Break  Location: In room no. HG G19.1 
11:0011:45

Timothy J. Barth, NASA, Ames Research Center
Energy Stable FEM Discretization of EulerMaxwell Systems
Abstract (click to expand/collapse)
The EulerMaxwell equations are a moment approximation of the kinetic VlasovMaxwell description.
These equations arise in the plasma physics modeling of plasma rockets, various fusion devices, lasers,
and astrophysics. Multifluid EulerMaxwell approximations have received considerable attention because of
the excellent prediction of magnetic reconnection in low viscosity plasma regimes [Loverich and Shumlak (2005),
Johnson and Rossmanith, (2008)]. Note that standard magnetohydrodynamics (MHD) approximations can be obtained as
simplifications of the EulerMaxwell plasma system. Even so, the differences between EulerMaxwell and MHD have a
profound effect on the theory and construction of numerical methods for each system.
In this presentation, we use the multifluid EulerMaxwell system to illustrate and review the construction of
energy stable discontinuous Galerkin approximations for nonlinear hyperbolic systems. Surprisingly, the stability
theory underpinning these numerical approximations is significantly simpler for EulerMaxwell systems when conpared to MHD!!
This occurs due to the different way solenoidal constraints (involutions) enter into the energy balance for each system.
In addition, energy stable boundary conditions (e.g. conducting walls) emerge naturally from the formulation. Finally, we
show calculations of 2fluid EulerMaxwell plasmas undergoing magnetic reconnection to assess properties of the numerical
methods that we have implemented.

11:4512:30

Giovanni Russo, Università di Catania
ImplicitExplicit RungeKutta schemes for hyperbolic systems with sti relaxation in the hyperbolic and diusive limit
Abstract (click to expand/collapse)
 Abstract pdf to download
Several mathematical models are described by hyperbolic systems with
stiff relaxation, defined by a small relaxation time ϵ. In
the socalled hyperbolic relaxation, as the ϵ vanishes, the
system relaxes to another hyperbolic system with smaller number of
equations. Classical method of line approach based on finite
difference schemes present the double difficulty: the stiffness of the
source term, and the requirement that in the limit of infinite
stiffness the scheme becomes a consistent discretization of the
relaxed system.
ImplicitExplicit (IMEX) schemes constitute a powerful tool to attach
this problem (see for example [4] and references therein).
In such schemes, the (non stiff) hyperbolic terms are treated
explicitly, while the (stiff) source terms are treated implicitly. It
will be shown that under certain conditions, IMEX schemes provide the
correct asymptotic behavior as the stiffness parameter ϵ
vanishes. Furthermore, singular perturbation method can be employed to
derive order conditions which will provide uniform accuracy in
ϵ [1].
In the case of diffusive relaxation the situation is much more
complicated. In this case the characteristic speeds of the hyperbolic
part depend on ϵ and diverge as ϵ→0. There are
methods that allow to overcome such stiffness, and that allow the
construction of asymptotic preserving shemes that, in the limit of
infinite stiffness, reduce to a consistent explicit scheme for the
underlying diffusion (or convectiondiffusion) equation [3].
Here we present two techniques for the construction of IMEX schemes
which capture the diffusive limit, without the classical stability
restriction on the time step ∆t = O(∆x ^{2}).
The first one, developed in collaboration with L.Pareschi,
is based on an implicit treatment of some hyperbolic
terms, which can however be explicitly computed, while the second
one, which treats the hyperbolic terms explicitly, is obtained by
applying additional condition on the RK coefficients, obtained by a
singular perturbation expansion of both the solution and the numerical
solution [2].
Several numerical tests will be presented that illustrate the
robustness and generality of the methods.
Most of the results presented have been developed in collaboration
with Sebastiano Boscarino, DMI, University of Catania.
[1] Boscarino S.: Error Analysis of IMEX RungeKutta Methods Derided from Differential Alge
braic Systems, SIAM J. Numer. Anal. 45, No 4, 16001621 (2007).
[2] Boscarino S., Russo G., Pareschi L.: IMEX RungeKutta schemes for hyperbolic systems of conservation laws with stiff diffusive relaxation, in preparation.
[3] Naldi G., Pareschi L.: Numerical Schens for Hyperbolic Systems of Conservation Laws with
Stiff Diffusive Relaxation. SIAM J. on Numer. Anal., 37, 12461270 (2000).
[4] Pareschi L., Russo G.: ImplicitExplicit RungeKutta schemes and applications to hyperbolic
systems with relaxations. Journal of Scientific Computing 25, 129155 (2005).

12:3013:45 
Lunch Break 
13:4514:30

Philippe G. LeFloch, University Pierre et Marie Curie, Paris
Latetime asymptoticpreserving approximations of hyperbolic equations with stiff relaxation
Abstract (click to expand/collapse)
We investigate the latetime asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff source term.
On one hand, we determine the relevant asymptotic expansion, derive a reduced
system in the limit, and discuss the role of an entropy condition to establish the diffusive nature of the reduced system. On the other hand,
we propose a new numerical scheme of finite volume type, which allows us to recover the correct asymptotic regime. The associated discrete form
of the diffusion system is achieved via
a suitable discretization compatible with the stiff source term. Our theoretical results are illustrated with several models from continuum physics and
numerical experiments demonstrating the relevance of the proposed theory and numerical strategy.
(This is a joint work with C. Berthon and R. Turpault.)

14:3015:15

Smadar Karni, University of Michigan
Numerical Approximation of Shock Waves in NonConservative Hyperbolic Systems
Abstract (click to expand/collapse)
Nonconservative hyperbolic systems arise in a wide range of applications.
The difficulty lies in the fact that shock relations depend not only on the immediate
states ahead/behind the shock, but also on the viscous path that connects them.
The mathematical theory of weak solutions has been generalized to the nonconservative
setup us ng viscosity and viscous path. While advances have been
made on the theoretical front, those advances have been slow to translate into successful
numerical methods. In this talk, we shed light on some of the difficulties involved by considering
the socalled pathconservative numerical scheme applied to an illuminating example from gas.
This is joint work with Remi Abgrall, University of Bordeaux, France

15:1516:30 
POSTER SESSION & Coffee Break  Location: In room no. HG G19.1 
16:3017:15

Randall J. LeVeque, University of Washington
The GeoClaw Software for Tsunamis and Other Hazardous Flows
Abstract (click to expand/collapse)
Many geophysical flows over topography can be modeled by
twodimensional depthaveraged fluid dynamics equations. The shallow
water equations are the simplest example of this type, though it is
often necessary to incorporate nonhydrostatic pressures, more
complicated rheologies (e.g. for avalanches, landslides, or debris
flows), or to use multilayer models, e.g. for capturing internal
waves or to model a landslideinduced tsunamis.
These equations are generally hyperbolic and can be modeled using
highresolution finite volume methods designed for such problems.
However, several features ew algorithmic
challenges, such as the fact that the depth goes to zero at the
edge of the flow and that vastly differing spatial scales must
often be modeled, making adaptive mesh refinement essential. I
will discuss some of these algorithms and the GeoClaw software,
a specialized version of Clawpack that is aimed at solving realworld
geophysical flow problems over topography. Inparticular I will
show results from some recent tsunamis and potential future events.
For information about the software, see www.clawpack.org/geoclaw.

17:1518:00

ChiWang Shu, Brown University
Maximumprinciplesatisfying and positivitypreserving
high order discontinuous Galerkin and finite volume
schemes for conservation laws
Abstract (click to expand/collapse)
We construct uniformly high order accurate discontinuous Galerkin
(DG) and weighted essentially nonoscillatory (WENO) finite volume
(FV) schemes satisfying a strict maximum principle for scalar
conservation laws and passive convection in incompressible flows, and
positivity preserving for density and pressure for compressible Euler
equations. A general framework (for arbitrary order of accuracy) is
established to construct a limiter for the DG or FV method with first
order Euler forward time discretization solving one dimensional scalar
conservation laws. Strong stability preserving (SSP) high order time
discretizations will keep the maximum principle and make the scheme
uniformly high order in space and time. One remarkable property of
this approach is that it is straightforward to extend the method to
two and higher dimensions. The same limiter can be shown to preserve
the maximum principle for the DG or FV scheme solving twodimensional
incompressible Euler equations in the vorticity streamfunction
formulation, or any passive convection equation with an incompressible
velocity field. A suitable generalization results in a high order DG
or FV scheme satisfying positivity preserving property for density and
pressure for compressible Euler equations. Numerical tests
demonstrating the good performance of the scheme will be reported.
This is a joint work with Xiangxiong Zhang.

19:30 
Conference Dinner at Hotel Zurichberg
(more details)



SATURDAY 19 February  Room: HG G3 
09:0009:45

Olavi Nevanlinna, Aalto University
Multicentric Holomoprhic Calculus
Abstract (click to expand/collapse)
Consider the following situation. We are given an element in a Banach algebra and the following operations are assumed: one can form polynomials from the algebra element and one can ask for the norm of such a polynomial.
Also, we are given an analytic function of which we can ask values of it and its derivatives at points of our choice.
Can we have an algorithm which evaluates the analytic function at the Banach algebra element, whenever it can be consistently defined.
One needs to know the spectrum of the element and then the function can be evaluated provided the function is analytic in a neighborhood of the convex hull of the spectrum. We have recently shown [1] that there exists an algorithm to represent the resolvent outside any open neighborhood of the polynomially convex hull of the spectrum. Then the holomorphic functional calculus can be used to define the function at the element.
In this talk we focus on computational aspects of using the representation of the resolvent within the Cauchy integral. The resolvent is written explicitly as a power series with help of just one polynomial. This in a natural way leads to a multicentric power series (Jacobi series) for the holomorphic function. The formulas are spelled out in [2].
References.
[1] O.Nevanlinna, Numer Funct Anal Optim 30, 10251047, 2009
[2] O.Nevanlinna, Multicentric holomorphic calculus, Helsinki University of Technology, Mathematics Research Reports, A596, 2010

09:4510:30

Martin Gutknecht, SAM  ETH Zurich
Deflation based preconditioning of linear systems
of equations
Abstract (click to expand/collapse)
Krylov solvers are currently the standard tool for solving very large sparse linear systems
of equations by iteration. But for most realworld problems they only converge in a
reasonable number of iterations if a suitable preconditioning technique is applied. This is
particularly true for problems where the linear operator has eigenvalues of small absolute
value  a situation that is very common in practice. One suitable technique for dealing
with such problems is to identify an approximately invariant subspace $\mathcal Z$ that belongs
to the set of these small eigenvalues. By using an orthogonal projection along $\mathcal Z$ the
Krylov solver can then be applied only to the orthogonal complement by restricting the
operator accordingly. The basis constructed implicitly or explicitly by this restricted
operator should then be augmented by a set of basis vectors for $\mathcal Z$. There are various
ways to handle and implement this approach. They differ not only algorithmically and
numerically, but sometimes also mathematically. Some keywords associated with such
methods are `(spectral) deflation', `augmented basis', `recycling Krylov subspaces', and
`singular preconditioning'.
While we quickly also review the `symmetric case', where the linear system is Hermitian
(or real and symmetric), we are mostly interested in the `nonsymmetric case', where our
main message is that the orthogonal projection should be replaced by a suitable oblique
projection, so that when its nullspace is invariant, so is its range.

10:3011:00 
Coffee Break  Location: In room no. HG G19.1 
11:0011:45

Achim Schroll, University of Southern Denmark
On automated computational modeling in the geo and life sciences
Abstract (click to expand/collapse)
We shall experience selfcalibrating computational models with applications in both geo and life sciences.
The automated implementation in the FEniCS software suite will be illustrated.

11:4512:30

Siegfried Müller, RWTH Aachen
Adaptive multiresolution finite volume discretization
of the Variational Multiscale Method
Abstract (click to expand/collapse)
In order to investigate turbulent phenomena in compressible flows
the Variational Multiscale Method (VMS) is used. This method is usually
applied to incompressible flows. In a first step, we derive the VMS
method for the compressible NavierStokes equations.
The resulting weak formulation of the flow equations
is split into resolved and unresolved scales using multiresolution
techniques based on biorthogonal wavelets.
Since the in principle infinitedimensional subspace of fluctuations is
also discretized, it needs to be stabilized by additional dissipative
terms. The compressible VMS method is then incorporated into
an adaptive multiresolution finite volume solver, where grid adaptation
is also performed by means of the multiresolution analysis.
Finally, first results are presented for a turbulent channel flow.
This is joint work with Wolfgang Dahmen, Thomas Gotzen and Roland Schäfer.

12:3015:00 
Lunch Break 
15:0015:45

Rémi Abgrall, INRIA Bordeaux
Recent advances in Residual distribution schemes
Applications to compressible fluid problems
Abstract (click to expand/collapse)
 Abstract pdf to download
The residual distribution schemes (RD), or fluctuation splitting schemes,
have been introduced by P.L. Roe in several papers, among which his 1981
JCP paper, and then in collaboration with VKI. Considering a transport
equation, the idea is to represent the solution by its nodal values, the mesh
being described in a non structured manner, and to evolve it using the
most possible compact stencil with the highest possible accuracy that can
be reached with the scheme stencil without sacrificing the non oscilalatory
properties of the exact solutions. For example, using a triangular mesh,
one can get second order accuracy only using the nearest neighbors of any
given vertex. The discrete scheme formulation shares many similarities
with stabilised finite element, though they are very different in that the
schemes can be proved to be L ∞ stable. They also share many similarities with standard finite volume schemes since any finite volume scheme
can be reformulated as a RD scheme, at least in their first order version.
Of course the classical MUSCL schemes violate the spencil compactness
requirements of RD schemes, hence at least from a pure computational
point of view, the second order version of the RD schemes are superior to
standard second order FV scheme.
Since the early versions of RD scheme, many improvement have been
realised. First, it is possible to construct very high order schemes on
hybrid meshes in two and three dimensions. Efficient unsteady schemes
exists now. Recently, it has been possible to design very high order non
oscilaltory schemes for advection diffusion equations.
In this lecture, we will describe the design principle of RD scheme
and show how very high order can be reached. Efficient unsteady version
will be presented as well as the very high order approximation of viscous
problems. I will also present some open questions.

15:4516:30

Tao Tang, Hong Kong Baptist University
Discontinuous Galerkin Method with Mesh Adaptivity
Abstract (click to expand/collapse)
In this talk, we will present moving grid strategies for solving hyperbolic conservations laws. In particular, we will discuss how to combine the Discontinuous Galerkin Method and the moving mesh methods.
Some relevant references can be found in
http://www.math.hkbu.edu.hk/~ttang/moving.html

16:3017:15

Eitan Tadmor, University of Maryland
A new model for selforganized dynamics
Abstract (click to expand/collapse)
Abstract. We introduce a new particlebased model for selforganized dynamics which, we argue, addresses several drawbacks of the celebrated CuckerSmale (CS) model. The new model does not involve any explicit dependence on the number of agents: only their selfdriven geometry in phase space enters the model. It lacks, however, the symmetry property, which is the key y for the various studies of CS flocking behavior. To this end,
we introduce here a new unifying framework to analyze the phenomenon of flocking for a general class of dynamical systems in the presence of nonsymmetric influence matrices. In particular, we prove the emerging behavior of flocking in the proposed model, when the pairwise longrange interactions between its agents decays sufficiently slow.
The methodology presented in this paper is based on the notion of active sets, which carries over from the particle to the kinetic and hydrodynamic descriptions.
In particular, we discuss the hydrodynamic description of our new model for selforganized dynamics, and we prove its unconditional flocking for sufficiently slowly decaying influence functions.

17:1517:30 
Closure 
