MAC colloquia

In 2011 we started the monthly MAC colloquium for talks that should be of interest to all of MAC. It takes place the first Tuesdays of the month 11.30-12.30h, unless it falls on near a vacation day.

MAC seminar

Since January 2004, a series of seminars has been organized jointly by the research groups MAC1, MAC2 and MAC3. Topics for the seminars include scientific computing, analysis and systems and control theory. Any scientific work related to these topics is welcome.

The meetings are informal and intended for anyone in MAC who is interested.

The basic format of the meetings starting this fall is:

• One speaker of 45-50 minutes, with a coffee/cookies before and after. In exceptional cases we also have two speakers.
• Informal presentations: interruptions and discussions are encouraged.
• Presentations need not concern finished work: work in progress or work that is stalled is also welcome.
• All work, from "numerical experiments only" or "modelling only" to numerical, pure or systems theoretical analysis, is welcome as long as it relates to a MAC theme.
• All presentation media from blackboard to laptop are welcome.

Speakers will normally not be known long in advance, however the dates/times are already reserved. Once known, the titles will be available on this site.

The contact persons are: Kees Oosterlee, Daan Crommelin, Jens Rademacher.

Also note the even more informal MAS work seminars.

Information for speakers

• The MAC seminars lasts 1-2 hours, including 1-2 speakers (with a coffee break in between).
• The format is informal: discussion and interruptions are encouraged.
• It is recommended that speakers shoot for roughly 45 minutes, which allows ample time for discussion and a break for coffee. In any case the presentation should not exceed 1 hour.
• The lecture room includes a blackboard, overhead projector, data projector (beamer), and TV/VCR. If additional equipment is needed, please inform one of the organizers.
• For traveling to CWI there are directions and maps.

Have a look at the past MAS seminars from 2004 till 2011.

2012 MAC colloquia

Date: 19.6.
Time: 11.30-12.30h
Room: L120

Speaker: James Brannick (Penn State University),
Title: Multigrid Methods for the Dirac PDE in Lattice Quantum Chromodynamics

In this talk, I will give an overview of recent research on designing Multigrid methods for solving the Wilson discretization of the Dirac equation in Lattice Quantum Chromodynamics, a commonly used numerical model problem in algorithm development for solving the linear systems arising in lattice field theory computations. Several variants of adaptive Multigrid have been developed for solving the Dirac equation, dating back to works in the early 1980's by Brower and Rebbi from Boston University. While these earlier efforts resulted in significant progress, both in lattice QCD computations and in MG algorithm development, they failed to provide speed ups over single level Krylov methods for actual simulations of that day. Recent progress on the design of robust adaptive MG methods has, however, led to new techniques that are now capable of delivering up to 25-fold speed ups. One such approach, which I review in detail, is an integrated bootstrap-adaptive method that combines a multilevel singular-value solver with an adaptive Multigrid setup. Results of the method applied to the 2D and the full 4D Wilson Dirac systems are presented, demonstrating that the proposed method handles both efficiently. It is also shown that the solver resulting from the bootstrap-adaptive setup can be applied to the Wilson Dirac system for mass shifts that yield indefinite problems. As such, the proposed solver is also expected to perform well for the chiral Domain Wall formulation of the Dirac equation.

Date: 2.3.
Time: 11.30-12.30h
Room: L120

Speaker: Rob Bisseling (Utrecht),
Title: Self-avoiding Walks

Abstract
A prototypical problem on which techniques for exact enumeration are tested and compared is the enumeration of self-avoiding walks on a lattice. Such walks are used for modelling the physics of polymers. Here, we present an advance in the methodology of enumeration, called length-doubling, which makes the process thousands or millions of times faster. This allowed us to enumerate self-avoiding walks on the simple cubic lattice up to a length of 36 steps, considerably improving the previous record of 30 steps from Clisby et al in 2007.
The computation of Z(36) = 2,941,370,856,334,701,726,560,670 took a total of 50000 hours using 200 processors of the Huygens supercomputer. This talk will discuss the new method, use of 48-fold symmetry, further details of the implementation, and the forthcoming release of the SAWdoubler software.

Biography:
Rob Bisseling is a professor in scientific computing at the Mathematics Institute of Utrecht University. Fridays he spends as a researcher at the MAC group of CWI. He is author of the book, "Parallel Scientific Computation: A Structured Approach using BSP and MPI", Oxford University Press, March 2004. He is co-author of the BSPlib communications library and the Mondriaan sparse matrix partitioning package.
His research interests are: graph algorithms, sparse matrix computations, parallel computing, polymer simulations.
Webpage: http://www.staff.science.uu.nl/~bisse101/

Date: 7.2.
Time: 11.30-12.30h
Room: L120

Speaker: Arjen Doelman (Leiden),
Title: Blooming in Phytoplankton-Nutrient Interactions: the Emergence and Dynamics of Spatially Localized Structures

2012 MAC seminars

Date: 12.6.
Time: 11.00-12.00h
Room: L120

Speaker: Georg Gottwald (University of Sydney)
Title: Using climatological information in data assimilation

Abstract: We investigate how to incorporate climatological information in ensemble data assimilation schemes. This can be done either on the level of providing additional observational, or on the level of parametrized forecast models.
In a first part, we consider the problem of an ensemble Kalman filter when only partial observations are available. For small ensemble sizes this leads to an overestimation of the error covariances. We show that by incorporating climatic information of the unobserved variables the variance can be controlled and superior analysis skill is obtained. We then employ this Variance Controlling Kalman Filter to control model error when the model is allowed to be void of stabilizing artificial numerical viscosity.
In a second part, we consider a deterministic multiscale toy model in which a chaotic fast subsystem triggers rare transitions between slow metastable regimes, akin to weather or climate regimes in the context of climate dynamics. Using homogenization techniques we derive a reduced stochastic model as a stochastic parametrization model for the slow dynamics only. We show that the stochastic reduced model can outperform the full deterministic model as forecast model in an ensemble data assimilation procedure, in particular in the realistic setting when observations are only available for the slow variables. We relate the observation intervals for which skill improvement can be obtained to the time scales of the system. We then set out to explain why stochastic climate models produce superior skill in an ensemble setting. The improvement in skill is due to the finite size of the ensemble, and we show that there is no skill improvement in very large ensembles or when the forecast variance is artificially and unreasonable inflated. We corroborate this with numerical simulations.

This is joint work with Lewis Mitchell and Sebastian Reich.

Date: 5.6.
Time: 11.30-12.30h
Room: L120

Speaker: Jutta Steiner (Palaiseau), visiting Jens
Title: The formation and coarsening of the concertina pattern

Abstract: The concertina is a magnetization pattern observed in elongated thin-film elements of a soft-magnetic material. It is a ubiquitous domain pattern that occurs in the switching process of the uniform magnetization due to the reversal of an applied magnetic field in the direction of the long axis of the small element. The almost periodic pattern consists of stripe-like quadrangular and triangular domains of uniform, in-plane magnetization. The domains are separated by sharp transition layers namely walls in which the magnetization quickly turns. Experimental observations suggest that the concertina pattern bifurcates from an oscillatory buckling mode simultaneously all over the sample. The existence of a corresponding parameter regime, i.e., thin, wide samples, was confirmed by Cantero & Otto on the level of a linear stability analysis based on the micromagnetic energy - a non-convex and due to Maxwell’s equations non-local variational model. On the basis of a reduced model derived in the particular parameter regime by Γ-convergence, we investigate the formation and the coarsening of the pattern using various tools from (asymptotic) analysis – non-linear interpolation estimates, Bloch-wave analysis, bifurcation analysis and amplitude functionals – and numerical simulations – path-following, branch-switching. Exploring the energy landscape with the help of these methods, we quantitatively predict the average period of the concertina pattern and qualitatively predict its hystere- sis. In particular, we argue that the experimentally observed coarsening of the concertina pattern is due to secondary bifurcations related to an Eckhaus instability. The latter is a non-linear instability that is known to occur in convective systems. We finally discuss the effect of a weak (crystalline or induced) anisotropy and contrast this instance of a quenched disorder to thermal fluctuations in the Landau-Lifschitz equations.
This is joint work with F. Otto, R. Schäfer, and H. Wiczoreck

Date: 15.5.
Time: 11.30-12.30h
Room: L120 (NB: different room than usual!)

Speaker: Ben Leimkuhler (University of Edinburgh), sabbatical visitor in MAC1
Title: Accurate averages from stochastic paths

Abstract:Stochastic differential equations (SDEs) are ubiquitous with a wide range of applications in chemistry, biology, physics, finance and geosciences. In this talk I will discuss the problem of computing an average with respect to a smooth distribution which may be viewed as the stationary distribution of a Langevin-type Brownian dynamics model which models the a thermal bath by Newtonian dynamics subject to random perturbations and friction forces. A numerical method is typically applied to the SDE and the paths of this SDE are used to sample the invariant measure, however all such methods introduce errors due to incomplete sampling, numerical discretization and other factors. By splitting the stochastic vector field into integrable components, I will show that it is possible to obtain an expansion of the invariant measure of the numerical method which allows the characterization of the discretization error. Using this idea, I will identify a superconvergent (fourth order) for Langevin dynamics using only a single force evaluation per timestep. I will also describe a simple, explicit modification of the Euler-Maruyama method for SDEs which is far better for computing averages and requires no additional computational work.

Date: 24.4.
Time: 11.30-12.30h
Room: L017 (NB: different room than usual!)

Speaker: Joseph Biello (University of California, Davis), sabbatical visitor in MAC1
Title: Multiscale Asymptotic models for large scale Tropical Atmosphere Waves

Abstract:Using systematic multiscale asymptotics, Majda and Klein arrived at an asymptotic closure for the ideal fluid equations governing dynamics on large scales in the tropical atmosphere. In collaboration with Majda, we considered a plausible model for smaller scale flows in the tropics and are able to calculate the structure of the Madden-Julian oscillation; this is a planetary scale organization of winds, the understanding of which has been called "the holy grail" of tropical meteorology.

In a second problem, we studied the equatorial primitive equations over longer time and spatial scales. The resultant coupled nonlinear dispersive equations for the amplitudes of interacting wave packets are novel both from the perspective of the atmospheric sciences and from a more general mathematical setting. These equations describe the influence of large scale tropical waves on midlatitude waves and, in particular, are relevant for understanding the effect of the Madden-Julian oscillation on midlatitude weather. I will also discuss the Hamiltonian structure of these waves and show that they admit some analytic solitary wave solutions.

Date: 13.3.
Time: 11.30-12.30h
Room: L120

Speaker: Victor Brena-Medina (Bristol, PhD student), visiting Jens
Title: Squeezing Out A Root Hair Plant Initiation Mathematical Model

Abstract:The process which triggers outgrow of a hair within a root hair cell (RH) of Arabidopsis, a key cellular-level in plant morphogenesis, is modelled mathematically. This process involves the dynamics of the small G-proteins known as Rho of Plants (ROPs) which bind to a specific location on the cell membrane, prompting cell wall softening and subsequent hair growth. The model takes the form of a generalised Schnakenberg reaction-diffusion system for the membrane bound ROPs. Relevant parameter values are carefully taken in order to capture biological features. Catalytic effect of auxins, on a spatially dependent gradient environment, is also included; these plant hormones are experimentally known to play an important role in the location of the hair cell particularly. Local analysis, numerical bifurcation analysis and numerical simulation in 1D are used to understand the dynamics of location point of the RH initiation on wildtype and mutant cases.

Date: 28.2.
Time: 11.30-12.30h
Room: L120

Speaker: Daniel Han-Kwan (Paris), visiting Jens
Title: Stability analysis of the confinement of a tokamak plasma

Abstract: A tokamak is a torus-shaped device designed to contain and confine a plasma. In this talk, I will propose a simple hydrodynamical non-linear model, in order to tackle the confinement issue from a mathematical point of view.
To this end, I will propose a stability (and instability) analysis of some steady states which allow to model the edge of the device. In particular, I will exhibit some unexpected stability when the "temperature gradient" will be large enough; this observation might correspond to the so-called "high confinement modes" (H-modes) appearing in experimental tokamaks.