# MAC Seminars

## Upcoming

Date: Tuesday 28th February 2017

Time: 15.00hrs

Room: L120

Speaker: Stephen Smith (Life Sciences, University of Edinburgh)

Title: Efficiently simulating the crowded cytoplasm

Brownian dynamics simulations are an increasingly popular tool for understanding spatially-extended biochemical reaction systems. Recent improvements in our understanding of the cellular environment show that volume exclusion and crowding effects are fundamental to reaction networks inside cells. These systems are frequently studied by incorporating inert hard spheres (crowders) into three-dimensional Brownian dynamics simulations, however these methods are extremely slow owing to the sheer number of possible collisions between particles. We propose a rigorous "crowder-free" method to dramatically increase simulation speed for crowded biochemical reaction systems by eliminating the need to explicitly simulate the crowders. We consider both the case where the reactive particles are point particles, and where they themselves occupy a volume. Using simulations of simple chemical reaction networks we show that the "crowder-free" method is up to three orders of magnitude faster than conventional BD and yet leads to nearly-indistinguishable results from the latter.

## Past

Date: Tuesday 7th February 2017

Time: 15.00hrs

Room: L120

Speaker: Alef Sterk (RU Groningen)

Title: On the predictability of extremes: does the butterfly effect ever decrease?

Abstract: This study investigates whether or not predictability always decreases for more extreme events. Predictability is measured by the Mean Squared Error (MSE), estimated here from the difference of pairs of ensemble forecasts, conditioned on one of the forecast variables (the “pseudo-observation”) exceeding a threshold.

Using an exchangeable linear regression model for pairs of forecast variables, we show that the MSE can be decomposed into the sum of three terms: a threshold-independent constant, a mean term that always increases with threshold, and a variance term that can either increase, decrease, or stay constant with threshold. Using the Generalised Pareto Distribution to model wind speed excesses over a threshold, we show that MSE always increases with threshold at sufficiently high threshold. However, MSE can be a decreasing function of threshold at lower thresholds but only if the forecasts have finite upper bounds.

The methods are illustrated by application to daily wind speed forecasts for London made using the 24 member Met Office Global and Regional Ensemble Prediction System from 1 Jan 2009 to 31 May 2011. For this example, the mean term increases faster than the variance term decreases with increasing threshold, and so predictability decreases for more extreme events.

This is joint work with David Stephenson, Mark Holland, and Ken Mylne.

Date: Wednesday 18th January 2017

Time: 15.00hrs

Room: L120

Speaker: Joris Bierkens (TU Delft)

Title: The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big Data

Abstract: Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational burden, but with the drawback that these algorithms no longer target the true posterior distribution. We introduce a new family of Monte Carlo methods based upon a multi-dimensional version of the Zig-Zag process of (Bierkens, Roberts, 2016), a continuous time piecewise deterministic Markov process. While traditional MCMC methods are reversible by construction the Zig-Zag process offers a flexible non-reversible alternative. The dynamics of the Zig-Zag process correspond to a constant velocity model, with the velocity of the process switching at events from a point process. The rate of this point process can be related to the invariant distribution of the process. If we wish to target a given posterior distribution, then rates need to be set equal to the gradient of the log of the posterior. Unlike traditional MCMC, We show how the Zig-Zag process can be simulated without discretisation error, and give conditions for the process to be ergodic. Most importantly, we introduce a sub-sampling version of the Zig-Zag process that is an example of an exact approximate scheme. That is, if we replace the true gradient of the log posterior with an unbiased estimator, obtained by sub-sampling, then the resulting approximate process still has the posterior as its stationary distribution. Furthermore, if we use a control-variate idea to reduce the variance of our unbiased estimator, then both heuristic arguments and empirical observations show that Zig-Zag can be super-efficient: after an initial pre-processing step, essentially independent samples from the posterior distribution are obtained at a computational cost which does not depend on the size of the data.

Date: Tuesday 20th December

Time: 15.00hrs

Room: L120

Speaker: Gemma Colldeforns (CRM, Barcelona)

Title: Wavelets for quantifying credit risk portfolio losses under multi-factor models

Abstract: We compute tail probability, Value at Risk and Expected Shortfall risk measures of the portfolio credit risk problem under multi-factor Gaussian and t-copula scenarios. To do so, we depart from the characteristic function of the portfolio density and we use a wavelet Fourier inversion method to recover it.

Date: Tuesday 13th December

Time: 15.00hrs

Room: L120

Speaker: Rob H. Bisseling (Utrecht University) http://www.staff.science.uu.nl/~bisse101/

Title: Parallel matching for big graphs

Abstract: We present a gentle introduction to the topic of parallelising graph algorithms through the example of an approximation algorithm for matching in big weighted graphs. This algorithm is based on locally dominant edges and partial edge sorting.

We will discuss how to parallelise the algorithm with special attention to load balancing in an irregular setting, tie-breaking between edge weights as a feature, not a bug, and the virtues of 2D (edge) vs. 1D (vertex) partitioning.

We use the Bulk Synchronous Parallel (BSP) model to structure the computation, to analyse the time complexity, and to reason about the correctness of the algorithm.

Date: Tuesday 22nd November

Time: 15.00hrs

Room: L120

Speaker: Fred Wubs (RUG)

Title: HYMLS: A robust multilevel solver for 3D steady flow problems

Abstract: Pseudo-arclength continuation is a powerful technique for investigating parameter sensitivity of complex dynamical systems. However, for three-dimensional fluid dynamics problems the application of this technique is difficult because of the ill-conditioned Jacobian matrices that arise during the process. The indefiniteness of the matrices and the computational complexity makes direct solvers inefficient in 3D, while iterative solvers typically lack robustness at high Reynolds numbers. In the talk we first will discuss general direct and iterative approaches to solve linear systems. Next we will indicate the special properties of the system of equations arising from the finite volume discretization of the incompressible Navier-Stokes equations and the difficulties this gives in solving them. Finally, we present the hybrid direct/iterative solver HYMLS for the Jacobian of the incompressible Navier-Stokes equations on structured grids. Among others, we will show results of computations on a 3D lid driven cavity near the first Hopf bifurcation.

Date: Tuesday 1st November

Time: 15.00hrs

Room: L120

Speaker: Richard Dwight (TU Delft)

Title: Data-mining for the design and analysis of turbulence closure models

Abstract: An introduction and overview of recent work in estimating model inadequacy (the error in simulation resulting from modelling assumptions) in Reynolds-averaged Navier-Stokes. The modelling problem is introduced, and the key modelling assumptions are analysed. The objective is to quantify the resulting error in the solution - and several approaches have been proposed, all founded on principles of uncertainty quantification. These will be discussed, and directions for future work considered.

Date: Tuesday 18th October

Time: 15.00hrs

Room: L120

Speaker: Anna Dubinova

Title: Modeling of streamer discharges near dielectrics

Abstract: Streamers developing near dielectrics or on dielectric surfaces are usually to be avoided in high voltage technology, because they are often precursors to sparks and dielectric breakdown. My PhD research was part of the "Creeping Sparks" project, which was initiated to better understand surface flashovers and thus to contribute to the development of more efficient and reliable high voltage infrastructures.

I will tell about the progress that was made in understanding streamer discharge behavior near dielectrics and about the dedicated numerical tools that I developed in the course of my PhD research. Among them are a Poisson solver with the Ghost Fluid Method incorporated in it and an alternative approach to calculation of integrals for photoionization and photoemission.

I will also tell about another application of my streamer discharge model. Essentially, the problem of streamer development near dielectrics is also relevant in the context of lightning inception in thunderclouds, and with my colleagues we proposed the first self-consistent model of lightning inception.

Date: Tuesday 27 September

Time: 15.00hrs

Room: L120

Speaker: Luis Ortiz Gracia (Department of Econometrics, Statistics and Applied Economics, University of Barcelona, Barcelona, Spain)

Title: A dimension reduction method for option pricing (in collaboration with Duy-Minh Dang)

Abstract: We present a robust and highly efficient Shannon-wavelet based dimension reduction method for computing plain-vanilla European option prices under general jump-diffusion models with stochastic variance and multi-factor Gaussian interest rates. Using the conditional Monte Carlo technique applied to the variance factor, the option price can be expressed as a two-level nested conditional expectation. The inner expectation is then evaluated analytically, with the variances associated with all the interest rates factors completely removed from the analytical solution. The outer expectation is approximated very efficiently by means of the Shannon Wavelets Inverse Fourier Technique (SWIFT) via evaluating a single integral that involves only the variance factor. Central to this process is a highly effcient recovery of the conditional density of the time-integrated variance process using the SWIFT method. Furthermore, the SWIFT method also allows us to develop sharp approximation error bounds for the option price. Numerical experiments confirm the robustness and efficiency of the proposed pricing method.

*[1] Dang D.M., Ortiz-Gracia, L. A dimension reduction Shannon-wavelet based method for option pricing. Submitted for publication, 2016. ** [2] Ortiz-Gracia L., Oosterlee, C.W. A highly efficient Shannon wavelet inverse Fourier technique for pricing European options. SIAM Journal on Scientific Computing, 38(1), B118-B143, 2016.*

Date: Friday 9 September

Time: 14.00hrs (different day and time!)

Room: L120

Speaker: Wim Vanroose, Department of Mathematics and Computer Science, U. Antwerpen. Belgium (guest of Menno Genseberger)

Title: Elimination of communication bottlenecks from Krylov Methods

Abstract: Modern HPC machines have three levels of parallelism: 1) Many CPUs 2) each CPU has multiple cores and 3) each core has SIMD instructions that work with long vectors. To handle this dramatic increase of parallelism communication and synchronisation is of increasing importance. Long latencies and limited memory bandwidth can lead to stalling performance. In this talk we discuss efforts to redesign Krylov subspace methods that avoid communication and hide latencies. These methods give a better scalability to a large number of CPUs.

Date: Tuesday 6 September

Time: 15.00hrs

Room: L120

Speaker: Benjamin Sanderse

Title: Energy, fluid flow, and numerical mathematics: from applications to differential equations

Abstract: What is the relation between flow of oil and gas in pipelines and index-3 differential-algebraic equations? How can shock waves appear in Darcy-type problems in reservoirs? And how can model averaging lead to ill-posed differential equations? These and other questions will be addressed in my talk, in which I will give an overview of my work on solving fluid flow problems for several problems in the energy industry: wind turbine wakes in wind farms, transport of oil and gas in pipelines, and multi-phase flow in subsurface reservoirs.

Date: Tuesday 14 June

Time: 15.00hrs

Room: L120

Speaker: Dirk Roose (KU Leuven)

Title: Multi-scale simulation of forming processes with polycrystalline materials

Date: Tuesday 24 May 2016

Time: 15.00hrs

Room: L120

Speaker: Chris Stolk (UvA)

Title: Recent results on the discretization and solution of time harmonic wave equations

Abstract: Time-harmonic wave equations, acoustic or electromagnetic, have many applications, e.g. in seismology and scattering theory. In this talk we consider the Helmholtz equation for time-harmonic acoustic waves in the high-frequency limit, i.e. in the case of waves propagating over long distances. We present a new finite difference discretization, based on Fourier analysis and geometrical optics. It yields accurate simulation results using very few grid points per wave length, in case the medium varies smoothly. By using it within a multigrid method, possibly combined with domain decomposition, more general Helmholtz problems can be efficiently solved.

Date Tuesday 3 May 2016

Time: 15.00hrs

Room: L120

Speaker: Martina Chirilus-Bruckner, Leiden University

Title: Dynamics and inverse spectral theory

Abstract: This talk will illustrate along the example of a nonlinear wave equation with periodic coefficients, how a classical dynamical systems technique such as center manifold reduction can be extended to settings that, at first sight, seem out of reach by solving an inverse spectral problem. This is joint work with C.E. Wayne.

Date Tuesday April 26

Different time: 14.00(!)-15.00

Room: L120

Speaker: Valerio Lucarini (Universität Hamburg, Meteorological Institute / University of Reading, UK)

Title: Response and Fluctuations in Geophysical Fluid Dynamics

Abstract: The climate is a complex, chaotic, non-equilibrium system featuring a limited horizon of predictability, variability on a vast range of temporal and spatial scales, instabilities resulting into energy transformations, and mixing and dissipative processes resulting into entropy production. Despite great progresses, we still do not have a complete theory of climate dynamics able to encompass instabilities, equilibration processes, and response to changing parameters of the system. We will outline some possible applications of the response theory developed by Ruelle for non-equilibrium statistical mechanical systems, showing how it allows for setting on firm ground and on a coherent framework concepts like climate sensitivity, climate response, and climate tipping points. We will show results for comprehensive global climate models. The results are promising in terms of suggesting new ways for approaching the problem of climate change prediction and for using more efficiently the enormous amounts of data produced by modeling groups around the world.

*V. Lucarini, R. Blender, C. Herbert, F. Ragone, S. Pascale, J. Wouters, Mathematical and Physical Ideas for Climate Science, Reviews of Geophysics 52, 809-859 (2014).*

Date: Tuesday 12 April 2016

Time: 15.00hrs

Room: L120

Speaker: Sonja Cox, UvA

Title: numerical approximation of stochastic partial differential equations

Abstract: In my talk I will give an overview of numerical analysis for stochastic partial differential equations. In particular, I will explain the different types of convergence one may consider, the rates of convergence one may expect, and explain under what conditions convergence has been proven. In particular, I will explain a little about my own work on weak convergence for semi-linear SPDEs.

Date: Tuesday 22 March 2016

Time: 15.00hrs

Room: L120

Speaker: Sander van Oers, NIOZ

Title: Hamiltonian discontinuous Galerkin FEM for linear, stratified (in)compressible Euler equations: internal gravity waves

Abstract: The linear equations governing internal gravity waves in a stratified ideal fluid possess a Hamiltonian structure. A discontinuous Galerkin finite element method has been developed in which this Hamiltonian structure is discretized, resulting in conservation of discrete analogs of phase space and energy. This required (1) the discretization of the Hamiltonian structure using alternating flux functions and symplectic time integration, (2) the discretization of a divergence-free velocity field using Dirac's theory of constraints and (3) the handling of the large-scale computational demands due to the three-dimensional nature of internal gravity waves and, in confined, symmetry-breaking fluid domains, possibly its narrow zones of attraction.

Date: Tuesday 8 March 2016

Time: 15.00hrs

Room: L120

Speaker: Jannis Teunissen, MD

Title: Developing 3D simulation models for electric discharges

Abstract: An electric discharge occurs when electric charge suddenly starts to flow through an insulator such as air. Examples of discharges are lightning, fluorescent lamps, and the small sparks that sometimes occur when taking of a sweater. After a brief introduction of the underlying mechanisms, my talk will focus on numerical models for discharges.

Discharges are often true multiscale phenomena, which makes adaptive mesh refinement combined with a very fast Poisson solver a necessity for 3D simulations. To fulfill these requirements, I have developed a small framework for finite volume simulations on quadtree/octree grids, which includes a geometric multigrid solver. I will demonstrate current possibilities, and conclude with an outlook on future improvements.

Date: Tuesday 23 February 2016

Time: 15.00hrs

Room: L120

Speaker: Dr. Sigrun Ortleb, University of Kassel, homepage (guest of Willem Hundsdorfer)

Title: On Patankar-type time integration preserving non-negative water height within a discontinuous Galerkin shallow water code

Abstract: Discontinuous Galerkin(DG) methods are a modern and popular class of numerical methods especially for computationally intensive fluid dynamics calculations. Their popularity is due to the fact that DG methods allow for high order approximations in combination with high flexibility – e.g. in choosing different polynomial degrees on neighbouring elements. In this talk, we consider the application of the DG scheme on unstructured triangular grids to hyperbolic conservation laws. Briefly, we will show their connection to summation-by-parts(SBP) operators which posess very convenient stability properties.

We then focus on the application of the DG scheme to shallow water flows with non-flat bottom topography. In particular, the DG scheme then has to guarantee non-negativity of the water height. For locally refined grids at wet/dry interfaces, the stability and positivity requirements of explicit time integration unfortunately lead to rather restrictive time step constraints. However, the non-negativity requirement usually restricts the time step in the implicit case as well. In this context, we consider modified Patankar-type time integration methods which preserve non-negativity of the water height for any time step size.

Date: Tuesday 2 February 2016

Time: 15.00hrs

Room: L120

Speaker: Wim Verkley, Royal Netherlands Meteorological Institute (KNMI), R&D Weather and Climate Models

Title: Parameterization of unresolved processes - can the principle of maximum entropy help us out?

Abstract: No matter how high the resolution of weather and climate models becomes, the need to represent all processes that are not resolved explicitly will stay with us in the foreseeable future. This is illustrated rather dramatically by the fact that in the atmosphere the ultimate sink of the kinetic energy of moving air is at spatial scales of the order of a millimeter. And there are many other processes whose intricacy makes it impossible to model these explicitly and deterministically. To take the unresolved processes into account, parameterizations have been devised such as the eddy viscosity proposed by Boussinesq or the eddy parameterizaton introduced by Smagorinsky his 1963 paper on one of the first general circulation models of the atmosphere. Although these and other parameterization schemes work reasonably well, there is a large heuristic element in their design and a corresponding need to tune their parameters. One particular problem is that they do not adjust themselves automatically to a change in model resolution. By representing the unresolved processes by a probability density function and determining its explicit form by applying the principle of maximum entropy, it is possible to derive parameterization schemes in a rather systematic way. The resulting schemes have some interesting properties such as the absence of tunable parameters. A simple two-dimensional fluid system will be used to illustrate how this works in practice.

Date: Tuesday 8 December 2015

Time: 15.00hrs

Room: L120

Speaker: Willem Hundsdorfer

Title: Multirate methods for conservation laws

Abstract: In this talk we will discuss explicit multirate one-step schemes for conservation laws and convection-dominated problems. Different regions of the spatial PDE domain may then have different (local) time steps. Such schemes can be conveniently represented as partitioned Runge-Kutta methods. It is known that standard Runge-Kutta methods may suffer from order reduction when used as time stepping scheme for a PDE with boundary conditions. For multirate schemes, the interfaces act as time-dependent boundary conditions. This may lead to a very disappointing accuracy. Theoretical results will be presented on the order of accuracy of some interesting multirate schemes, with cell-based and flux-based decompositions, together with numerical illustrations.

Date: Tuesday 24 November 2015

Time: 15.00hrs

Room: L120

Speaker: Laurent van den Bos

Title: Fast Non-Intrusive Uncertainty Quantification, with Applications to Fluid Flows

Abstract: here.

Date: Thursday 5 November 2015

Time: 15.00hrs

Room: L120

Speaker: Prof. Carsten Carstensen (Humboldt-Universität zu Berlin, Germany)

Title: Axioms of Adaptivity: Rate optimality of adaptive algorithms with separate marking

Abstract: here.

Date: 3 July 2015

Time: 11.30hrs

Room: L120

Speaker: A/Prof Frances Kuo, School of Mathematics and Statistics, University of New South Wales, Sydney NSW Australia

Title: Multi-Level Quasi-Monte Carlo Methods for PDEs with random coefficients

Abstract: High dimensional problems are coming to play an ever more important role in applications, including, for example, option pricing problems in mathematical finance, maximum likelihood problems in statistics, and porous flow problems in computational physics and uncertainty quantification. High dimensional problems pose immense challenges for practical computation, because of a nearly inevitable tendency for the cost of computation to increase exponentially with dimension. Effective and efficient methods that do not suffer from this "curse of dimensionality" are in great demand, especially since some practical problems are in fact infinite dimensional.

In this talk I will start with an introduction to "quasi-Monte Carlo methods", focusing on the theory and construction of "lattice rules" (order one) and "interlaced polynomial lattice rules" (higher order) developed in the past decade. Then I will showcase our very latest work on how this modern theory can be "tuned" for a given application. The motivating example will involve an elliptic PDE with a random coefficient, which is based on a simplified porous flow problem where the permeability is modeled as a random field.

Date: 2 February 2015

Time: 14.30hrs

Room: L120

Speaker: Mario Annunziato, Università degli Studi di Salerno (www.dipmat.unisa.it/people/annunziato/www/)

Title: Fokker-Planck optimal control of anomalous diffusion processes

Abstract: We deal with the optimal control of stochastic processes related to the anomalous diffusion. To achieve this aim we use the Model Predictive Control technique associated to a new framework based on the fractional Fokker-Planck equation. It is based on the probability density function (PDF) as representative of the state of the stochastic system and it is formulated as the problem of minimizing a cost function in terms of the PDF. The problem to find the controller that minimize the cost function is solved by solving an optimality system of fractional forward and backward partial differential equations. We illustrate the numerical scheme and the results of the related experiments. Finally, the extension of this technique to the control of piecewise deterministic process is outlined.

Date: 12 January 2015

Time: 10.30 - 11.30hrs

Room: L120

Speaker: Halldora Thorsdottir

Title: Infinite servers in a random environment

Abstract: Queueing theory provides a simple framework to model discrete, stochastic systems, with applications ranging from telecommunications to chemical reaction networks. For many cases, it offers exact analytical expressions for moments and distributions of classical performance measures, such as number-in-system and time-in-system. By embedding an infinite server queueing system in a random environment, we allow for a Markovian variation of the main parameters which makes the model more realistic and complex to analyze, preventing us from finding exact expressions. Simultaneous, but unequal, scaling of the two-layered system exaggerates its two time-scales and leads to approximations for the distributions of the quantities of interest. Here the right balance in the scaling is required, and will determine the variance of the resulting process. We see at which level the main system behaves almost independently of the environmentand vice versa. The result is a central limit theorem, with techniques including generating functions and ODEs.

Speaker: Jeroen Witteveen

Title: Quantifying Errors and Uncertainties in Wind Engineering

Abstract: Predictions of computer simulation codes need to be validated in comparisons with experimental measurements. However, these observations also contain errors and uncertainties, usually reported as experimental confidence bars. The errors and uncertainties in the numerical results therefore have to be quantified as well to enable a rigorous comparison. Important examples of these are numerical discretization error, model form uncertainty, and uncertainty in model input parameter values. The Benchmark on the Aerodynamics of a Rectangular Cylinder (BARC) is an interesting example in this respect. It is a test case from the field of wind engineering for the flow of wind around buildings and bridges. A large number of computer simulations and wind tunnel experiments have been performed by different research groups for this challenging benchmark. However, none of these numerical studies have quantified the uncertainties in a robust probabilistic way so far. We are quantifying the impact of the spatial discretization error, the turbulence model uncertainty, and the probabilistic input parameter uncertainty in this case for the first time. The challenge is to develop methods that can rigorously combine these different sources of uncertainty and error. The results will be compared to the extensive BARC database. This is collaborative work with TNO and the University of Pisa.