Spring Meeting WSC 2011
Spring meeting WSC 2011
Participants WSC Spring meeting 2010
Monday June 6-th, 2010, the Werkgemeenschap Scientific Computing is organizing, together with the faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) of the Technical University of Delft, a spring meeting in Delft. A mixture of eight young and senior researchers have been selected to give a presentation on their research.
Location
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The spring meeting will be in Room LR-D |
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Travelling
The next URL will help you with a good trip description.
Program
| 10.00-10.30 uur | Registration, coffee/tea, reception | |
| 10.30-11.20 uur | Prof.dr. Joost Batenburg (CWI / Universiteit Antwerpen) | |
| Computational imaging: computing what we cannot see [abstract] | ||
| 11.20-11.45 uur | Reijer Idema (TU Delft - EWI) | |
| Convergence of inexact Newton methods in the number of linear iterations [abstract] | ||
| Break | ||
| 12.05-12.30 uur | Bas Fagginger Auer (Universiteit Utrecht) | |
| A Geometric Approach to Matrix Ordering [abstract] | ||
| 12.30-12.55 uur | Julia Mikhal (TU Twente) | |
| Development of an immersed boundary method for analyzing pulsatile flow in cerebral aneurysms [abstract] | ||
| Lunch |
Lunch will be served in the old restaurant of Lucht en Ruimtevaart across the road (Kluyverweg 6). | |
| 14.00-14.25 uur | Benjamin Sanderse (CWI / ECN) | |
| Energy-conserving time integration methods for the incompressible Navier-Stokes equations [abstract] | ||
| 14.25-14.50 uur | Maria Rudjana (TU Eindhoven) | |
| Gradient-based fast autofocus method [abstract] | ||
| Pauze | ||
| 15.15-15.40 uur | Oliver Salazar Celis (Universiteit Antwerpen) | |
| Nonlinear multidimensional modelling in scientific computing [abstract] | ||
| 15.40-16.30 uur | Dr.ir. Fred Vermolen (TU Delft - EWI) | |
| A suite of mathematical models for wound healing processes [abstract] | ||
Organisation and participation
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This spring meeting is organised yearly by the de Werkgemeenschap Scientific Computing (WSC), this year in coorporation with the TU Delft, faculty Electrical Engineering, Mathematics and Computer Science (EWI). Subsidy Financial support for this meeting has been obtained from the 3TU Applied Mathematics Institute (3TU.AMI) and from Centrum Wiskunde & Informatica (CWI). The Werkgemeenschap Scientific Computing is very grateful for that support. Participation (including lunch) is free of charge but registration is obligatory. Organising comittee: Prof.dr.ir. Kees Vuik (TU Delft - EWI) Prof.dr.ir. Jaap van der Vegt (U Twente - EWI) Drs. Margreet Nool (CWI, secretaris) |
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Questions? Please ask: Margreet Nool |
Abstracts
Prof.dr. Joost Batenburg (CWI / Universiteit Antwerpen)
Computational imaging: computing what we cannot see
In many situations in daily life, we want to see the interior of an object without taking it apart. In medicine, for example, various types of scans (e.g., CT, MRI) provide detailed images of internal organs in a noninvasive way. In industry, nondestructive testing is used extensively for inspecting crucial parts of airplanes. One of the general techniques for revealing the interior of an object is tomography: based on a series of projection images, taken from a range of angles, a three-dimensional image of the object is computed by a reconstruction algorithm. Depending on the application, the projection images can be recorded in various ways, by sending some kind of beam (e.g., X-rays, electrons, neutrons) through the object and measuring various properties of the beam after beam-object interaction.
Efficient algorithms for image reconstruction from projections have been available for several decades now. However, these algorithms break down if the available projection data is limited. Surprisingly, the complexity of the algorithms, as well as the amount of computation power needed to compute accurate reconstructions, actually increases as less and less data is available. Computing techniques from various fields of Mathematics and Computational Science must be combined to obtain the best results. This talk deals with the problem of image reconstruction from severely limited data, where traditional algorithms are useless. Is it possible to extract meaningful results from just a few projections? And what are the risks involved in doing so?
We also discuss more recent work on the use of parametrized linear system solvers for quasi-Newton numerical optimization methods and the solution of parametrized linear systems with multiple right-hand sides.
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Reijer Idema (TU Delft - EWI)
Convergence of inexact Newton methods in the number of linear iterations
In our research on iterative methods for the power flow problem in large power systems, we have been using inexact Newton methods with preconditioned GMRES for the linear solves. We observed that the Newton convergence was often approximately linear in the total number of GMRES iterations, independent of the number of GMRES iterations used in each Newton iteration. This inspired us to further research the theoretical convergence of the inexact Newton method.
We present convergence theory that relates the reduction in the Newton error to the reduction in the residual error in the GMRES iterations. Using this theory we show that under certain circumstances Newton convergence is indeed linear in the total number of GMRES iterations, and independent of the number of GMRES iterations used in each Newton iteration. Experiments illustrate the practical use of the convergence theory, and visualize how GMRES convergence influences the Newton convergence.
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Bas Fagginger Auer (Universiteit Utrecht)
A Geometric Approach to Matrix Ordering
With the advent of many-core desktop processors and GPUs it is important to have algorithms that are able to make use of the computational power these systems have to offer. In this context we present a recursive method to partition hypergraphs which creates and exploits hypergraph geometry and is suitable for many-core parallel architectures. The generated partitionings are useful to bring sparse matrices in a recursive Bordered Block Diagonal form (for parallel LU decomposition and fill-in reduction) or recursive Separated Block Diagonal form (for cache-oblivious sparse matrix-vector multiplication).
Quality of the obtained partitionings was measured by comparing obtained fill-in for LU decomposition with SuperLU (with better results for 8 of the 28 test matrices) and comparing cut sizes for sparse matrix-vector multiplication with Mondriaan (with better results for 4 of the 12 test matrices). During this benchmark the new partitioning method was, on average, 21 times as fast as Mondriaan.
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Julia Mikhal (TU Twente)
Development of an immersed boundary method for analyzing pulsatile flow in cerebral aneurysms
We present a numerical method for simulating the flow of blood inside highly complex shaped cerebral aneurysms as may occur in the human brain. The application focus is on understanding the flow behavior, shear stresses and long-term aneurysm development. The mathematical focus is on de- veloping practical upper- and lower bounding solutions for the velocity and stress fields that quantify the sensitivity of the solution to inherent uncer- tainties in the definition of the flow domain. Such uncertainties are due to the spatial resolution of the somewhat noisy medical images from which the domain definition is derived. The introduction of �inner� and �outer� masking functions in an Immerse Boundary (IB) method allows to simu- late practical upper- and lower numerical solutions. We follow a staggered grid approach and approximate blood as an incompressible Newtonian fluid.
The full Navier-Stokes equations are solved in 3D with the use of a skew- symmetric finite-volume discretization. A volume-penalizing IB method is applied to represent complex vessel and aneurysm shapes. We analyze time dependent pulsatile flow in model aneurysms at a variety of physiologically relevant flow conditions. Relatively slow flow is dominated by the pulsatile forcing, while faster flows display unsteady vortical structures that are less correlated with the forcing profile. The IB method was found to reliably capture flow structures and shear forces near fluid-solid interfaces already at modest grid resolution.
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Benjamin Sanderse (CWI / ECN)
Energy-conserving time integration methods for the incompressible Navier-Stokes equations
In recent years interest has grown in the CFD community in so-called energy-conserving discretization methods. Conserving energy (in the inviscid limit) is important for a realistic simulation of turbulence and provides a non-linear stability bound to the solution, meaning that simulations can be performed with any mesh size and any time step. In this talk we focus on the temporal discretization and show the application of high-order accurate energy conservation schemes to the incompressible Navier-Stokes equations.
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Maria Rudjana (TU Eindhoven)
Gradient-based fast autofocus method
Most automatic focusing methods are based on a sharpness function, which delivers a real-valued estimate of an image quality. We study an L2-norm derivative-based sharpness function, which has been used before based on heuristic consideration. We give a more solid mathematical foundation for this function and get a better insight into its analytical properties. Moreover an efficient autofocus method is presented, in which an artificial blur variable plays an important role.
We prove that for a noise-free image formation our sharpness function has a unique optimum at the in-focus image. We show that for a specific choice of the artificial blur control variable, the function is approximately a quadratic polynomial, which implies that after obtaining of at least three images one can find the approximate position of the optimal defocus. This provides the speed improvement in comparison with existing approaches, which usually require recording of more than ten images for autofocussing. The new autofocus method is employed for the scanning transmission electron microscopy. To be more specific, it has been implemented in the FEI scanning transmission electron microscope and its performance has been tested as a part of a particle analysis application.
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Oliver Salazar Celis (Universiteit Antwerpen)
Nonlinear multidimensional modelling in scientific computing
We present a new approximation technique in which a generalized multivariate rational function is fitted through a set of interval data. The advantage of working with interval data instead of point data is that the problem statement inherently takes the data errors, coming from measurements or simulations, into consideration. The data are allowed to be scattered in the multidimensional space and the problem as posed does not suffer the curse of dimensionality. A unique solution can be obtained by solving a quadratic programming problem.
We illustrate the technique with a variety of applications in sci- entific computing. The problems range from video signal filtering, reflectance rendering in graphics, metamodelling in microwave theory and materials science, to communication networks, queueing problems and computational finance. The number of data can run up to a few million. The model complexity on the other hand, is very moderate in all our illustrations, from a few coefficients to a few dozen. The required accuracy (relative error) varies between applications, from a few promille to a few percent.
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Dr.ir. Fred Vermolen (TU Delft - EWI)
A suite of mathematical models for wound healing processes
Wound healing phenomena, whether cutaneous wounds, or trauma on organs or bone, is a crucial biological process for the viability of a living organism. These healing processes in general proceed by signaling processes from for instance platelets, that trigger the cells in surrounding undamaged tissues to come into action. This action can be mobility, cell movement in the direction of a signaling or growth factor concentration gradient or by (biased) random motion, or the proliferation of cells (division and growth). In this talk, we will review some of the mathematical models we are working on. These models are predominantly based on systems of reaction-diffusion-convection equations and on the equations of visco-elasticity. Here, we show some results from finite-element simulations, as well as some mathematical analysis. This model is applied to modeling wound contraction.
With respect to wound closure, we will discuss a model that is based on a moving boundary problem. Here we present our numerical method, which is based on a level-set method to track the interface, combined with a cut-cell method to update the balance of the growth factor that stimulates wound closure. Next to these numerical simulations, we will guide the audience through some interesting analytic results, such as the existence of waiting times before actual wound healing sets in.
We will also deal with a brand new formulation of cellular based model on wound closure and growth of cell cultures. This model, not based on any partial differential equations, is based on the mechanical forces that are exerted and sensed by cells. Furthermore, cellular motion contains a somewhat random component and therefore, the model is semi-stochastic. Cell death and cell division are incorporated into this model as stochastic processes as well.
If time allows, we will also show the newest applications to modeling angiogenesis on fibrosis impaired areas on the surface of a heart.
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