Research team

Expertise

Mathematical modelling of biological, physical and chemical processes and the numerical solution of the resulting equations Efficient numerical methods that solve large-scale linear algebra problems, optimalisatie problems and systems of non-linear equations on high-performances computer hardware Large scale planningsproblems.

HugeOPT: Krylov accelerated splitting methods for huge-scale network optimization. 01/10/2023 - 30/09/2027

Abstract

Efficiently solving huge-scale optimization problems is undoubtedly very important in science and technology. Many optimization problems can be described using some underlying network structure. For example, the optimal assignment of a crew to a given flight schedule can be formulated as an optimization problem over a very large graph. Similarly, constraint based modelling of biochemical networks also leads to optimization problems with millions of unknowns. A network structure typically induces useful structure in the constraints, which then of course can be exploited by using suitably chosen linear algebra techniques. Current off-the-shelf software is not able to efficiently solve such problems when the number of variables is very large, especially when the objective function is nonconvex and possibly contains a nonsmooth term. Hence, there is a need to develop high-performance structure exploiting algorithms. In this project we aim to develop a wide range of efficient optimization algorithms for both convex and nonconvex problems, possibly containing a nonsmooth term in the objective function, by exploiting structure that arises from the networks. High-performance implementations of the resulting algorithms will be made available in an open- source software package such that non-expert practitioners can easily them.

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  • Research Project

Agreement on the financing of large computing capacity at the University of Antwerp and Association Antwerp University and Antwerp Colleges (2021). 01/01/2021 - 31/12/2021

Abstract

This project represents a formal agreement between UAntwerpen and on the other hand the Flemish Public Service. UAntwerpen provides HPC infrastructure and support to researchers under the conditions as stipulated in this contract.

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  • Research Project

FleXray: Flexible X-ray imaging for the next generation of tomographic applications. 01/05/2018 - 30/04/2021

Abstract

PC-CT reveals complementary information to traditional attenuation based X-ray imaging (i.e. higher contrast in soft tissue). The FleXray system will allow us to acquire data to fully explore a far wider range of applications and opportunities for PC-CT that are currently not possible: ● Exploration of advanced CT acquisition models to enable reconstruction from (1) fewer projection images and (2) projection images acquired during continuous sample rotation. This will result in faster PC-CT imaging (currently up to 8 times longer than regular CT). ● Dark field tomography is only in its infancy but recently showed huge potential in material characterisation. The FleXray system will open new research lines on dark field tomography, in particular in accurate and precise estimation of localized scattering profiles. ● Development of Krylov solvers with much faster convergence for simultaneous multimodal reconstruction of full 3D images of attenuation, phase and dark field signals.

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  • Research Project

Asynchronous Krylov methods with deep pipelines. 01/01/2018 - 31/12/2018

Abstract

In recent years a major trend towards solving scientific problems of ever larger scales that include larger and larger data sets can be observed in practically all academic and industrial applications. These include the simulation of vast ocean circulation models, global climate prediction models, extremely fine-scale combustion models, etc. The representation of these models on a computer requires the solution of a large-scale system of equations that typically consists of millions of unknowns. Due to the huge size of these model calculations, computations are often spread across parallel computer platforms to reduce the time-to-solution. Krylov methods have been established as the benchmark iterative solvers for the sparse linear algebra problems that appear in these applications. However, Krylov methods are not adapted to scale to future parallel hardware due to the long communication latencies. Hence, new numerical methods have to be designed and analyzed mathematically. The aim of this project is to develop and analyze new scalable iterative methods based on asynchronous communication that hide the communication latency by overlapping compute and communication tasks. Furthermore we will develop blocked versions of these algorithms for problems where the same matrix equation needs to be solved for multiple right hand sides. Demonstrators will be built that show the performance improvements for a wide range of applications in data science and scientific computing.

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  • Research Project

High performance iterative reconstruction methods for Talbot‐Lau grating interferometry based phase contrast tomography. 01/01/2017 - 31/12/2020

Abstract

Phase Contrast X‐ray Computed Tomography (CT) measures besides the intensity also changes in the phase of a transmitted X‐rays. These changes give exquisite and complementary information about the object, in particular about soft tissues. More and more CT systems are able to measure these phases. However, the development of efficient mathematical reconstruction algorithms that reconstruct the 3D object from the measured data is only in its early stages. This project will make progress in the modelling of the data acquisition process and the reconstruction algorithms. It is a collaboration between the group A pplied Mathematics and the V ision Lab . Valorisation will be realized by the distribution of the new algorithms through the ASTRA toolbox and the initiation of research collaborations, licensing deals and contract research with industry.

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  • Research Project

Scalable and error resilient iterative solvers for large scale linear algebra problems. 01/10/2016 - 30/09/2019

Abstract

In recent years, a major trend towards solving scientific problems of ever larger scales can be observed in practically all academic and industrial applications. These include the simulation of vast ocean circulation models, global climate prediction models, seismic oil reservoir models spanning hundreds of kilometers, extremely fine-scale combustion models, etc. The representation of these models on a computer requires the solution of a large-scale system of equations that typically consists of millions of unknowns. Due to the huge size of these model calculations, computations are often spread across parallel computer platforms to reduce computational time. Furthermore, only the numerical methods with optimal compute and communication complexity are able to efficiently solve these large scale problems. Krylov methods have been established as the benchmark iterative solvers for sparse linear algebra problems due to their robustness and good performance in function of the number of unknowns. However, present-day Krylov methods are not adapted to scale to future parallel hardware. Hence, new numerical methods have to be designed and analyzed mathematically, taking into account numerical rounding error propagation, which possibly has a detrimental effect on convergence. The aim of this project is to develop and analyze new scalable iterative methods that are numerically stable and resilient to the errors that typically arise in these large-scale computations.

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  • Research Project

Exaptation: Scalable solutions for image-based and across-partner compound activity prediction and application to compound selection 01/04/2016 - 30/09/2018

Abstract

The aim of the project is to extend the applicability of prediction of compound activity and the extension of the number of data sources that can be combined. We alos aim to apply the the methods to currently running drug development. Due to the scale and the size of the data sets high performance computing is required.

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  • Research Project

Emergent Phenomena in Multicomponent Quantum Condensates. 01/01/2015 - 31/12/2018

Abstract

Quantum effects usually only matter at the microscopic scale. However, in superconductors and superfluids these quantum effects appear on a macroscopic level, leading to surprising properties such as frictionless or lossless flow. The macroscopic quantum state arises from the collective behavior of a large number of microscopic particles (Bose-Einstein condensation). In the case of fermionic particles these must first pair up. Neutral particles lead to superfluidity, charged ones to superconductivity. Both cases are described by the same underlying mathematical formalism. The discovery of superfluidity in magnesium diboride in 2001 marked the appearance of a new class of macroscopic quantum systems, the so-called multiband systems. They are characterized by multiple types of pairs, leading to a mixture of quantum condensates. This mixing of different types of quantum fluids within the confines of a single fluid or solid leads to a rich set of novel phenomena. Experimentally not only multiband superconductors have been realized but also multiband superfluids. The goal of the project is to study the interplay between these multiple quantum condensates and to quantify the effects of mixing. We aim to develop and extend the mathematical formalism to the multiband case, and to develop efficient solvers for the non-linear field equations characteristic for this formalism. This will be applied to study a wide range of macroscopic quantum phenomena, both for multiband superfluids and for multiband superconductors.

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  • Research Project

Exascale Algorithms and Advanced Computational Techniques (EXA2CT). 01/09/2013 - 31/08/2016

Abstract

The EXA2CT project brings together experts at the cutting edge of the development of solvers, related algorithmic techniques, and HPC software architects for programming models and communication. It will take a revolutionary approach to exascale solvers and programming models, rather thean the incremental approach of other projects.

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  • Research Project

Statistical inference for varying coefficient functions. 01/10/2012 - 30/09/2016

Abstract

We consider models with varying coefficients, i.e. linear models in which the response and/or explanatory variables vary with another variable, for example time. These types of models can for example be used in HIV research, where the number of T-cells decreases over time and in addition depends on the number of T-cells at the time of infection. Moreover we study ordinary differential equations with varying coefficients that allow describing the dynamics of continuously changing processes. We estimate the varying coefficients by P-splines. This widely used sparse flexible smoothing technique has as an important advantage (over other smoothing techniques such as B-splines or smoothing splines) that the unknown functions can be modeled in a rich basis, while introducing sparsity by adding a penalty. The main aim of this project is to develop statistical methods that focus on qualitative features of the varying coefficients functions, e.g. whether a coefficient is really varying (in contrast to being constant) or whether it is a monotonic increasing function. Moreover we want to test general hypotheses concerning the coefficient functions, by exploiting the nice properties of P-splines such as its linearity in the basis functions.

Researcher(s)

  • Promoter: Vanroose Wim
  • Promoter: Verhasselt Anneleen
  • Fellow: Ahkim Mohamed

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  • Research Project

Simulation of image formation in X-ray phase contrast tomography 01/07/2011 - 31/12/2015

Abstract

Grating based differential phase contrast tomography is a new experimental technique to offers very exquisite images of soft tissues. However, the artifacts in the current images prohibit the accurate reconstruction of the inside of an object. The project aims to develop the algorithms that allow a quantitative reconstruction of this technique

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  • Research Project

A Systems Biology Approach of Leaf Morphogenesis. 01/01/2011 - 31/12/2014

Abstract

Developmental processes involve a complex network of interactions between multiple regulatory processes that traditionally are studied separately. We propose a systems biology approach, whereby experimental biologists closely interact with mathematical modellers, to unravel the functional relationships between auxin signalling, cell division and expansion and whole leaf morphogenesis.

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  • Research Project

Numerical methods for vortex patterns in nonlinear partial differential equations. 01/10/2010 - 30/09/2012

Abstract

In this work, we focus on the numerical treatment of vortex patterns in realistic systems modeled by the Ginzburg-Landau equations, i.e., phase field equations that are frequently used to model physical systems exhibiting patterns. They are used, amongst others, to model superconductors, Bose-Einstein condensates, nonlinear waves, and objects of string field theory.

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  • Research Project

Flanders High Performance Computing Lab. 01/07/2010 - 31/12/2015

Abstract

This project represents a research agreement between the UA and on the onther hand IWT. UA provides IWT research results mentioned in the title of the project under the conditions as stipulated in this contract.

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  • Research Project

Computational methods for the exact dynamics of molecules in intense lasers. 01/01/2010 - 31/12/2012

Abstract

This is a fundamental research project financed by the Research Foundation - Flanders (FWO). The project was subsidized after selection by the FWO-expert panel.

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  • Research Project

Hybrid macroscopic and microscopic simulation of laser ablation. 01/07/2009 - 30/06/2013

Abstract

An accurate simulation of laser ablation requires a good description of the solid state, melt, Knudsen layer, plasma and interaction with the laser beam. We propose a hybrid model for these simulations that combines particle-based simulations with partial differential equations. The project will develop and analyze the numerical methods and apply them to realistic systems. The new approach may have a large impact on the field.

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  • Research Project

A 3-D simulation model of leaf growth in Arabidopsis thaliana. 01/07/2009 - 30/06/2013

Abstract

The aim of the project is to develop a 3-D mathematic simulation model of inter-actions at the molecular, cellular and organ level during leaf growth in Arabidopsis thaliana. We will start from an existing 2-D model of vascular development that was build in the previous research group of the Promotor. This model will be extended to include multiple cell layers and modules for cell division and expansion.

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  • Research Project

Numerical analysis of hierarchical methods for phase field problems. 01/10/2008 - 30/09/2010

Abstract

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  • Research Project

Scattering and reaction calculations in microscopic many-cluster models for light nuclei with exterior complex scaling and interative methods. 01/01/2008 - 31/12/2011

Abstract

The main aim of this project is to introduce new computational tools, based on the External Complex Scaling methodology developed in atomic and molecular physics, for microscopic scattering and reaction calculations in cluster models for light nuclei.

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  • Research Project

Iterative methods for linear and non-linear Schrodinger equations 01/01/2008 - 31/12/2011

Abstract

The aim of the project is to develop efficient computational methods, based on Krylov space methods, to solve the linear and non-linear Schrödinger equations. This will enable the theoretical methods to move from the approximate 2D models to the more realistic 3D description. The methods will be applied to practical physical problems: to solve the non-linear time-dependent and time-independent Ginzburg-Landau equations for the study of the vortex structure and dynamics in mesoscopic superconductors and to solve the linear Schrödinger equation for realistic self-assembled quantum dots.

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  • Research Project

Hybrid macroscopic and microscopic modelling of laser ablation and expansion. 01/01/2008 - 31/12/2011

Abstract

The aim of the project is to develop hybrid methods that divide the spatial domain into subdomains where an appropriate microscopic or macroscopic model is used. The domains are connected in a physical and mathematically correct way. This makes it possible to limit the use of the expensive particle based methods to the regions of space where they are strictly necessary. We will apply this method to decribe the transport of particles in laser ablation from the surface. More specifically, the Knudsen layer, which is formed between the surface and the bulk, will be described at the particle level.

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  • Research Project

Support maintenance scientific equipment (Computational Mathematics). 01/01/2007 - 31/12/2023

Abstract

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  • Research Project

Iterative and multigrid solvers for wave and scattering problems. 01/01/2007 - 31/12/2009

Abstract

This project proposes to develop numerical and mathematical methods for wave and scattering problems that are scalable to a large number of unknowns. The aim is to be able to simulate realistic problems in their full dimension and complexity. The focus is to extend multigrid methods to the Helmholtz probem

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  • Research Project

Iterative methods for deterministic micro/macro problems. 01/01/2007 - 31/12/2007

Abstract

Many systems in science and technology are well understood at the level of the individuals e.g.: the atoms, molecules, or bacteria. In this project we will develop numerical and mathematical techniques to predict the macroscopic and collective behavior of a system with a large number of individuals. We use the micro/macro techniques to translate the behavior of individuals to the macroscopic evolution.

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  • Research Project

Partial differential equations and models based on individuals. 01/10/2006 - 30/09/2016

Abstract

This project represents a research contract awarded by the University of Antwerp. The supervisor provides the Antwerp University research mentioned in the title of the project under the conditions stipulated by the university.

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  • Research Project