Publications
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Projected Newton method for noise constrained Tikhonov regularization University of Antwerp
Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter is given by Morozov's discrepancy principle. However, most approaches require the solution of the Tikhonov problem for many different values of the regularization parameter, which is computationally demanding for large scale problems. We propose a new ...
A robust simulator for physiologically structured population models University of Antwerp
A framework to simulate physiologically structured population (PSP) models on high performance compute (HPC) infrastructure is built. Based on the model of a single cell, billions of cells can be simulated in an efficient way, allowing fast simulation of the interaction of an entire organ with other body parts. Trough combination of three state-of-the-art algorithms, the simulation time is decreased with multiple orders of magnitude. First: PSP ...
Numerically stable recurrence relations for the communication hiding pipelined conjugate gradient method University of Antwerp
Pipelined Krylov subspace methods (also referred to as communication-hiding methods) have been proposed in the literature as a scalable alternative to classic Krylov subspace algorithms for iteratively computing the solution to a large linear system in parallel. For symmetric and positive definite system matrices the pipelined Conjugate Gradient method, p($l$l)-CG, outperforms its classic Conjugate Gradient counterpart on large scale distributed ...
Algorithm for the reconstruction of dynamic objects in CT-scanning using optical flow University of Antwerp KU Leuven
Computed Tomography is a powerful imaging technique that allows non-destructive visualisation of the interior of physical objects in different scientific areas. In traditional reconstruction techniques the object of interest is mostly considered to be static, which gives artefacts if the object is moving during the data acquisition. In this paper we present a method that, given only scan results of multiple successive scans, can estimate the ...
Regula falsi based automatic regularization method for PDE constrained optimization University of Antwerp
Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related-to-its solution. This can be-seen as a constrained minimization problem where one wishes to minimize the mismatch between the observed data and the model predictions, including an extra regularization term, and use the PDE as a constraint. Often, a suitable regularization parameter is determined by solving the ...
Automatic exploration techniques of numerical bifurcation diagrams illustrated by the Ginzburg-Landau equation University of Antwerp
This paper considers the extreme type-II Ginzburg-Landau equations, a nonlinear PDE model that describes the states of a wide range of superconductors. For two-dimensional domains, a robust method is developed that performs a numerical continuation of the equations, automatically exploring the whole solution landscape. The strength of the applied magnetic field is used as the bifurcation parameter. Our branch switching algorithm is based on ...
Dynamic simulation and steady-state computation of 3D physiologically structured population models University of Antwerp
The PSP modelling approach allows you to model biological/pharmaceutical behaviour by combining micro-scale ordinary differential equation (ODE) models with macro-scale ODE models and their bi-directional interaction. E.g.: based on the model of a single cell, billions of cells can be simulated to get the response of an entire organ (also incorporating the organ to cell reaction). The PSP approach allows to simulate this in a mathematically ...
Constrained runs algorithm as a lifting operator for the one-dimensional in space boltzmann equation with bgk collision term University of Antwerp
Lifting operators play an important role in starting a kinetic Boltzmann model from given macroscopic information. The macroscopic variables need to be mapped to the distribution functions, mesoscopic variables of the Boltzmann model. The Constrained Runs (CR) algorithm is used in the literature for the initialization of lattice Boltzmann models, special discretizations of the Boltzmann equation. It is based on the attraction of the dynamics ...
Efficient implementation of total FETI solver for graphic processing units using schur complement University of Antwerp
This paper presents a new approach developed for acceleration of FETI solvers by Graphic Processing Units (GPU) using the Schur complement (SC) technique. By using the SCs FETI solvers can avoid working with sparse Cholesky decomposition of the stiffness matrices. Instead a dense structure in form of SC is computed and used by conjugate gradient (CG) solver. In every iteration of CG solver a forward and backward substitution which are sequential ...