Numerical Analysis and Applied Mathematics Section

Person in chargeDescriptionProjectsDoctoral projectsExpertisesNederlands

Person in charge:
Prof. dr. ir. Roose Dirk

Research team:
Senior academic staff members: 11.10 VTE
Junior academic staff members:  1.00 VTE
Administrative and technical staff members: 1.00 VTE
Scientific staff members:26.25 VTE
Localisation in KU Leuven organogram

Research team description: Top

NUMERICAL APPROXIMATION AND NUMERICAL LINEAR ALGEBRA GROUP (A. Bultheel): * Fast and stable algorithms to solve many pro- blems in mathematics connected to continued fractions, orthogo- nal functions, rational approximation & interpolation, etc. with applications in signal processing, linear systems, etc.. * Nume- rical solution of recurrence relations with continued fractions. * Fast and stable algorithms to solve structured linear systems of equations. * Understanding and developing robust numerical methods for the calculation of the (rightmost) eigenvalue(s) of large sparse matrices with applications in the study of stabili- ty of equilibrium solutions of dynamical systems. Wavelet based techniques in image processing: compression, denoising, etc.. * Analysis and applications of spline functions: smoothing of curves and surfaces with and without constraints. Modelling of surface with splines in CAGD. Development of a software package smoothing using splines. * Development of educational software for mathematics. NUMERICAL INTEGRATION, NONLINEAR EQUATIONS AND SOFTWARE (R.Cools) Construction of cubature formulas for approximating multivariate integrals using group theory, ideal theory & invariant theory. * Derivation of error expansions and lower bounds for the cost of a cubature formula. * Development of software packages for auto- matic numerical integration based on heuristic error estimators, adaptive subdivision strategies, etc.. * Root counting of systems of polynominal equations and systems of nonlinear analytic equa- tions. * Understanding and developing homotopy continuation methods for computing all common zeros of systems of polynominal equations. * Development of a software package for solving systems of polynomial equations using homotopy continuation me- thods and for solving sytems of analytic equations using numeri- cal integration and structural linear systems. SCIENTIFIC COMPUTING (D. Roose) The research group focuses on the development of numerical methods for solving large scale simulation problems in science & engineering. Efficiency, robustness and amenability to implemen- tation on high performance (parallel) computers, are important aspects in the design of the algorithms. * Fast solvers for stationary and time-dependent partial diffe- rential equations: iterative methods for elliptic and hyperbolic problems, predonditionig for Krylov subspace methods, multigrid accelaration, domain decomposition; acceleration of waveform relaxation methods for tume-dependent parabolic problems; application and integration of these solvers in software forfluid dynamics. * Fast and robust methods for solving large-scale eigenvalue problems, and application in linear stability analysis * Numerical methods for nonlinear dynamical systems and for bi- furcation analysis of nonlinear parameter-dependent problems. Emphasis on partial differential equations and delay differential equations. * Parallel computing aspects ofnumerical simulation : parallelisation of numerical software for fluid dynamics, hydro- dynamics, etc., algorithms and tools for load balancing and grid partioning for geometrically parallel applications on irregular adaptively refined grids. * Application of wavelet-based methods in image processing: image compression, noise reduction, edge detection; combination of wavelet-based techniques with Bayesian statistics; application to large images in Geographical Image Systems, and to video sequences.>

Research projects of research team Numerical Analysis and Applied Mathematics Section


Spectral properties of (perturbed) normal matrices and their applications.
Reestablishing smoothness for matrix manifold optimization via resolution of singularities.
Exploiting space-scale separation in a multiscale method for plastic defn of polycrystalline materia...
Dynamical systems, control and optimization. (Dysco)
Novel algorithms for multiscale simulation: mapping macroscopic to miscroscopic states (MATCHMAKER)....
Can Unconventional Eigenvalue Algorithms Supersede the State of the Art.
Multiscale simulation of stochastic and kinetic models.
Cubature for infinite-dimensional problems

Multivariate polynomial and rational interpolation and approximation.

Frame computing for the simulation of oscillatory phenomena (Waves).
Numerical algorithms for large scale matrices with uncertain coefficients.
High performance computing software for bioinformatics applications.
Efficient Uncertainty quantification For Optimization  in Robust design of Industrial Appl...
DeMoPreCi-MDT: Development, Monitoring and prediction of Coupled Interactions in Material Durability...
Coping with redundancy: frame-based discretizations of operator equations.
Robust identification of patient-specific parameters for bolus calculators in type 1 diabetic p...
Large-scale eigenvalue problems with eigenvector nonlinearities

The geometry of the tensor rank decomposition: Perturbation theory  

UCoCoS: Understanding and controlling complex systems.

Doctoral projects of research team Numerical Analysis and Applied Mathematics Section


Matrix computations and orthogonal functions
Numerical methods for the simulation of a kinetic multiscale model for tumor growth.
* Short Recurrence Relations for (Extended) Krylov Subspaces
Analysis and Applications of Orthogonal Polynomials with Zeros in the Complex Plane
Texture control in asymmetric rolling for improved sheet metal formability.

* Advanced Quasi-Monte Carlo Algorithms for High-dimensional Integration and Approximation
Structured Eigenvalue Problems: Normal and Hamiltonian Matrices
multiscale simulation of kinetic equations
Simulations of the properties and morphology of polymers at interfaces
Introducing redundancy into numerical algorithms: computing with frames
Numerical-asymptotic methods for high-frequency scattering problems
BIM-modeleren van binnenruimtes gebruikmakend van terrestriële laserscanning
Multi-scale simulation algorithms and software
Model order reduction for linear systems with stochastic parameters
Numerical methods for infinite-dimensional integrals
Multi-scale multi-physics algorithms for coupled interactions in advanced materials for offshore ind...
A least squares shadowing approach for the optimization of chaotic systems
Efficient Uncertainty Quantification for Optimization in Robust Design of Industrial Applications
Rational Krylov Methods, Reliable Algorithm and Application
Use of Physiologically Structured Population models for mechanistic multi-scale tissue modelling
Numerical Methods for Infinite-Dimensional Integrals
Noise Reduction in Coarse Bifurcation Analysis of Stochastic Agent-based Network Models
* Computational methods for robus control of large-scale interconnected systems
Numerical methods for infinite-dimensional integrals
* Computational Tools for the Analysis of Dynamical Systems with UncertainParameters

Expertises of research team Numerical Analysis and Applied Mathematics Section :Top

Numerical solution of nonlinear systems especially systems of polynomial equations.
Numerical computation of multidimensional integrals.
The software package GLAS, which is an acronym for Generic Linear Algebra Software, is a user friend...

Research team number: 50000532