Research team Numerical Analysis and Applied Mathematics Section

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

Research team:
Senior academic staff members: 11.00 VTE
Junior academic staff members:  2.80 VTE
Administrative and technical staff members: 1.00 VTE
Scientific staff members:23.00 VTE
Localisation in KU Leuven organigram

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


Analysis and applications of orthogonal polynomials with zeros in the complex plane.
Waves: new techniques in analysis, modelling and numerical simulation.
Computational aspects of uncertainty propagation in large and multiscale systems.   &...
Control and optimization of large-scale systems and networks with delays. 
Numerical algorithms for large scale matrices with uncertain coefficients.
Algorithmic advances based on low-discrepancy point sets.  
Numerical simulation of highly oscillatory problems with applications.
Analysis of (equation-free) multiscale methods and their applications.
Multi-parameter model order reduction and its applications.
Multscale particle based simulation software. 
Fixed-order controller design for linear infinite-dimensional and parameter-varying systems, optimiz...
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...
Optimization based controller synthesis for interconnected dynamical system.
Advanced algoritms for optimal numerical integration.  
Can Unconventional Eigenvalue Algorithms Supersede the State of the Art.
Multiscale simulation of stochastic and kinetic models.
Optimization and control of nonsmooth dynamical systems with time-delays
Rational interpolatory quadrature formulas on the interval.
Cubature for infinite-dimensional problems
Novel algorithms for multiscale simulation: mapping macroscopic to miscroscopic states (MATCHMAKER)....
Dynamical systems, control and optimization. (Dysco)
Exploiting unconventional QR-algorithms for fast and accurate computatiooots of polynomials

Multivariate polynomial and rational interpolation and approximation.

Dynamics and control of nonsmooth time-delay systems.
Higher order multivariate spline functions.   
Frame computing for the simulation of oscillatory phenomena (Waves).
High performance computing software for bioinformatics applications.
Computational techniques for engineering applications.
Robust identification of patient-specific parameters for bolus calculators in type 1 diabetic p...
DeMoPreCi-MDT: Development, Monitoring and prediction of Coupled Interactions in Material Durability...
Coping with redundancy: frame-based discretizations of operator equations.
Efficient Uncertainty quantification For Optimization  in Robust design of Industrial Appl...

Doctoral projects of research team Numerical Analysis and Applied Mathematics Section


Analysis and computational control of large-scale systems and networks with delays
Parallel algorithms for solving large scale dynamical systems
Numerical methods for infinite-dimensional integrals
The computation of fuzzy eigenvalues
Matrix computations and orthogonal functions
Parallel Smoothed Particle Hydrodynamics for Multiscale Simulations
Numerical algorithms for the optimization of periodic systems governed by partial differential equat...
Study of elliptic curves with applications in cryptography.
Model Reduction Techniques for the Efficient Solution of Multiparameter Linear Models in Engineering...
The development and implementation of quasi-Monte Carlo methods for large scale and real-time applic...
The Solution of Linear Systems with Parameters Arising in Structures and Vibrations
Numerical controller design methods for infinite-dimensional linear systems with time-varying parame...
Reestablishing smoothness for matrix manifold optimization via resolution of singularities
Simulations of the properties and morphology of polymers at interfaces
BIM-modeleren van binnenruimtes gebruikmakend van terrestriële laserscanning
Introducing redundancy into numerical algorithms: computing with frames
Multi-Scale Modelling of Plastic Metal-Forming Processes.
Spectral Properties of (Perturbed) Norma Matrices and their Applications
Numerical methods for the simulation of a kinetic multiscale model for tumor growth.
Multi-scale simulation algorithms and software
Analysis and applications of orthogonal polynomials in the complex plane
Quasi-Monte Carlo Methods for the Schrödinger Equation
The numerical solution of multi-parameter eigenvalue problems.
Model order reduction for linear systems with stochastic parameters
Non-negative polynomials
multiscale simulation of kinetic equations
The development of quasi-Monte Carlo methods for problems in finance
Multi-scale multi-physics algorithms for coupled interactions in advanced materials for offshore ind...
Numerical-asymptotic methods for high-frequency scattering problems
Fuzzy finite elements: uncertainty propagation in dynamical systems
Ontwikkelen van een rekenmethode en rekencode voor de bepaling van een optimale kernlading voor MYRR...
Multiscale simulation software for industrial metal forming processes.
A least squares shadowing approach for the optimization of chaotic systems
Low-order approximations of large-scale nonlinear dynamical systems: theory, algorithms and applicat...

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