Full chronoogical publications list of submitted and published papers is on my google scholar profile

Krylov solvers that hide latencies and avoid communication.

The current generation of iterative methods give a poor performance on modern hardware since communication and synchronization costs dominate over the cost of the floating point operations. We are working on communication avoiding and hiding in iterative Krylov methods and introduced so-called pipelined Krylov methods where the latency associated with dot-products is hidden behind other computations. It offers a much better performance in strong scaling experiments. We are currently also working on high-arithmetic intensity Krylov methods that are build on top of kernels that can be SIMD vectorized.

S. Cools, J. Cornelis and W. Vanroose, Numerically Stable Recurrence Relations for the Communication Hiding Pipelined Conjugate Gradient Method, accepted in IEEE transactions on parallel and distributed systems, preprint arXiv:1902.03100 (2019). [PDF]
E. Agullo, S. Cools, E. Fatih-Yetkin, L. Giraud and W. Vanroose, On soft errors in the Conjugate Gradient method: sensitivity and robust numerical detection,submitted , Inria RESEARCH REPORT 9226, HAL Id: hal-01929738 (2018). [PDF]
J. Cornelis, S. Cools and W. Vanroose, The Communication-Hiding Conjugate Gradient Method with Deep Pipelines submitted, arXiv preprint arXiv:1801.04728, (2018). [PDF]
S. Cools, E. F. Yetkin, E. Agullu, L. Giraud, W.Vanroose, Analyzing the effect of local rounding error propagation on the maximal attainable accuracy of the pipelined conjugate gradient method, SIAM journal on matrix analysis and applications 39:1, p. 426-450 (2018). [PDF]
S. Cools and W. Vanroose,The communication-hiding pipelined BiCGstab method for the parallel solution of large unsymmetric linear systems, Parallel Computing, 65 p1-20 (2017). [URL]
W. Vanroose, P. Ghysels, D. Roose, and K.Meerbergen, Hiding global communication latency and increasing the arithmetic intensity in extreme-scale Krylov solvers, Position Paper at DOE/ASCR workshop on Applied Mathematics Research for Exascale Computing. August 21-22, 2013, PDF.
P. Ghysels and W. Vanroose, Modeling the performance of geometric multigrid on many-core computer architectures, SIAM J. on Scientific Computing, 37 I2 pC194-C216 (2015) (2013). PDF
P. Ghysels and W. Vanroose, Hiding global synchronization latency in the preconditioned Conjugate Gradient algorithm, Parallel Computing, In Press, p1-15 (2014) PDF
P. Ghysels, T. Ashby, K. Meerbergen, and W. Vanroose, Hiding global communication latency in the GMRES algorithm on massively parallel machines, SIAM Journal on Scientific Computing, 35 (1) C48-C71, ExaScience Lab Technical Report 04.2012.1 (2013) PDF
P. Ghysels, P. Klosiewicz, and W. Vanroose, Improving the arithmetic intensity of multigrid with the help of polynomial smoothers, Numerical Linear Algebra with Applications, 19 p253-267 (2012) PDF
W. Heirman, T.E. Carlson, S. Sarkar, P. Ghysels, W. Vanroose, and L. Eeckhout, Using Fast and Accurate Simulation to Explore Hardware/Software Trade-offs in the Multi-Core Era, ParCo Proceedings. (2011). PDF
T. Ashby, P. Ghysels, W. Heirman, and W. Vanroose, The Impact of Global Communication Latency at Extreme Scales on Krylov Methods Springer Lecture Notes in Computer Science, proceedings of ICA3PP-12, (2012).

Bottom-up models in systems biology.

D. Draelants, D. Avitabile, and W. Vanroose, Localised auxin peaks in concentration-based transport models for plants, Royal Society Interface, 12 106 p20141407 (2015) PDF.
D. Draelants, J. Broeckhove, G. Beemster and W. Vanroose, Pattern formation in a cell based auxin transport model with numerical bifurcation analysis, Journal of Mathematical Biology, 67 p1279-1305 (2013) PDF
D. De Vos, A. Dzhurakhalov, D. Draelants, I. Bogaerts, S. Kalve, E. Prinsen, K. Vissenberg, W. Vanroose, J. Broeckhove, and G. Beemster, Towards mechanistic models of plant organ growth, Journal of Experimental Botany 63 p3325-3337 (2012) PDF
D. Draelants, W. Vanroose, J. Broeckhove, and G. Beemster, Influence of an exogeneous model parameter on the steady states in an auxin transport model, 4th International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA) (2012).

Solvers for Helmholtz and Schrödinger equations

We are developing methods to solve the d-dimensional scattering Helmholtz and Schrödinger equations based on multigrid.

S. Cools and W. Vanroose, On the Optimality of Shifted Laplacian in a Class of Polynomial Preconditioners for the Helmholtz Equation, In: Lahaye D., Tang J., Vuik K. (eds) Modern Solvers for Helmholtz Problems. Birkhauser (2017).
S. Cools and W.Vanroose, A fast and robust computational method for the ionization cross sections of the driven Schrodinger equation using an O(N) multigrid-based scheme,Journal of Computational Physics, 308 p20-39 (2016).[URL]
S. Cools, B. Reps and W. Vanroose, An efficient multigrid method calculation of the far field map for Helmholtz and Schrödinger problems, SIAM journal of Scientific Computing, 36(4) B367-B395 (2014) PDF
S. Cools, B. Reps and W. Vanroose, A new level-dependent coarse grid correction scheme for indefinite Helmholtz problems, Numerical Linear Algebra with Applications, In Press, (2013) PDF
S. Cools and W. Vanroose, Local Fourier Analysis of the Complex Shifted Laplacian preconditioner for Helmholtz problems, Numerical Linear Algebra with Applications, 20(4) p575-597 (2013) PDF
B. Reps, W. Vanroose, and H. bin Zubair, GMRES-based multigrid for the complex scaled preconditoner for the indefinite Helmholtz equation, Numerical Linear Algebra with Applications, Submitted, (2013). PDF.
B. Reps and W. Vanroose, Analyzing the wave number dependency of the convergence rate of a multigrid preconditioned Krylov method for the helmholtz equation with an absorbing layer, Numerical Linear Algebra with Applications, 19 p232-252 (2012) PDF
H. bin Zubair, B. Reps, and W. Vanroose, A preconditioned iterative solver for the scattering solutions of the Schrödinger equation, Communications in Computational Physics, 11 p415-434 (2012) PDF
B. Reps, W. Vanroose, and H. bin Zubair, On the indefinite Helmholtz equation: Complex stretched absorbing boundary layers, iterative analysis, and preconditioning, Journal of Computational Physics, 229, p8384--405 (2010) PDF

Inverse problems and Tomography

N. Schenkels and W. Vanroose, Projected Newton method for a system of Tikhonov-Morozov equations, submitted, arXiv:1809.01627 (2018). [PDF]
N. Schenkels and W. Vanroose, Regula falsi based automatic regularization method for PDE constrained optimization Journal of Computational and Applied Mathematics, 348, 14-25 (2019). [URL]
K. Ruymbeek and W.Vanroose, Algorithm for the reconstruction of dynamic objects in CT-scanning using optical flow, submitted arXiv:1905.00723 (2018). [PDF]
V. Melicher, T.Haber, and W. Vanroose, Fast derivatives of likelihood functionals for ODE based models using adjoint-state method, Computational Statistics, 32, p1621-1643 (2017). [PDF]
S. Cools, P. Ghysels, W. van Aarle, and W. Vanroose A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems,J. Computational and Applied Mathematics arxiv:1310.0956 PDF
W. van Aarle, P. Ghysels, J. Sijbers, and W. Vanroose, Memory access optimization for iterative tomography on many-core architectures, Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, 369-372. (2012) PDF

Multiscale Methods for Kinetic Models.

We are developing new numerical lifting operators for problems described by the Boltzmann equation.

Y. Vanderhoydonc and W. Vanroose, Constrained runs algorithm as a lifting operator for the one-dimensional in space boltzmann equation with BGK collision term, SIAM Multiscale Modeling & Simulation 14 p1488-1512 (2016). [PDF]
Y. Vanderhoydonc and W. Vanroose, Initialization of lattice Boltzmann models with the help of the numerical Chapman-Enskog expansion, Procedia Computers Science, 18 p1036-1045 (2013). PDF
Y. Vanderhoydonc and W. Vanroose, Numerical extraction of macroscopic pde and lifting operator from a lattice boltzmann model, SIAM Multiscale Modeling & Simulation, 10(3) p766-791, PDF
Y. Vanderhoydonc and W. Vanroose, Lifting in hybrid lattice Boltzmann and PDE models, Computing and Visualization in Science, 14 p67-78 (2011), PDF
Y. Vanderhoydonc, W. Vanroose, C. Vandekerckhove, P. Van Leemput, and D. Roose, Numerical lifting for lattice Boltzmann models. chapter in "Novel Trends in Lattice Boltzmann Methods: Reactive Flow, Physicochemical Transport and Fluid-Structure Interaction". Bertham Publisher, (2012).
G. Samaey, C. Vandekerckhove, and W. Vanroose, A multilevel algorithm to compute steady states of lattice Boltzmann models, Coping with complexity : model reduction and data analysis / Gorban, Alexander N. [edit.]; et al. [edit.] PDF
G. Samaey and W. Vanroose, An analysis of equivalent operator preconditioning for equation-free Newton-Krylov methods, SIAM Journal on Numerical Analysis, 48 p633-658 (2010) PDF
G. Samaey, W. Vanroose, D. Roose, and I.G. Kevrekidis, Newton-Krylov solvers for the equation-free computation of coarse traveling waves, Computer Methods in Applied Mechanics and Engineering, 197 (43-44) p3480--3491 (2008) PDF
P. Van Leemput, C. Vandekerckhove, W. Vanroose, and D. Roose, Accuracy of hybrid lattice boltzmann/finite difference schemes for reaction-diffusion systems, SIAM Multiscale Modeling & Simulation, 6, p838--857 (2007) PDF
P. Van Leemput, W. Vanroose, and D. Roose, Mesoscale analysis of the equation-free constrained runs initialization scheme, SIAM Multiscale Modeling & Simulation 6 p1234--1255 (2007) PDF

Solvers for Nonlinear Schrödinger equations.

Nonlinear Schrödinger equations are used to model a wide range of applications. We have developed efficient solvers that scale optimally.

M. Wouters and Wim Vanroose, Automatic exploration techniques for the numerical bifurcation study of the Ginzburg-Landau equation submitted to SIAM dynamical systems, 2019, PDF
N. Schlömer, M.V. Milosevic, B. Partoens, and W. Vanroose, Exploration of stable and unstable vortex patterns in a superconductor under a magnetic disc, arxiv:1304.8081 PDF
N. Schlömer, D. Avitabile, M. V. MiloÅ¡eviÄ‡, B. Partoens, and W. Vanroose Efficient determination of the energy landscape of nonlinear Schrödinger-type equations, arxiv:1209.6064 PDF
N. Schlömer and W. Vanroose, An optimal linear solver for the Jacobian system of the extreme type-II Ginzburg--Landau problem, Journal of Computational Physics, 234 p560-572 (2013) PDF
N. Schlömer, D. Avitabile, and W. Vanroose, Numerical bifurcation study of superconducting patterns on a square, SIAM Journal of Applied Dynamical Systems, 11 p447-477 (2012) PDF

Numerical Continuation of Resonances.

We have have introduced numerical continuation to track resonances in quantum mechanical systems. Numerical Continuation is frequently used in dynamical systems. The method can track transition betweenresonant and bound state in single channel problems, coupled channel problems with equal and unequal tresholds.

P. Klosiewicz, W. Vanroose, and J. Broeckhove, Numerical continuation of bound and resonant state of the two channel Schrödinger equation, Physical Review A., 85 p012709 (2012) PDF
P. Klosiewicz, J. Broeckhove and W. Vanroose, Numerical Continuation of resonances and bound states in coupled channel Schrödinger equation, Communications in Computational Physics, 11 p435-455 (2012). PDF
P. Klosiewicz, J. Broeckhove, and W. Vanroose, Using pseudo-arclength continuation to trace the resonances of the Schrödinger equation, Computer Physics Communications, 180 (4) p545--548 (2009) URL
W. Vanroose, J. Broeckhove, and P. Klosiewicz, Tracing the parameter dependence of quantum resonances with numerical continuation, Journal of physics B - Atomic Molecular and Optical Physics, 42 p044002 (2009) PDF

Scattering and breakup of molecular systems.

L. Tao, W. Vanroose, B. Reps, T.N. Rescigno, and C.W. McCurdy, Long-time solution of the time-dependent Schrödinger equation for an atom in an electromagnetic field using complex coordinate contours, Physical Review A, 80 p063419 (2009) PDF
T.N. Rescigno, W. Vanroose, D.A. Horner, F.Martin, and C.W. McCurdy, First principles study of double photoionization of H-2 using exterior complex scaling,Journal of Electron Spectroscopy and Related Phenomena 161 p85--89 (2007) PDF.
D.A. Horner, W. Vanroose, T.N. Rescigno, F. Martin, and C.W. McCurdy, Role of nuclear motion in double ionization of molecular hydrogen by a single photon, Physical Review Letters, 98 (cover story) p073001 (2007) PDF
W. Vanroose, D. A. Horner, F. Martin, T. N. Rescigno, and C. W. McCurdy, Double photoionization of aligned molecular hydrogen, Physical Review A 74 p052702 (2006) PDF
W. Vanroose, F. Martin, T.N. Rescigno, and C.W. McCurdy, Complete photo-induced breakup of the H-2 molecule as a probe of molecular electron correlation, Science, 310 p1787--1789, (2005)PDF
W. Vanroose, F. Martin, T.N. Rescigno, and C.W. McCurdy, Nonperturbative theory of double photoionization of the hydrogen molecule, Physical Review A, 70 ({5}), (rapid) p050703 (2004). PDF
Z.Y. Zhang, W. Vanroose, C.W. McCurdy, A.E. Orel, and T.N.Rescigno, Low-energy electron scattering of NO: Ab initio analysis of the (3)Sigma(-), (1)Delta, and (1)Sigma(+) shape resonances in the local complex potential model, Physical Review A, 69 p062711 (2004) PDF
W. Vanroose, Z.Y. Zhang, C.W. McCurdy, and T.N. Rescigno, Threshold vibrational excitation of CO2 by slow electrons, Physical Review Letters, 92 ({5}) p053201 (2004) PDF
W. Vanroose, C.W. McCurdy, and T.N. Rescigno, Scattering of slow electrons by polar molecules: Application of effective-range potential theory to HCl, Physical Review A, 68({5}) p05713 (2003) PDF
W. Vanroose, C.W. McCurdy, and T.N.Rescigno, Interpretation of low-energy electron-CO2 scattering, Physical Review A, 66 ({3}) p032713 (2002) PDF

Scattering in the oscillator representation

Y. Bidasyuk and W. Vanroose, Improving the convergence of scattering calculations in the oscillator representation, Journal Computational Physics, 234 p60-78 (2013) PDF
Y. Bidasyuk, W. Vanroose, J.Broeckhove, F. Arickx, and V. Vasilevsky, Hybrid method (JM-ECS) combining the J-matrix and exterior complex scaling methods for scattering calculations, Physical Review C, 82 p064603 (2010) PDF
J. Broeckhove, F. Arickx, W. Vanroose, and V.S. Vasilevsky, The modified J-matrix method for short range potentials, Journal of Physics A - mathematical and general, 37 p7769--7781 (2004) PDF
W. Vanroose, J. Broeckhove, and F. Arickx, Modified J-matrix method for scattering, Physical Review Letters, 88, p010404 (2002) PDF