Wim Vanroose

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Scalability of Krylov subspace methods suffers from costly global synchronization steps that arise in dot-products and norm calculations on parallel machines. In this work, a modified Conjugate Gradient (CG) method is presented that removes the costly global synchronization steps from the standard CG algorithm by only performing a single non-blocking(More)
In the Generalized Minimal Residual Method (GMRES), the global all-to-all communication required in each iteration for orthogonalization and normalization of the Krylov base vectors is becoming a performance bottleneck on massively parallel machines. Long latencies, system noise and load imbalance cause these global reductions to become very costly global(More)
Transport models of growth hormones can be used to reproduce the hormone accumulations that occur in plant organs. Mostly, these accumulation patterns are calculated using time step methods, even though only the resulting steady state patterns of the model are of interest. We examine the steady state solutions of the hormone transport model of Smith et al.(More)
Despite decades of progress in quantum mechanics, electron correlation effects are still only partially understood. Experiments in which both electrons are ejected from an oriented hydrogen molecule by absorption of a single photon have recently demonstrated a puzzling phenomenon: The ejection pattern of the electrons depends sensitively on the bond(More)
This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formulated with absorbing boundary layers based on complex coordinate stretching. The preconditioner problem is a Helmholtz problem where not only the coordinates in the absorbing layer have an imaginary part, but also the coordinates in the interior region. This(More)
This paper considers the extreme type-II Ginzburg–Landau equations that model vortex patterns in superconductors. The nonlinear PDEs are solved using Newton’s method, and properties of the Jacobian operator are highlighted. Specifically, this paper illustrates how the operator can be regularized using an appropriate phase condition. For a two-dimensional(More)
We modify the J-matrix technique for scattering so that problems with long-range interactions are easily solved. This is done by introducing additional terms in the asymptotic three-term recurrence relation that take into account asymptotic effects of the potential. The solutions of this modified recurrence relation are a very good approximation of the(More)
Writing well-performing parallel programs is challenging in the multicore processor era. In addition to achieving good per-thread performance, which in itself is a balancing act between instruction-level parallelism, pipeline effects and good memory performance, multi-threaded programs complicate matters even further. These programs require synchronization,(More)
Modelling and simulation are increasingly used as tools in the study of plant growth and developmental processes. By formulating experimentally obtained knowledge as a system of interacting mathematical equations, it becomes feasible for biologists to gain a mechanistic understanding of the complex behaviour of biological systems. In this review, the(More)