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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)
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)
Fast and efficient numerical solvers for indefinite Helmholtz problems are of great interest in many scientific domains that study acoustic, seismic or electromagnetic wave scattering. Applications such as engine design, oil exploration, medical imaging , but even quantum mechanical problems describing particle interaction [1], are governed by underlying(More)
In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schrödinger's equation. The new technique is based upon a reformulation of the classical real-valued Green's function integral for the far field(More)
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)
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)
SUMMARY The basic building blocks of a classic multigrid algorithm, which are essentially stencil computations, all have a low ratio of executed floating point operations per byte fetched from memory. This important ratio can be identified as the arithmetic intensity. Applications with a low arithmetic intensity are typically bounded by memory traffic and(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)
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)