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 achieve only a small percentage of the theoretical peak performance of the underlying hardware. We propose a polynomial Chebyshev smoother, which we implement using cache‐aware tiling, to increase the arithmetic intensity of a multigrid V‐cycle. This tiling approach involves a trade‐off between redundant computations and cache misses. Unlike common conception, we observe optimal performance for higher degrees of the smoother. The higher‐degree polynomial Chebyshev smoother can be used to smooth more than just the upper half of the error frequencies, leading to better V‐cycle convergence rates. Smoothing more than the upper half of the error spectrum allows a more aggressive coarsening approach where some levels in the multigrid hierarchy are skipped. Copyright © 2012 John Wiley & Sons, Ltd.

Motivation: Computational modeling of plant developmental processes is becoming increasingly important. Cellular resolution plant tissue simulators have been developed, yet they are typically describing physiological processes in an isolated way, strongly delimited in space and time.Results: With plant systems biology moving toward an integrative perspective on development we have built the Virtual Plant Tissue (VPTissue) package to couple functional modules or models in the same framework and across different frameworks. Multiple levels of model integration and coordination enable combining existing and new models from different sources, with diverse options in terms of input/output. Besides the core simulator the toolset also comprises a tissue editor for manipulating tissue geometry and cell, wall, and node attributes in an interactive manner. A parameter exploration tool is available to study parameter dependence of simulation results by distributing calculations over multiple systems.Availability: Virtual Plant Tissue is available as open source (EUPL license) on Bitbucket (https://bitbucket.org/vptissue/vptissue). The project has a website https://vptissue.bitbucket.io.

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In molecular reactions at the microscopic level the appearance of resonances has an important influence on the reactivity. It is important to predict when a bound state transitions into a resonance and how these transitions depend on various system parameters such as internuclear distances. The dynamics of such systems are described by the time-independent Schrödinger equation and the resonances are modeled by poles of the S-matrix.Using numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, we are able to develop efficient and robust methods to study the transitions of bound states into resonances. By applying Keller's Pseudo-Arclength continuation, we can minimize the numerical complexity of our algorithm. As continuation methods generally assume smooth and well-behaving functions and the S-matrix is neither, special care has been taken to ensure accurate results.We have successfully applied our approach in a number of model problems involving the radial Schrödinger equation.