All-at-once preconditioning in PDE-constrained optimization

The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound constraints for the control are introduced. Numerical results will illustrate the competitiveness of our techniques

Relationship between endogenous hormone levels of grapevine callus cultures and their morphogenetic behaviour

Dark callus cultures from leaves and anthers of three grapevine genotypes (Seyval blanc, Riesling and Trollinger) were propagated in vitro for almost two years on medium deprived of growth regulators. Three different callus lines originated from these initial callus cultures: A dark non-embryogenic one, another composed by clusters of somatic embryos and a friable, whitish callus line that can produce somatic embryos under appropriate circumstances, Endogenous hormone levels viz, indole-3-acetic acid (IAA), abscisic acid (ABA), gibberellins A1, A3 and A20, zeatin/zeatin riboside and N6(∆2-isopentenyl) adenine/ N6(∆2-isopentenyl) adenosine, were analysed in the different callus types. Only higher ABA levels correlated with the morphogenetic capacity of the cultures. When endogenous hormone levels were analysed in the line constituted by conglomerates of somatic embryos at different dates during the whole culture period, higher levels of IAA and ABA were found during the winter months even if the cultures were maintained permanently under constant temperature and photoperiod conditions. A 4-week chilling period led to a reduction of the endogenous ABA level

I’m stuck! How to efficiently debug computational solid mechanics models so you can enjoy the beauty of simulations

A substantial fraction of the time that computational modellers dedicate to developing their models is actually spent trouble-shooting and debugging their code. However, how this process unfolds is seldom spoken about, maybe because it is hard to articulate as it relies mostly on the mental catalogues we have built with the experience of past failures. To help newcomers to the field of material modelling, here we attempt to fill this gap and provide a perspective on how to identify and fix mistakes in computational solid mechanics models. To this aim, we describe the components that make up such a model and then identify possible sources of errors. In practice, finding mistakes is often better done by considering the symptoms of what is going wrong. As a consequence, we provide strategies to narrow down where in the model the problem may be, based on observation and a catalogue of frequent causes of observed errors. In a final section, we also discuss how one-time bug-free models can be kept bug-free in view of the fact that computational models are typically under continual development. We hope that this collection of approaches and suggestions serves as a “road map” to find and fix mistakes in computational models, and more importantly, keep the problems solved so that modellers can enjoy the beauty of material modelling and simulation.EC and JPP wish to thank their former supervisor Paul Steinmann for the inspiration to write this paper, which can be traced back to the talk we prepared for the ECCM-ECFD conference held in Glasgow in 2018. EC’s work was partially supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 841047. WB’s work was partially supported by the National Science Foundation under award OAC-1835673; by award DMS-1821210; by award EAR-1925595; and by the Computational Infrastructure in Geodynamics initiative (CIG), through the National Science Foundation under Award EAR-1550901 and The University of California – Davis .Peer ReviewedPostprint (published version