The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science.

Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N(3)) with the size of the investigated problem, N (e.g. the electron count in electronic structure theory), and thus often defines the system size limit that practical calculations cannot overcome. In many cases, more than just a small fraction of the possible eigenvalue/eigenvector pairs is needed, so that iterative solution strategies that focus only on a few eigenvalues become ineffective. Likewise, it is not always desirable or practical to circumvent the eigenvalue solution entirely. We here review some current developments regarding dense eigenvalue solvers and then focus on the Eigenvalue soLvers for Petascale Applications (ELPA) library, which facilitates the efficient algebraic solution of symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries, respectively, on parallel computer platforms. ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the Scalable Linear Algebra PACKage (ScaLAPACK) library but replacing all actual parallel solution steps with subroutines of its own. For these steps, ELPA significantly outperforms the corresponding ScaLAPACK routines and proprietary libraries that implement the ScaLAPACK interface (e.g. Intel's MKL). The most time-critical step is the reduction of the matrix to tridiagonal form and the corresponding backtransformation of the eigenvectors. ELPA offers both a one-step tridiagonalization (successive Householder transformations) and a two-step transformation that is more efficient especially towards larger matrices and larger numbers of CPU cores. ELPA is based on the MPI standard, with an early hybrid MPI-OpenMPI implementation available as well. Scalability beyond 10,000 CPU cores for problem sizes arising in the field of electronic structure theory is demonstrated for current high-performance computer architectures such as Cray or Intel/Infiniband. For a matrix of dimension 260,000, scalability up to 295,000 CPU cores has been shown on BlueGene/P.

Time-resolved study of biofilm architecture and transport processes using experimental and simulation techniques: the role of EPS.

Cellular material and extracellular polymeric substances are the basic structural elements in biofilm systems. The structure and role of EPS for biofilm development and metabolic processes have not been precisely determined and, therefore, have not yet been included as a necessary element in modelling and simulation studies. This is due to the difficulty of experimentally detecting the extracellular polymeric substances in situ and differentiating them from cellular material on the one hand, and to the subsequent uncertainty about appropriate models--e.g. rigid hindrances, porous microstructure or visco-elastic structure--on the other hand. In this work, we report on the use of confocal laser scanning microscopy to monitor the development of a monoculture biofilm of Sphingomonas sp. grown in a flow cell. The bacterial strain was genetically labelled resulting in strong constitutive expression of the green fluorescent protein. The development of extracellular polymeric substances was followed by binding of the lectin concavalin A to cell exopolysaccharides. The growth of the resulting strain was digitally recorded by automated confocal laser scanning microscopy. In addition, local velocity profiles of fluorescent carboxylate-modified microspheres were observed on pathlines throughout the biofilm. The CLSM image stacks were used as direct input for the explicit modelling and three-dimensional numerical simulation of flow fields and solute transport processes based on the conservation laws of continuum mechanics. At present, a strongly simplifying EPS-model is applied for numerical simulations. The EPSs are preliminarily assumed to behave like a rigid and dense hindrance with diffusive-reactive solute transport.

Automated confocal laser scanning microscopy and semiautomated image processing for analysis of biofilms.

The purpose of this study was to develop and apply a quantitative optical method suitable for routine measurements of biofilm structures under in situ conditions. A computer program was designed to perform automated investigations of biofilms by using image acquisition and image analysis techniques. To obtain a representative profile of a growing biofilm, a nondestructive procedure was created to study and quantify undisturbed microbial populations within the physical environment of a glass flow cell. Key components of the computer-controlled processing described in this paper are the on-line collection of confocal two-dimensional (2D) cross-sectional images from a preset 3D domain of interest followed by the off-line analysis of these 2D images. With the quantitative extraction of information contained in each image, a three-dimensional reconstruction of the principal biological events can be achieved. The program is convenient to handle and was generated to determine biovolumes and thus facilitate the examination of dynamic processes within biofilms. In the present study, Pseudomonas fluorescens or a green fluorescent protein-expressing Escherichia coli strain, EC12, was inoculated into glass flow cells and the respective monoculture biofilms were analyzed in three dimensions. In this paper we describe a method for the routine measurements of biofilms by using automated image acquisition and semiautomated image analysis.