Computational complexity of weighted splitting schemes on parallel computers

In models of complicated physical-chemical processes operator splitting is very often applied in order to achieve sufficient accuracy as well as efficiency of the numerical solution. The recently rediscovered weighted splitting schemes have the great advantage of being parallelizable on operator level, which allows us to reduce the computational time if parallel computers are used. In this paper, the computational times needed for the weighted splitting methods are studied in comparison with the sequential (S) splitting and the Marchuk-Strang (MSt) splitting and are illustrated by numerical experiments performed by use of simplified versions of the Danish Eulerian model (DEM).

Comparison of the computational cost of a Monte Carlo and deterministic algorithm for computing bilinear forms of matrix powers

In this paper we consider bilinear forms of matrix polynomials and show that these polynomials can be used to construct solutions for the problems of solving systems of linear algebraic equations, matrix inversion and finding extremal eigenvalues. An almost Optimal Monte Carlo (MAO) algorithm for computing bilinear forms of matrix polynomials is presented. Results for the computational costs of a balanced algorithm for computing the bilinear form of a matrix power is presented, i.e., an algorithm for which probability and systematic errors are of the same order, and this is compared with the computational cost for a corresponding deterministic method.

Computational chemistry for elucidating protein function: energetics and dynamics of myoglobin-ligand systems

State-of-the-art computational methodologies are used to investigate the energetics and dynamics of photodissociated CO and NO in myoglobin (Mb···CO and Mb···NO). This includes the combination of molecular dynamics, ab initio MD, free energy sampling, and effective dynamics methods to compare the results with studies using X-ray crystallography and ultrafast spectroscopy metho ds. It is shown that modern simulation techniques along with careful description of the intermolecular interactions can give quantitative agreement with experiments on complex molecular systems. Based on this agreement predictions for as yet uncharacterized species can be made.

Electronic properties of 4,4 ',5,5 '-tetramethyl-2,2 '-biphosphinine (tmbp) in the redox series fac-[Mn(Br)(CO)(3)(tmbp)], [Mn(CO)(3)(tmbp)](2), and [Mn(CO)(3)(tmbp)](-): crystallographic, spectroelectrochemical, and DFT computational study

Stepwise electrochemical reduction of the complex fac-[Mn(Br)(CO)(3)(tmbp)] (tmbp = 4,4',5,5'-tetramethyl-2,2'-biphosphinine) produces the dimer [Mn(CO)(3)(tmbp)](2) and the five-coordinate anion [Mn(CO)(3)(tmbp)](-). All three members of the redox series have been characterized by single-crystal X-ray diffraction. The crystallographic data provide valuable insight into the localization of the added electrons on the (carbonyl)manganese and tmbp centers. In particular, the formulation of the two-electron-reduced anion as [Mn-0(CO)(3)(tmbp(-))](-) also agrees with the analysis of its IR nu(CO) wavenumbers and with the results of density functional theoretical (DFT) MO calculations on this compound. The strongly delocalized pi-bonding in the anion stabilizes its five-coordinate geometry and results in the appearance of several mixed Mn-to-tmbp charge-transfer/IL(tmbp) transitions in the near-UV-vis spectral region. A thorough voltammetric and UV-vis/IR spectroelectrochemical study of the reduction path provided evidence for a direct formation of [Mn(CO)(3)(tmbp)](-) via a two-electron ECE mechanism involving the [Mn(CO)(3)(tmbp)](.) radical transient. At ambient temperature [Mn(CO)(3)(tmbp)](-) reacts rapidly with nonreduced fac-[Mn(Br)(CO)(3)(tmbp)] to produce [Mn(CO)(3)(tmbp)](2). Comparison with the analogous 2,2'-bipyridine complexes has revealed striking similarity in the bonding properties and reactivity, despite the stronger pi-acceptor character of the tmbp ligand.

Titanocene anticancer complexes and their binding mode of action to human serum albumin: a computational study

Due to the pivotal role played by human serum albumin (HSA) in the transport and cytotoxicity of titanocene complexes, a docking study has been performed on a selected set of titanocene complexes to aid in the current understanding of the potential mode of action of these titanocenes upon binding HSA. Analysis of the docking results has revealed potential binding at the known drug binding sites in HSA and has provided some explanation for the specificity and subsequent cytotoxicity of these titanocenes. Additionally, a new alternative binding site for these titanocenes has been postulated.

Computational modes and grid imprinting on five quasi-uniform spherical C-grids

Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations. We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid, despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity.

A tutorial on pseudospectral methods for computational optimal control

[English] This paper is a tutorial introduction to pseudospectral optimal control. With pseudospectral methods, a function is approximated as a linear combination of smooth basis functions, which are often chosen to be Legendre or Chebyshev polynomials. Collocation of the differential-algebraic equations is performed at orthogonal collocation points, which are selected to yield interpolation of high accuracy. Pseudospectral methods directly discretize the original optimal control problem to recast it into a nonlinear programming format. A numerical optimizer is then employed to find approximate local optimal solutions. The paper also briefly describes the functionality and implementation of PSOPT, an open source software package written in C++ that employs pseudospectral discretization methods to solve multi-phase optimal control problems. The software implements the Legendre and Chebyshev pseudospectral methods, and it has useful features such as automatic differentiation, sparsity detection, and automatic scaling. The use of pseudospectral methods is illustrated in two problems taken from the literature on computational optimal control. [Portuguese] Este artigo e um tutorial introdutorio sobre controle otimo pseudo-espectral. Em metodos pseudo-espectrais, uma funcao e aproximada como uma combinacao linear de funcoes de base suaves, tipicamente escolhidas como polinomios de Legendre ou Chebyshev. A colocacao de equacoes algebrico-diferenciais e realizada em pontos de colocacao ortogonal, que sao selecionados de modo a minimizar o erro de interpolacao. Metodos pseudoespectrais discretizam o problema de controle otimo original de modo a converte-lo em um problema de programa cao nao-linear. Um otimizador numerico e entao empregado para obter solucoes localmente otimas. Este artigo tambem descreve sucintamente a funcionalidade e a implementacao de um pacote computacional de codigo aberto escrito em C++ chamado PSOPT. Tal pacote emprega metodos de discretizacao pseudo-spectrais para resolver problemas de controle otimo com multiplas fase. O PSOPT permite a utilizacao de metodos de Legendre ou Chebyshev, e possui caractersticas uteis tais como diferenciacao automatica, deteccao de esparsidade e escalonamento automatico. O uso de metodos pseudo-espectrais e ilustrado em dois problemas retirados da literatura de controle otimo computacional.

Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.