Numerical ‘health check’ for scientific codes: the CADNA approach

Scientific computation has unavoidable approximations built into its very fabric. One important source of error that is difficult to detect and control is round-off error propagation which originates from the use of finite precision arithmetic. We propose that there is a need to perform regular numerical `health checks' on scientific codes in order to detect the cancerous effect of round-off error propagation. This is particularly important in scientific codes that are built on legacy software. We advocate the use of the CADNA library as a suitable numerical screening tool. We present a case study to illustrate the practical use of CADNA in scientific codes that are of interest to the Computer Physics Communications readership. In doing so we hope to stimulate a greater awareness of round-off error propagation and present a practical means by which it can be analyzed and managed.

Iron abundances from optical FeIII absorption lines in B-type stellar spectra

The role of optical FeIII absorption lines in B-type stars as iron abundance diagnostics is considered. To date, ultraviolet Fe lines have been widely used in B-type stars, although line blending can severely hinder their diagnostic power. Using optical spectra, covering a wavelength range ~3560-9200Å, a sample of Galactic B-type main-sequence and supergiant stars of spectral types B0.5 to B7 are investigated. A comparison of the observed FeIII spectra of supergiants, and those predicted from the model atmosphere codes TLUSTY [plane-parallel, non-local thermodynamic equilibrium (LTE)], with spectra generated using SYNSPEC (LTE), and CMFGEN (spherical, non-LTE), reveal that non-LTE effects appear small. In addition, a sample of main-sequence and supergiant objects, observed with the Fiber-fed Extended Range Optical Spectrograph (FEROS), reveal LTE abundance estimates consistent with the Galactic environment and previous optical studies. Based on the present study, we list a number of FeIII transitions which we recommend for estimating the iron abundance from early B-type stellar spectra.

On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.

2-D R-matrix propagation: A large scale electron scattering simulation dominated by the multiplication of dynamically changing matrices

We examine the computational aspects of propagating a global R-matrix, R, across sub-regions in a 2-D plane. This problem originates in the large scale simulation of electron collisions with atoms and ions at intermediate energies. The propagation is dominated by matrix multiplications which are complicated because of the dynamic nature of R, which changes the designations of its rows and columns and grows in size as the propagation proceeds. The use of PBLAS to solve this problem on distributed memory HPC machines is the main focus of the paper.

Utilisation of ionic liquid solvents for the synthesis of Lily-of-the-Valley fragrance {beta-Lilial (R); 3-(4-t-butylphenyl)-2-methylpropanal}

The Heck arylation of 2-methylprop-2-en- I -ol in ionic liquids and organic solvents is reported using a range of homogeneous and heterogeneous palladium catalysts. Higher activity is observed in the ionic liquid media compared with N-methyl pyrrolidinone and under solventless conditions. The ionic liquid-catalyst system may be recycled easily with little loss in activity, although significant palladium leaching from the heterogeneous catalyst was observed. In the case of Trans-bis(2,3-dihydro-3-methylbenzothiazole-2-ylidene)diiodopalladium (11) reported to be highly active for this transformation, significant induction petiods were observed indicating that nanoparticles may be responsible for the catalysis. Using the ionic liquid Heck reaction, a recyclable synthesis for the fragrance beta-Lilial((R)) has been developed. (c) 2004 Elsevier B.V. All rights reserved.

Synthesis of 3-(4-tert-butylphenyl)-2-propen-1-one, a precursor to Lilial (R), via an aldol condensation in an ionic liquid

An efficient synthesis of a precursor to Lilial(R), based on an aldol condensation in an ionic liquid, is described, utilising piperidine as the base catalyst. The yields obtained with this methodology are significantly increased in comparison with those reported in organic solvents to date. In the ionic liquid, the self-aldol condensation of propanal is suppressed and leads to an increased selectivity with respect to the cross-aldol condensation product without the need to use an excess of 4-tert-butylbenzaldehyde to obtain high selectivities.