Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

Iterative substructuring Domain Decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. It is less known that classical overlapping DD methods can also be formulated in substructured form, i.e., as iterative methods acting on variables defined exclusively on the interfaces of the overlapping domain decomposition. We call such formulations substructured domain decomposition methods. We introduce here a substructured version of Restricted Additive Schwarz (RAS) which we call SRAS. We show that RAS and SRAS are equivalent when used as iterative solvers, as they produce the same iterates, while they are substantially different when used as preconditioners for GMRES. We link the volume and substructured Krylov spaces and show that the iterates are different by deriving the least squares problems solved at each GMRES iteration. When used as iterative solvers, SRAS presents computational advantages over RAS, as it avoids computations with matrices and vectors at the volume level. When used as preconditioners, SRAS has the further advantage of allowing GMRES to store smaller vectors and perform orthogonalization in a lower dimensional space. We then consider nonlinear problems, and we introduce SRASPEN (Substructured Restricted Additive Schwarz Preconditioned Exact Newton), where SRAS is used as a preconditioner for Newton’s method. In contrast to the linear case, we prove that Newton’s method applied to the preconditioned volume and substructured formulation produces the same iterates in the nonlinear case. Next, we introduce two-level versions of nonlinear SRAS and SRASPEN. Finally, we validate our theoretical results with numerical experiments.

     

DNA-binding studies of mixed ligand cobalt(III) complexes

The DNA binding characteristics of mixed ligand complexes of the type [Co(en)₂(L)]Br₃ where en = N,N′-ethylenediamine and L = 1,10-phenanthroline (phen), 2,2′-bipyridine (bpy), 1,10-phenanthroline-5,6-dione (phendione), dipyrido[3,2-a:2′,3′-c]phenazine (dppz) have been investigated by absorption titration, competitive binding fluorescence spectroscopy and viscosity measurements. The order of intercalative ability of the coordinated ligands is dppz > phen > phendione > bpy in this series of complexes.     

Multipole plasmon resonances of submicron silver particles

Single crystal, silver particles of 215 +/- 10 nm size were synthesized in solution using the hydrogen reduction method and were characterized by UV-visible extinction spectroscopy and electron microscopy. The extinction spectra reveal the presence of higher order multipoles of the plasmon resonance, such as quadrupole, octupole, and hexadecapole, in addition to the dipole. The formation of higher order multipoles was continuously monitored during the particles growth. Mie extinction calculations were performed and are in good agreement with the measured extinction spectra. The frequency shift of all plasmon modes was measured as a function of the refractive index of the surrounding dielectric medium.     

Polarographic reduction behaviour of copper in the presence of 1-amino-3-methoxypropane and 2-dimethylaminoethanol

1-Amino-3-methoxypropane (3MPA) and 2-dimethylaminoethanol (DMAE) are potential volatile amines for boiler water treatment and were investigated for their complexation behaviour with copper. Their pK_b values were 3.67 and 4.52 at 25°C and they formed coloured complexes with absorption in the region of 644 and 510 nm, respectively. In the pH range 10–11, the Cu-3MPA complex exhibited stepwise reduction and [Cu(3MPA)₂]⁺ was identified, with a stability constant of 10^9.52. In the pH range 8–10.5, the Cu-DMAE complex exhibited 2e^? reduction and the species [Cu(DMAE)₂(OH)₂] was identified, with a stability constant of 10^20.39. A correlation between visible and ESR spectra and reduction behaviour was established.     

Bis-amino methylation for the synthesis of spiro-fused piperidines using iron(III) trifluroacetate in aqueous micellar medium

An environmentally benign, multicomponent integrated chemical process has been developed for the synthesis of 3,5-dispirosubstituted piperidines by cyclo-condensation reaction of amines, formaldehyde, and dimedone using iron(III) trifluroacetate [Fe(F₃CCO₂)₃] Lewis acid in aqueous micellar medium at ambient temperature (25–30 °C). The heterogeneous solid acid catalyst conveniently promotes this double amino methylation reaction in which six molecules condense in one pot to form six new covalent bonds. The synthesized 3,5-dispirosubstituted piperidines have been screened for their in vitro antibacterial activity using agar well method. Many of these compounds showed satisfactory antibacterial activity as compared to standard drugs against all the bacteria tested.     

Trifluoroethanol and liquid-assisted grinding method: a green catalytic access for multicomponent synthesis

Research on Chemical Intermediates - An efficient and versatile mechanochemical route for the synthesis of chromene and isoindolo[2,1-a]quinazoline scaffolds has been developed via a simple mortar...