A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations

Integration of the subsurface flow equation by finite elements (FE) in space and finite differences (FD) in time requires the repeated solution to sparse symmetric positive definite systems of linear equations. Iterative techniques based on preconditioned conjugate gradients (PCG) are one of the most attractive tool to solve the problem on sequential computers. A present challenge is to make PCG attractive in a parallel computing environment as well. To this aim a key factor is the development of an efficient parallel preconditioner. FSAI (factorized sparse approximate inverse) and enlarged FSAI relying on the approximate inverse of the coefficient matrix appears to be a most promising parallel preconditioner. In the present paper PCG using FSAI, diagonal and pARMS (parallel algebraic recursive multilevel solvers) preconditioners is implemented on the IBM SP4/512 and CLX/768 supercomputers with up to 32 processors to solve underground flow problems of a large size. The results show that FSAI may allow for a parallel relative efficiency larger than 50% on the largest problems with p=32 processors. Moreover, FSAI turns out to be significantly less expensive and more robust than pARMS. Finally, it is shown that for p in the upper range may be much improved if PCG–FSAI is implemented on CLX.     

Ekeland’s principle for vector equilibrium problems

In this paper, the authors deal with bifunctions defined on complete metric spaces and with values in locally convex spaces ordered by closed convex cones. The aim is to provide a vector version of Ekeland’s theorem related to equilibrium problems. To prove this principle, a weak notion of continuity of a vector-valued function is considered, and some of its properties are presented. Via the vector Ekeland’s principle, existence results for vector equilibria are proved in both compact and noncompact domains.     

Properties of ITO films prepared by reactive magnetron sputtering

Indium tin oxide (ITO) thin films were deposited by mid frequency pulsed dual magnetron sputtering using a metallic alloy target with 10 wt.% tin in an atmosphere of argon and oxygen. The aim of the work was to study the interdependence of structural, electrical and optical properties of ITO films deposited in the reactive and transition target mode, respectively. The deposition rate in the transition mode exceeds the deposition rate in the reactive mode by a factor of six, a maximum value of 100 nm·m min⁻¹ could be achieved. This corresponds to a static deposition rate of 200 nm min⁻¹. The lowest electrical resistivity of 1.1·10⁻³ Ω cm was measured at samples deposited in the high oxygen flow range in the transition mode. The samples show a good transparency in the visible range corresponding to extinction coefficients being below 10⁻². X-ray diffraction was used to characterise crystalline structure as well as film stress. ITO films prepared in the transition mode show a slightly preferred orientation in (211) direction, whereas films deposited in the reactive mode are strongly (222) oriented. Compared to undoped In₂O₃ all samples have an enlarged lattice. The lattice strain perpendicular to the surface is about 0.8% and 2.0% for films grown in the transition and the reactive mode, respectively. Deposition in the transition mode introduces a biaxial film stress in the range of −300 MPa, while stress in reactive mode samples is −1500 MPa.     

Highly efficient recycling of a "sandwich" type polyoxometalate oxidation catalyst using solvent resistant nanofiltration

A "sandwich" type polyoxometalate catalyst ([MeN(n-C8H17)3]12[WZn3(ZnW9O34)2]) was very efficiently recycled by nanofiltration with almost quantitative retention, using an alpha-alumina supported mesoporous gamma-alumina membrane.     

Direct aerobic epoxidation of alkenes catalyzed by metal nanoparticles stabilized by the H5PV2Mo10O40 polyoxometalate

Ag and Ru nanoparticles stabilized by H5PV2Mo10O40, prepared by a sequence of redox reactions and supported on alpha-alumina, were effective catalysts for the direct aerobic epoxidation of alkenes in the liquid phase.     

Chiral hydroperoxides as oxygen source in the catalytic stereoselective epoxidation of allylic alcohols by sandwich-type polyoxometalates: control of enantioselectivity through a metal-coordinated template

The epoxidation of allylic alcohols is shown to be efficiently and selectively catalyzed by the oxidatively resistant sandwich-type polyoxometalates, POMs, namely [WZnM(2)(ZnW(9)O(34))(2)](q)(-) [M = OV(IV), Mn(II), Ru(III), Fe(III), Pd(II), Pt(II), Zn(II); q = 10-12], with organic hydroperoxides as oxygen source. Conspicuous is the fact that the nature of the transition metal M in the central ring of polyoxometalate affects significantly the reactivity, chemoselectivity, regioselectivity, and stereoselectivity of the allylic alcohol epoxidation. For the first time, it is demonstrated that the oxovanadium(IV)-substituted POM, namely [ZnW(VO)(2)(ZnW(9)O(34))(2)](12-), is a highly chemoselective, regioselective, and also stereoselective catalyst for the clean epoxidation of allylic alcohols. A high enantioselectivity (er values up to 95:5) has been achieved with [ZnW(VO)(2)(ZnW(9)O(34))(2)](12)(-) and the sterically demanding TADOOL-derived hydroperoxide TADOOH as regenerative chiral oxygen source. Thus, a POM-catalyzed asymmetric epoxidation of excellent catalytic efficiency (up to 42 000 TON) has been made available for the development of sustainable oxidation processes. The high reactivity and selectivity of this unprecedented oxygen-transfer process are mechanistically rationalized in terms of a peroxy-type vanadium(V) template.     

An efficient, catalytic, aerobic, oxidative iodination of arenes using the H5PV2Mo10O40 polyoxometalate as catalyst

Iodination of arenes was carried out by reacting 1 equiv of arene substrate with 0.5 equiv of iodine under an oxygen atmosphere with H5PV2Mo10O40 as oxidation catalyst. The synthesis is an inherently waste-free method for the preparation of iodoarenes.     

Mild, aqueous, aerobic, catalytic oxidation of methane to methanol and acetaldehyde catalyzed by a supported bipyrimidinylplatinum-polyoxometalate hybrid compound

We have demonstrated that a bipyrimidinylplatinum-polyoxometalate, [Pt(Mebipym)Cl2]+[H4PV2Mo10O40]-, supported on silica is an active catalyst for the aerobic oxidation of methane to methanol in water under mild reaction conditions. Further oxidation of methanol yields acetaldehyde. The presence of the polyoxometalate is presumed to allow the facile oxidation of a Pt(II) intermediate to a Pt(IV) intermediate and to aid in the addition of methane to the Pt catalytic center.     

Phenanthroline-polyoxometalate hybrid compounds and the observation of intramolecular charge transfer

A phenanthroline ligand has been covalently modified at the 2 and 9 positions by an aminophenylhexamolybdate substituent. The 1H NMR spectrum indicated a strong electron-withdrawing effect of the hexamolybdate (Mo6O19(2-)) moiety on the phenanthroline ligand. UV-vis and cyclic voltammetry showed extended conjugation of the hybrid phenanthroline-polyoxometalate compound and the possibility of easy oxidation of the extended phenanathroline ligand. Further EPR experiments provided strong evidence for an intramolecular charge-transfer process with the formation of a phenanthroline cation radical and a reduced hexamolybdate.