A two-level additive Schwarz preconditioner for nonconforming plate elements

Summary. A two-level additive Schwarz preconditioner is developed for the systems resulting from the discretizations of the plate bending problem by the Morley finite element, the Fraeijs de Veubeke finite element, the Zienkiewicz finite element and the Adini finite element. The condition numbers of the preconditioned systems are shown to be bounded independent of mesh sizes and the number of subdomains in the case of a generous overlap. Received February 1, 1994 / Revised version received October 24, 1994     

A balancing domain decomposition by constraints preconditioner for a weakly over‐penalized symmetric interior penalty method

We develop a balancing domain decomposition by constraints preconditioner for a weakly over‐penalized symmetric interior penalty method for second‐order elliptic problems. We show that the condition number of the preconditioned system satisfies similar estimates as those for conforming finite element methods. Corroborating numerical results are also presented. Copyright © 2012 John Wiley & Sons, Ltd.     

A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations

A new numerical method for computing the divergence-free part of the solution of the time-harmonic Maxwell equations is studied in this paper. It is based on a discretization that uses the locally divergence-free Crouzeix-Raviart nonconforming vector fields and includes a consistency term involving the jumps of the vector fields across element boundaries. Optimal convergence rates (up to an arbitrary positive ) in both the energy norm and the norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.

     

Very large acceleration of the photoinduced electron transfer in a Ru(bpy)3-naphthalene bisimide dyad bridged on the naphthyl core

By linking a naphthalenebisimide (NBI) unit to [Ru(bpy)3]2+ on the naphthyl core the rate of photoinduced Ru-to-NBI electron transfer was 1000-fold increased compared to the case with a conventional linking on the nitrogen.     

Prototypical phosphorus analogues of ethane: general and versatile synthetic approaches to hexaalkylated P-P diphosphonium cations

Versatile alkylation reactions give access to symmetric, homoleptic nonsymmetric, and heteroleptic symmetric hexaalkylated 1,2-diphosphonium derivatives as bottleable salts in high yields. A series of 1,2-diphosphonium salts has been isolated and characterized, representing prototypical phosphorus analogues of ethane. Additionally, the solid-state structures for four derivatives have been determined crystallographically. Nonsymmetrically substituted derivatives of 1,2-diphosphonium cations enable the direct observation of 1J(PAPB) coupling constants for two tetracoordinate phosphorus centers. The synthetic approaches promise access to a vast array of derivatives and will provide means to the systematic development of phosphorus analogues of hydrocarbon chemistry.     

Synthesis of well-defined Locust Bean Gum-graft-copolymers using ambient aqueous atom transfer radical polymerisation

The first atom transfer radical graft copolymerisation at ambient temperature in water from a soluble polysaccharide is demonstrated for a range of monomer types.