An interior–exterior Schwarz algorithm and its convergenceUn algorithme de Schwarz intérieur–extérieur et sa convergence

In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926.     

Addendum and Corrigendum to "Local Saturation of Conservative Operators'

In this note we make a correction in the paper [1] by two of the authors. Specifically we modify an auxiliary localization result and prove that the applications to the saturation theory of some outstanding conservative operators remain valid. Moreover, we enrich a corollary dealing with the well-known Szász-Mirakjan operators. This revised version was published online in June 2006 with corrections to the Cover Date.     

A nodal coupling of finite and boundary elements

This article presents and analyzes a simple method for the exterior Laplace equation through the coupling of finite and boundary element methods. The main novelty is the use of a smooth parametric artificial boundary where boundary elements fit without effort together with a straight approximate triangulation in the bounded area, with the coupling done only in nodes. A numerically integrated version of the algorithm is also analyzed. Finally, an isoparametric variant with higher order is proposed. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 555–570, 2003     

Relaxing the hypotheses of Bielak–MacCamy’s BEM–FEM coupling

In this paper we show that the quasi-symmetric coupling of finite and boundary elements of Bielak and MacCamy can be freed of two very restricting hypotheses that appeared in the original paper: the coupling boundary can be taken polygonal/polyhedral and coupling can be done using the normal stress instead of the pseudostress. We will do this by first considering a model problem associated to the Yukawa equation, where we prove how compactness arguments can be avoided to show stability of Galerkin discretizations of a coupled system in the style of Bielak–MacCamy’s. We also show how discretization properties are robust in the continuation parameter that appears in the formulation. This analysis is carried out using a new and very simplified proof of the ellipticity of the Johnson–Nédélec BEM–FEM coupling operator. Finally, we show how to apply the techniques that we have fully developed in the model problem to the linear elasticity system.     

Asymptotic properties of some triangulations of the sphere

In this paper we analyse a method for triangulating the sphere originally proposed by Baumgardner and Frederickson in 1985. The method is essentially a refinement procedure for arbitrary spherical triangles that fit into a hemisphere. Refinement is carried out by dividing each triangle into four by introducing the midpoints of the edges as new vertices and connecting them in the usual ‘red’ way. We show that this process can be described by a sequence of piecewise smooth mappings from a reference triangle onto the spherical triangle. We then prove that the whole sequence of mappings is uniformly bi-Lipschitz and converges uniformly to a non-smooth parameterization of the spherical triangle, recovering the Baumgardner and Frederickson spherical barycentric coordinates. We also prove that the sequence of triangulations is quasi-uniform, that is, areas of triangles and lengths of the edges are roughly the same at each refinement level. Some numerical experiments confirm the theoretical results.     

Convergence analysis of a high-order Nyström integral-equation method for surface scattering problems

In this paper we present a convergence analysis for the Nyström method proposed in [J Comput Phys 169 (1):80–110, 2001] for the solution of the combined boundary integral equation formulations of sound-soft acoustic scattering problems in three-dimensional space. This fast and efficient scheme combines FFT techniques and a polar change of variables that cancels out the kernel singularity. We establish the stability of the algorithms in the $L^2$ norm and we derive convergence estimates in both the $L^2$ and $L^\infty $ norms. In particular, our analysis establishes theoretically the previously observed super-algebraic convergence of the method in cases in which the right-hand side is smooth.     

Excited state dynamics in recombinant water-soluble chlorophyll proteins (WSCP) from cauliflower investigated by transient fluorescence spectroscopy

The present study describes the fluorescence emission properties of recombinant water-soluble chlorophyll (Chl) protein (WSCP) complexes reconstituted with either Chl a or Chl b alone (Chl a only or Chl b only WSCP, respectively) or mixtures of both pigments at different stoichiometrical ratios. Detailed investigations were performed with time and space correlated ps fluorescence spectroscopy within the temperature range from 10 to 295 K. The following points were found: (a) The emission spectra at room temperature (295 K) are well characterized by bands with a dominating Lorentzian profile broadened due to phonon scattering and peak positions located at 677, 684 and 693 nm in the case of Chl a only WSCP and at 665, 675 and 689 nm for Chl b only WSCP. In addition, all spectra contain minor bands in the longer wavelength region. (b) The emission spectra at 10 K of samples suspended in buffer containing 50% glycerol are dominated by bands peaking at 668 nm for Chl b only WSCP and at 685 nm for Chl a only WSCP and samples reconstituted with mixtures of Chl a and Chl b. (c) At 10 K and in buffer with 50% glycerol the decay kinetics of WSCP samples with Chl a only are dominated by a component with a time constant of 6.2 (+/-0.2) ns at 685 nm while those of WSCP containing mixtures of Chl a and Chl b are characterized by a slightly shorter value of 6.0 (+/-0.2) ns. WSCP containing Chl b only exhibits a distinctly longer value of 7.0 (+/-0.3) ns at an emission wavelength of 668 nm. (d) The decay associated emission spectra at 10 K of all samples exhibit at least 3 decay components with time constants of 80-120 ps, 2-4 ns and 6-7 ns in 50% glycerol. These results are consistently described within the framework of our previously presented model (J. Phys. Chem. B 2007, 111, No. 46, 13325; J. Phys. Chem. B 2007, 111, No. 35, 10487) , for the structural motifs of chlorophyll binding to the tetrameric protein matrix of WSCP. It is shown that formation of strongly coupled open sandwich dimers does not lead to quenching of 1Chl a* or 1Chl b*.     

Superbulky metallocene complexes of the heavier alkaline-earth metals strontium and barium

Superbulky sandwich complexes with the cyclopentadienyl ligand (4-nBu-C(6)H(4))(5)Cp (abbreviated here as Cp(BIG)) have been prepared by reaction of Cp(BIG)H with benzylic strontium or barium reagents. Both metallocenes have been structurally characterized by single crystal X-ray diffraction. Even for the larger metallocene (Cp(BIG))(2)Ba a highly symmetric sandwich complex with parallel Cp rings was isolated (Cp(center)-Ba = 2.667(1) A). Both structures show evidence for a C-HC(pi) network between the Cp ligands. These attractive forces induce an inward out-of-plane bending of the aryl substituents (Sr 3.4(2) degrees ; Ba 5.3(2) degrees ). A linear correlation between this bending angle and metal size has been found.     

Full collocation methods for some boundary integral equations

In this paper we propose a fully discretized version of the collocation method applied to integral equations of the first kind with logarithmic kernel. After a stability and convergence analysis is given, we prove the existence of an asymptotic expansion of the error, which justifies the use of Richardson extrapolation. We further show how these expansions can be translated to a new expansion of potentials calculated with the numerical solution of a boundary integral equation such as those treated before. Some numerical experiments, confirming our theoretical results, are given. This revised version was published online in August 2006 with corrections to the Cover Date.     

Symmetric boundary integral formulations for Helmholtz transmission problems

In this work we propose and analyze numerical methods for the approximation of the solution of Helmholtz transmission problems in two or three dimensions. This kind of problems arises in many applications related to scattering of acoustic, thermal and electromagnetic waves. Formulations based on boundary integral methods are powerful tools to deal with transmission problems in unbounded media. Different formulations using boundary integral equations can be found in the literature. We propose here new symmetric formulations based on a paper by Martin Costabel and Ernst P. Stephan (1985), that uses the Calderón projector for the interior and exterior problems to develop closed expressions for the interior and exterior Dirichlet-to-Neumann operators. These operators are then matched to obtain an integral system that is equivalent to the Helmholtz transmission problem and uses Cauchy data on the transmission boundary as unknowns. We show how to simplify the aspect and analysis of the method by employing an additional mortar unknown with respect to the ones used in the original paper, writing it in an appropriate way to devise Krylov type iterations based on the separate Dirichlet-to-Neumann operators.