Strict bounding of quantities of interest in computations based on domain decomposition

This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution of reference and adjoint problems : on the one hand the discretization error due to the finite element method and on the other hand the algebraic error due to the use of the iterative solver. Beside practical considerations on the parallel computation of the bounds, it is shown that the interface conformity can be slightly relaxed so that local enrichment or refinement are possible in the subdomains bearing singularities or quantities of interest which simplifies the improvement of the estimation. Academic assessments are given on 2D static linear mechanic problems.Comment: Computer Methods in Applied Mechanics and Engineering, Elsevier, 2015, online previe

A strict error bound with separated contributions of the discretization and of the iterative solver in non-overlapping domain decomposition methods

This paper deals with the estimation of the distance between the solution of a static linear mechanic problem and its approximation by the finite element method solved with a non-overlapping domain decomposition method (FETI or BDD). We propose a new strict upper bound of the error which separates the contribution of the iterative solver and the contribution of the discretization. Numerical assessments show that the bound is sharp and enables us to define an objective stopping criterion for the iterative solverComment: Computer Methods in Applied Mechanics and Engineering (2013) onlin

Strict lower bounds with separation of sources of error in non-overlapping domain decomposition methods

This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate the algebraic error (due to the use of a DD iterative solver) from the discretization error (due to the FE), which enables the steering of the iterative solver by the discretization error. These lower bounds are also used to improve the goal-oriented error estimation in a substructured context. Assessments on 2D static linear mechanic problems illustrate the relevance of the separation of sources of error and the lower bounds' independence from the substructuring. We also steer the iterative solver by an objective of precision on a quantity of interest. This strategy consists in a sequence of solvings and takes advantage of adaptive remeshing and recycling of search directions.Comment: International Journal for Numerical Methods in Engineering, Wiley, 201

Amorphous calcium phosphates: synthesis, properties and uses in biomaterials

This review paper on amorphous calcium phosphates (ACPs) provides an update on several aspects of these compounds which have led to many studies and some controversy since the 1970s, particularly because of the lack of irrefutable proof of the occurrence of an ACP phase in mineralised tissues of vertebrates. The various synthesis routes of ACPs with different compositions are reported and the techniques used to characterise this phase are reviewed. We focus on the various physico-chemical properties of ACPs, especially the reactivity in aqueous media, which have been exploited to prepare bioactive bone substitutes, particularly in the form of coatings and cements for orthopaedic applications and composites for dental application

Improved recovery of admissible stress in domain decomposition methods - application to heterogeneous structures and new error bounds for FETI-DP

This paper investigates the question of the building of admissible stress field in a substructured context. More precisely we analyze the special role played by multiple points. This study leads to (1) an improved recovery of the stress field, (2) an opportunity to minimize the estimator in the case of heterogeneous structures (in the parallel and sequential case), (3) a procedure to build admissible fields for FETI-DP and BDDC methods leading to an error bound which separates the contributions of the solver and of the discretization

Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems

This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature, we present a procedure based on a selection of relevant approximations of the eigenspaces for extracting, selecting and reusing information from the Krylov subspaces generated by previous solutions in order to accelerate the current iteration. Assessments of the method are proposed in the cases of both linear and nonlinear structural problems.Comment: International Journal for Numerical Methods in Engineering (2013) 24 page

Formation and evolution of hydrated surface layers of apatites

Nanocrystalline apatites exhibit a very fragile structured hydrated surface layer which is only observed in aqueous media. This surface layer contains mobile ionic species which can be easily exchanged with ions from the surrounding fluids. Although the precise structure of this surface layer is still unknown, it presents very specific spectroscopic characteristics. The structure of the hydrated surface layer depends on the constitutive mineral ions: ion exchanges of HPO42- ions by CO32- ions or of Ca2+ by Mg2+ ions result in a de-structuration of the hydrated layer and modifies its spectroscopic characteristics. However, the original structure can be retrieved by reverse exchange reaction. These alterations do not seem to affect the apatitic lattice. Stoichiometric apatite also shows HPO42- on their surface due to a surface hydrolysis after contact with aqueous solutions. Ion exchange is also observed and the environments of the surface carbonate ions seem analogous to that observed in nanocrystalline apatites. The formation of a hydrated layer in aqueous media appears to be a property common to apatites which has to be taken into account in their reactivity and biological behavior

Chemical Diversity of Apatites

Apatites can accommodate a large number of vacancies and afford multiple ionic substitutions determining their reactivity and biological properties. Unlike other biominerals they offer a unique adaptability to various biological functions. The diversity of apatites is essentially related to their structure and to their mode of formation. Special charge compensation mechanisms allow molecular insertions and ion substitutions and determine to some extent their solubility behaviour. Apatite formation at physiological pH involves a structured surface hydrated layer nourishing the development of apatite domains. This surface layer contains relatively mobile and exchangeable ions, and is mainly responsible for the surface properties of apatite crystals from a chemical (dissolution properties, ion exchange ability, ion insertions, molecule adsorption and insertions) and a physical (surface charge, interfacial energy) point of view. These characteristics are used by living organisms and can also be exploited in material science