Quasi-optimal Schwarz methods for the conforming spectral element discretization

The spectral element method is used to discretize self-adjoint elliptic equations in three-dimensional domains. The domain is decomposed into hexahedral elements, and in each of the elements the discretization space is the set of polynomials of degree N in each variable. A conforming Galerkin formulation is used, the corresponding integrals are computed approximately with Gauss-Lobatto-Legendre (GLL) quadrature rules of order N, and a Lagrange interpolation basis associated with the GLL nodes is used. Fast methods are developed for solving the resulting linear system by the preconditioned conjugate gradient method. The conforming finite element space on the GLL mesh, consisting of piecewise Q(1) or P-1 functions, produces a stiffness matrix K-h that is known to be spectrally equivalent to the spectral element stiffness matrix K-N. K-h is replaced by a preconditioner Kh which is well adapted to parallel computer architectures. The preconditioned operator is then K-N. Techniques for nonregular meshes are developed, which make it possible to estimate the condition number of K-N, where is a standard finite element preconditioner of K-h, based on the GLL mesh. Two finite element-based preconditioners: the wirebasket method of Smith and the overlapping Schwarz algorithm for the spectral element method are given ay examples of the use of these tools. Numerical experiments performed by Pahl are briefly discussed to illustrate the efficiency of these methods in two dimensions.3462482250

Diagonal edge preconditioners in p-version and spectral element methods

Domain decomposition preconditioners fur high-order Galerkin methods in two dimensions are often built Born modules associated with the decomposition of the discrete space into subspaces of functions related to the interior of elements, individual edges, and vertices. The restriction of the original bilinear form to a particular subspace gives rise to a diagonal block of the preconditioner, and the action of its inverse on a vector has to be evaluated in each iteration. Each block can be replaced by a preconditioner in order to decrease the cost. Knowledge of the quality of this local preconditioner can he used directly in a study of the convergence rate of the overall iterative process. The Schur complement of an edge with respect to the variables interior to two adjacent elements is considered. The assembly and factorization of this block matrix are potentially expensive, especially for polynomials of high degree. It is demonstrated that the diagonal preconditioner of one such bIock has a condition number that increases approximately Linearly with the degree of the polynomials. Numerical results demonstrate that the actual condition numbers are relatively small.18261062

Protective effect of topical Cordia verbenacea in a rat periodontitis model: immune-inflammatory, antibacterial and morphometric assays

Background: This study evaluated the effects of C. verbenacea essential oil topically administered in a rat periodontitis model. Methods: Periodontitis was induced on rats in one of the mandibular first molars assigned to receive a ligature. Animals were randomly divided into two groups: a) non-treatment group (NT) (n = 18): animals received 1mL of vehicle; b) C. verbenacea group (C. v.) (n = 18): animals received 5mg/Kg of essential oils isolated from C. verbenacea. The therapies were administered topically 3 times daily for 11 days. Then, the specimens were processed for morphometric analysis of bone loss. The ligatures were used for microbiological assessment of the presence of Aggregatibacter actinomycetemcomitans, Tannerella forsythia and Porphyromonas gingivalis using PCR. The gingival tissue was collected to Elisa assay of interleukin (IL)-1 alpha and IL-10 levels. Results: Bone loss was inhibited by C. verbenacea when compared to the NT group (p < 0.05). A decrease in the levels of IL-1 alpha and increase in the IL-10 amounts was observed in the C. v. group as compared to NT group (p < 0.05). A lower frequency of P. gingivalis was found in C. v. group (p < 0.05). Conclusion: C. verbenacea essential oil topically administered diminished alveolar bone resorption, promoting a positive local imbalance in the pro/anti-inflammatory system and reducing the frequency of detection of P. gingivalis.1

Osteopontin, osteocalcin, and osteoprotegerin expression in human tissue affected by cleft lip and palate

Cleft lip and palate (CLP) is a common congenital anomaly with a complex etiology which has not been elucidated yet. This study investigated whether expression of osteopontin (OPN), osteoprotegerin (OPG), and osteocalcin (OC), which are essential for the normal craniofacial bone remodelling, is not regulated in children with CLP. Alveolar bone tissue samples were obtained from patients with complete bilateral (CB) CLP (n= 14) during corrective plastic surgery and unaffected control subjects (n= 9). OPN, OPG, and OC expression was assessed by immunohistochemistry, and data were analyzed with the Mann-Whitney test. OPN expression was observed only sporadically in the alveolar bone of 3 patients, in contrast to the control group (z= - 2.962; P< 0.003). The number of OPG-positive bone cells varied from occasional to moderate, in contrast to the control group (z= - 2.247; P= 0.025). OC-positive osteocytes were present in moderate to numerous numbers in both patients and controls, with no significant difference between them (z= - 1.356; P< 0.175). The prominent expression of OC characteristic for CBCLP affected hard tissue indicates a high potential of bone mineralization. Few OPG-positive osteocytes in the bone tissue implicate the disregulation of osteoclast differentiation, maturation, and activity, but few OPN-containing cells may prove the common disregulation of bone remodelling during cleft morphopathogenesis.publishersversionPeer reviewe

Development of lyophilized spherical particles of poly(epsilon-caprolactone) and examination of their morphology, cytocompatibility and influence on the formation of reactive oxygen species

A common limitation of using polymeric micro- and nanoparticles in long-term conservation is due to their poor physical and chemical stability. Freeze-drying is one of the most convenient methods that enable further reconstitution of micro- and nanoparticles for therapeutical use. Nevertheless, this process generates various stresses during freezing and desiccation steps. This paper underlines the combined outcomes of freeze drying method and physicochemical solvent/non-solvent approach to design biocompatible poly(epsilon-caprolactone) (PCL) nanospheres and evaluate influence of different cryoprotectants (glucose, saccharose, polyvinyl alcohol or polyglutamic acid) on the outcome of freeze-dried PCL particles. Samples were characterized using Fourier transform infrared spectroscopy (FT-IR). scanning electron microscopy (SEM) and dynamic light scattering method (DLS). In vitro studies used, include MTT assay (3-(4,5-Dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide). testing cytotoxicity as the quality of being toxic to cells, and DCFH-DA assay (2',7'-dichlordihydrofluorescein-diacetate), testing the possible increase in ROS levels. It was found that cryoprotection with 1% glucose solution is an optimal for obtaining uniform, spherical but also biocompatible PCL nanoparticles for biomedical purposes

Impact of supragingival therapy on subgingival microbial profile in smokers versus non-smokers with severe chronic periodontitis

The aim of this study was to assess subgingival microbiological changes in smokers versus non-smokers presenting severe chronic periodontitis after supragingival periodontal therapy (ST).Non-smokers (n=10) and smokers (n=10) presenting at least nine teeth with probing pocket depth (PPD) (&#x2265;5 mm), bleeding on probing (BoP), and no history of periodontal treatment in the last 6 months were selected. Clinical parameters assessed were plaque index (PI), BoP, PPD, relative gingival margin position (rGMP) and relative clinical attachment level (rCAL). Subgingival biofilm was collected before and 21 days after ST. DNA was extracted and the 16S rRNA gene was amplified with the universal primer pair, 27F and 1492R. Amplified genes were cloned, sequenced, and identified by comparison with known 16S rRNA sequences. Statistical analysis was performed by Student&#x0027;s t and Chi-Square tests (&#x03B1;=5%).Clinically, ST promoted a significant reduction in PI and PPD, and gain of rCAL for both groups, with no significant intergroup difference. Microbiologically, at baseline, data analysis demonstrated that smokers harbored a higher proportion of Porphyromonas endodontalis, Bacteroidetes sp., Fusobacterium sp. and Tannerella forsythia and a lower number of cultivated phylotypes (p&#60;0.05). Furthermore, non-smokers featured significant reductions in key phylotypes associated with periodontitis, whereas smokers presented more modest changes.Within the limits of the present study, ST promoted comparable clinical improvements in smokers and non-smokers with severe chronic periodontitis. However, in smokers, ST only slightly affected the subgingival biofilm biodiversity, as compared with non-smokers

Concentração de fluoreto em arroz, feijão e alimentos infantis industrializados

OBJETIVO: Determinar a concentração de fluoreto na refeição brasileira típica (arroz e feijão) e em alimentos infantis industrializados e estimar suas contribuições para fluorose dental. MÉTODOS: Os alimentos foram adquiridos de supermercados das cidades de Piracicaba e Campinas, SP, Brasil. Os alimentos infantis industrializados foram comprados em 2001 e o arroz e feijão em 2003, e imediatamente analisados. Foram analisadas três marcas de arroz, três de feijão e 36 amostras de alimentos infantis divididos em cinco grupos: prontos para o consumo; mingaus; alimentos formulados; leites em pó e outros alimentos. No arroz e feijão, foram determinadas as concentrações de fluoreto nas sementes "in natura" e após cozimento com água destilada ou fluoretada (0,7 ppm). Todas as análises de fluoreto foram feitas com eletrodo específico. Considerou-se 0,07 mg/kg/dia como a dose limite de exposição a fluoreto para risco de fluorose. RESULTADOS: A concentração de fluoreto encontrada nos grãos de arroz e feijão foi baixa. Porém, a concentração aumentou 100-200 vezes após cozimento em água fluoretada e mesmo assim, foi menor que a encontrada em alguns alimentos industrializados. Uma refeição com arroz e feijão preparada com água fluoretada seria responsável por 29% da dose limite de ingestão de fluoreto em termos de fluorose aceitável; a contribuição de alguns alimentos industrializados atingiria 45%. CONCLUSÕES: A alimentação típica brasileira, mesmo preparada com água fluoretada, é mais segura em termos de risco de fluorose dental que alguns alimentos infantis industrializados

Three-dimensional lanthanide-organic frameworks based on di-, tetra-, and hexameric clusters

Three-dimensional lanthanide-organic frameworks formulated as (CH3)2NH2[Ln(pydc)2] · 1/2H2O [Ln3+ ) Eu3+ (1a) or Er3+ (1b); pydc2- corresponds to the diprotonated residue of 2,5-pyridinedicarboxylic acid (H2pydc)], [Er4(OH)4(pydc)4(H2O)3] ·H2O (2), and [PrIII 2PrIV 1.25O(OH)3(pydc)3] (3) have been isolated from typical solvothermal (1a and 1b in N,N-dimethylformamide - DMF) and hydrothermal (2 and 3) syntheses. Materials were characterized in the solid state using single-crystal X-ray diffraction, thermogravimetric analysis, vibrational spectroscopy (FT-IR and FT-Raman), electron microscopy, and CHN elemental analysis. While synthesis in DMF promotes the formation of centrosymmetric dimeric units, which act as building blocks in the construction of anionic ∞ 3{[Ln(pydc)2]-} frameworks having the channels filled by the charge-balancing (CH3)2NH2 + cations generated in situ by the solvolysis of DMF, the use of water as the solvent medium promotes clustering of the lanthanide centers: structures of 2 and 3 contain instead tetrameric [Er4(μ3-OH)4]8+ and hexameric |Pr6(μ3-O)2(μ3-OH)6| clusters which act as the building blocks of the networks, and are bridged by the H2-xpydcx- residues. It is demonstrated that this modular approach is reflected in the topological nature of the materials inducing 4-, 8-, and 14-connected uninodal networks (the nodes being the centers of gravity of the clusters) with topologies identical to those of diamond (family 1), and framework types bct (for 2) and bcu-x (for 3), respectively. The thermogravimetric studies of compound 3 further reveal a significant weight increase between ambient temperature and 450 °C with this being correlated with the uptake of oxygen from the surrounding environment by the praseodymium oxide inorganic core

Schwarz preconditioners for the spectral element discretization of the steady Stokes and Navier-Stokes equations

The Q(N_)Q(N-2) spectral element discretization of the Stokes equation gives rise to an ill-conditioned. indefinite, symmetric linear system for the velocity and pressure degrees of freedom. We propose a domain decomposition method which involves the solution of a low-order global, and several local problems, related to the vertices, edges, and interiors of the subdomains. The original system is reduced to a symmetric equation for the velocity. which can be solved with the conjugate gradient method. We prove that the condition number of the iteration operator is bounded from above by C(1 + log(N))(3/)beta (n), where C is a positive constant independent of the degree N and the number of subdomains, and beta (N) is the inf-sup condition of the pair Q(N-)Q(n-2).We also consider the stationary Navier-Stokes equations;, in each Newton step, a non-symmetric indefinite problem is solved using a Schwarz preconditioner. By using an especially designed low-order global space, and the solution of local problems analogous to those decribed above for the Stokes equation, we are able to present a complete theory for the method. We prove that the number of iterations of the GMRES method, at each Newton step, is bounded from above by C(1 + log(N))(3)/beta (N). The constant C does not depend on the number of subdomains or N. and it does not deteriorate as the Newton iteration proceeds.89230733