Telescopic hybrid fast solver for 3D elliptic problems with point singularities

This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver

Quasi-optimal elimination trees for 2D grids with singularities

We construct quasi-optimal elimination trees for 2D finite element meshes with singularities.These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination process model the execution of the multifrontal algorithms in serial and in parallel shared-memory executions. Since the meshes considered are a subspace of all possible mesh partitions, we call these minimizers quasi-optimal.We minimize the cost functionals using dynamic programming. Finding these minimizers is more computationally expensive than solving the original algebraic system. Nevertheless, from the insights provided by the analysis of the dynamic programming minima, we propose a heuristic construction of the elimination trees that has cost O(log(Ne log(Ne)), where N e is the number of elements in the mesh.We show that this heuristic ordering has similar computational cost to the quasi-optimal elimination trees found with dynamic programming and outperforms state-of-the-art alternatives in our numerical experiments

Orofacial manifestations in outpatients with anorexia nervosa and bulimia nervosa focusing on the vomiting behavior

Objective: This case-control study aims to evaluate the oral health status and orofacial problems in a group of outpatients with eating disorders (ED)—either anorexia nervosa (AN) or bulimia nervosa (BN)—further focusing on the influence of vomit. Materials and methods: Fifty-five women outpatients with AN or BN diagnosis were invited to participate, of which 33 agreed. ED outpatients and matched controls were submitted to a questionnaire and clinical oral examination. Results: Multivariate analysis identified a significantly higher incidence of teeth-related complications (i.e., tooth decay, dental erosion, and self-reported dentin hypersensitivity), periodontal disease, salivary alterations (i.e., hyposalivation and xerostomia), and oral mucosa-related complications in ED outpatients. Dental erosion, self-reported dentin hypersensitivity, hyposalivation, xerostomia, and angular cheilitis were found to be highly correlated with the vomiting behavior. Conclusions: ED outpatients were found to present a higher incidence of oral-related complications and an inferior oral health status, compared to gender- and age-matched controls. Alterations verified within outpatients were acknowledged to be quite similar to those previously reported within inpatients, in both of nature and severity, thus sustaining that the cranio-maxillofacial region is significantly affected by ED, even in the early/milder forms of the condition, as expectedly verified within outpatients.The work was supported by the Faculty of Dental Medicine, U. Porto

Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids

The hp-adaptive Finite Element Method (hp-FEM) generates a sequence of adaptive grids with different polynomial orders of approximation and element sizes. The hp-FEM delivers exponential convergence of the numerical error with respect to the mesh size. In this paper, we propose a heuristic algorithm to construct element partition trees. The trees can be transformed directly into the orderings, which control the execution of the multi-frontal direct solvers during the hp refined finite element method. In particular, the orderings determine the number of floating point operations performed by the solver. Thus, the quality of the orderings obtained from the element partition trees is important for good performance of the solver. Our heuristic algorithm has been implemented in 3D and tested on a sequence of hp-refined meshes. We compare the quality of the orderings found by the heuristic algorithm to those generated by alternative state-of-the-art algorithms. We show 50% reduction in flops number and execution time