Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive Finite Element simulations in which we use preconditioned Conjugate Gradient solvers based on domain-decomposition. The load balancing is designed to maintain good partition aspect ratio and we show that cut size is not always the appropriate measure in load balancing. Furthermore, we attempt to answer the question why the aspect ratio of partitions plays an important role for certain solvers. We define and rate different kinds of aspect ratio and present a new center-based partitioning method of calculating the initial distribution which implicitly optimizes this measure. During the adaptive simulation, the load balancer calculates a balancing flow using different versions of the diffusion algorithm and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. Experimental results for Bramble's preconditioner and comparisons to state-of-the-art load balancers show the benefits of the construction.

R-matrix-Floquet theory of multiphoton processes:VIII. A linear equations method

A new linear equations method for calculating the R-matrix, which arises in the R-matrix-Floquet theory of multiphoton processes, is introduced. This method replaces the diagonalization of the Floquet Hamiltonian matrix by the solution of a set of linear simultaneous equations which are solved, in the present work, by the conjugate gradient method. This approach uses considerably less computer memory and can be readily ported onto parallel computers. It will thus enable much larger problems of current interest to be treated. This new method is tested by applying it to three-photon ionization of helium at frequencies where double resonances with a bound state and autoionizing states are important. Finally, an alternative linear equations method, which avoids the explicit calculation of the R-matrix by incorporating the boundary conditions directly, is described in an appendix.

Evaluating Asymmetric Multicore Systems-on-Chip using Iso-Metrics

The end of Dennard scaling has pushed power consumption into a first order concern for current systems, on par with performance. As a result, near-threshold voltage computing (NTVC) has been proposed as a potential means to tackle the limited cooling capacity of CMOS technology. Hardware operating in NTV consumes significantly less power, at the cost of lower frequency, and thus reduced performance, as well as increased error rates. In this paper, we investigate if a low-power systems-on-chip, consisting of ARM's asymmetric big.LITTLE technology, can be an alternative to conventional high performance multicore processors in terms of power/energy in an unreliable scenario. For our study, we use the Conjugate Gradient solver, an algorithm representative of the computations performed by a large range of scientific and engineering codes.

Performance and Fault Tolerance of Preconditioned Iterative Solvers on Low-Power ARM Architectures

As the complexity of computing systems grows, reliability and energy are two crucial challenges asking for holistic solutions. In this paper, we investigate the interplay among concurrency, power dissipation, energy consumption and voltage-frequency scaling for a key numerical kernel for the solution of sparse linear systems. Concretely, we leverage a task-parallel implementation of the Conjugate Gradient method, equipped with an state-of-the-art pre-conditioner embedded in the ILUPACK software, and target a low-power multi core processor from ARM.In addition, we perform a theoretical analysis on the impact of a technique like Near Threshold Voltage Computing (NTVC) from the points of view of increased hardware concurrency and error rate.

Histogram filtering as a tool in variational Monte Carlo optimization

Optimization of wave functions in quantum Monte Carlo is a difficult task because the statistical uncertainty inherent to the technique makes the absolute determination of the global minimum difficult. To optimize these wave functions we generate a large number of possible minima using many independently generated Monte Carlo ensembles and perform a conjugate gradient optimization. Then we construct histograms of the resulting nominally optimal parameter sets and "filter" them to identify which parameter sets "go together" to generate a local minimum. We follow with correlated-sampling verification runs to find the global minimum. We illustrate this technique for variance and variational energy optimization for a variety of wave functions for small systellls. For such optimized wave functions we calculate the variational energy and variance as well as various non-differential properties. The optimizations are either on par with or superior to determinations in the literature. Furthermore, we show that this technique is sufficiently robust that for molecules one may determine the optimal geometry at tIle same time as one optimizes the variational energy.

Offline Handwritten Malayalam Character Recognition Based on Chain Code Histogram

Optical Character Recognition plays an important role in Digital Image Processing and Pattern Recognition. Even though ambient study had been performed on foreign languages like Chinese and Japanese, effort on Indian script is still immature. OCR in Malayalam language is more complex as it is enriched with largest number of characters among all Indian languages. The challenge of recognition of characters is even high in handwritten domain, due to the varying writing style of each individual. In this paper we propose a system for recognition of offline handwritten Malayalam vowels. The proposed method uses Chain code and Image Centroid for the purpose of extracting features and a two layer feed forward network with scaled conjugate gradient for classification

Approximate factorization constraint preconditioners for saddle-point matrices

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions.

A benchmark method for global optimization problems in structure determination from powder diffraction data

Quasi-Newton-Raphson minimization and conjugate gradient minimization have been used to solve the crystal structures of famotidine form B and capsaicin from X-ray powder diffraction data and characterize the chi(2) agreement surfaces. One million quasi-Newton-Raphson minimizations found the famotidine global minimum with a frequency of ca 1 in 5000 and the capsaicin global minimum with a frequency of ca 1 in 10 000. These results, which are corroborated by conjugate gradient minimization, demonstrate the existence of numerous pathways from some of the highest points on these chi(2) agreement surfaces to the respective global minima, which are passable using only downhill moves. This important observation has significant ramifications for the development of improved structure determination algorithms.

Simple adaptive momentum: new algorithm for training multilayer perceptrons

The speed of convergence while training is an important consideration in the use of neural nets. The authors outline a new training algorithm which reduces both the number of iterations and training time required for convergence of multilayer perceptrons, compared to standard back-propagation and conjugate gradient descent algorithms.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

Improving ultimate convergence of an augmented Lagrangian method

Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the comparative success of interior-point Newtonian algorithms, which are asymptotically faster. In this research, a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its `pure` counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:http://www.ime.usp.br/similar to egbirgin/tango/.

Crystallization, preliminary X-ray analysis and Patterson search of a new aspartic protease isolated from human urine

Aspartic protease (EC 3.4.23) make up a widely distributed class of enzymes in animals, plants, microbes and, viruses. In animals these enzymes perform diverse functions, which range from digestion of food proteins to very specific regulatory roles. In contrast the information about the well-characterized aspartic proteases, very little is known about the corresponding enzyme in urine. A new aspartic protease isolated from human urine has been crystallized and X-ray diffraction data collected to 2.45 Angstrom resolution using a synchrotron radiation source. Crystals belong to the space group P2(1)2(1)2(1) the cell parameters obtained were a=50.99, b=75.56 and c=89.90 Angstrom. Preliminary analysis revealed the presence of one molecule in the asymmetric unit. The structure was determined using the molecular replacement technique and is currently being refined using simulated annealing and conjugate gradient protocols.

A fast electric load forecasting using neural networks

The objective of this work is the development of a methodology for electric load forecasting based on a neural network. Here, it is used Backpropagation algorithm with an adaptive process based on fuzzy logic. This methodology results in fast training, when compared to the conventional formulation of Backpropagation algorithm. Results are presented using data from a Brazilian Electric Company and the performance is very good for the proposal objective.

Otimização vetorial e técnicas de mistura de herbicidas aplicadas ao controle de plantas daninhas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Um método previsor-corretor primal-dual de pontos interiores barreira logarítmica modificada, com estratégias de convergência global e de ajuste cúbico, para problemas de programação não-linear e não-convexa

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)