An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons

In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination of fundamental solutions. The solution is obtained by minimizing a least-squares functional, which we discretize in such a way that a matrix least-squares problem is obtained. We give computable exponential bounds on the rate of convergence of the least-squares functional that are in very good agreement with the observed numerical convergence. Challenging numerical examples, including a nonconvex polygon with several corner singularities, and a cavity domain, are solved to around 10 digits of accuracy with a few seconds of CPU time. The examples are implemented concisely with MPSpack, a MATLAB toolbox for wave computations with nonpolynomial basis functions, developed by the authors. A code example is included.

Sparse space-time boundary element methods for the heat equation

The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(h

An efficient heuristic for total flowtime minimisation in no-wait flowshops

In this paper, we address the problem of scheduling jobs in a no-wait flowshop with the objective of minimising the total completion time. This problem is well-known for being nondeterministic polynomial-time hard, and therefore, most contributions to the topic focus on developing algorithms able to obtain good approximate solutions for the problem in a short CPU time. More specifically, there are various constructive heuristics available for the problem [such as the ones by Rajendran and Chaudhuri (Nav Res Logist 37: 695-705, 1990); Bertolissi (J Mater Process Technol 107: 459-465, 2000), Aldowaisan and Allahverdi (Omega 32: 345-352, 2004) and the Chins heuristic by Fink and Voa (Eur J Operat Res 151: 400-414, 2003)], as well as a successful local search procedure (Pilot-1-Chins). We propose a new constructive heuristic based on an analogy with the two-machine problem in order to select the candidate to be appended in the partial schedule. The myopic behaviour of the heuristic is tempered by exploring the neighbourhood of the so-obtained partial schedules. The computational results indicate that the proposed heuristic outperforms existing ones in terms of quality of the solution obtained and equals the performance of the time-consuming Pilot-1-Chins.

Comparison of BR and QR Eigenvalue Algorithms for Power System Small Signal Stability Analysis

The BR algorithm is a novel and efficient method to find all eigenvalues of upper Hessenberg matrices and has never been applied to eigenanalysis for power system small signal stability. This paper analyzes differences between the BR and the QR algorithms with performance comparison in terms of CPU time based on stopping criteria and storage requirement. The BR algorithm utilizes accelerating strategies to improve its performance when computing eigenvalues of narrowly banded, nearly tridiagonal upper Hessenberg matrices. These strategies significantly reduce the computation time at a reasonable level of precision. Compared with the QR algorithm, the BR algorithm requires fewer iteration steps and less storage space without depriving of appropriate precision in solving eigenvalue problems of large-scale power systems. Numerical examples demonstrate the efficiency of the BR algorithm in pursuing eigenanalysis tasks of 39-, 68-, 115-, 300-, and 600-bus systems. Experiment results suggest that the BR algorithm is a more efficient algorithm for large-scale power system small signal stability eigenanalysis.

Practical parallel coset enumeration

Coset enumeration is a most important procedure for investigating finitely presented groups. We present a practical parallel procedure for coset enumeration on shared memory processors. The shared memory architecture is particularly interesting because such parallel computation is both faster and cheaper. The lower cost comes when the program requires large amounts of memory, and additional CPU's. allow us to lower the time that the expensive memory is being used. Rather than report on a suite of test cases, we take a single, typical case, and analyze the performance factors in-depth. The parallelization is achieved through a master-slave architecture. This results in an interesting phenomenon, whereby the CPU time is divided into a sequential and a parallel portion, and the parallel part demonstrates a speedup that is linear in the number of processors. We describe an early version for which only 40% of the program was parallelized, and we describe how this was modified to achieve 90% parallelization while using 15 slave processors and a master. In the latter case, a sequential time of 158 seconds was reduced to 29 seconds using 15 slaves.

Selecting methods to solve multi-well master equations

There are several competing methods commonly used to solve energy grained master equations describing gas-phase reactive systems. When it comes to selecting an appropriate method for any particular problem, there is little guidance in the literature. In this paper we directly compare several variants of spectral and numerical integration methods from the point of view of computer time required to calculate the solution and the range of temperature and pressure conditions under which the methods are successful. The test case used in the comparison is an important reaction in combustion chemistry and incorporates reversible and irreversible bimolecular reaction steps as well as isomerizations between multiple unimolecular species. While the numerical integration of the ODE with a stiff ODE integrator is not the fastest method overall, it is the fastest method applicable to all conditions.

POST-PROCESSING TECHNIQUES SUITABILITY FOR MESOLEVEL FREE BOUNDARY FLOWS

Reliable flow simulation software is inevitable to determine an optimal injection strategy in Liquid Composite Molding processes. Several methodologies can be implemented into standard software in order to reduce CPU time. Post-processing techniques might be one of them. Post-processing a finite element solution is a well-known procedure, which consists in a recalculation of the originally obtained quantities such that the rate of convergence increases without the need for expensive remeshing techniques. Post-processing is especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly. In previous works influence of smoothness of non-homogeneous Dirichlet condition, imposed on smooth front was examined. However, usually quite a non-smooth boundary is obtained at each time step of the infiltration process due to discretization. Then direct application of post-processing techniques does not improve final results as expected. The new contribution of this paper lies in improvement of the standard methodology. Improved results clearly show that the recalculated flow front is closer to the ”exact” one, is smoother that the previous one and it improves local disturbances of the “exact” solution.

Implementation and comparison of different switching techniques for shunt active power filters

This paper presents a comparison between three switching techniques that can be used in three-phase four-wire Shunt Active Power Filters (SAPFs). The implemented switching techniques are: Periodic-Sampling (PS), Triangular Carrier Pulse-Width Modulation (TC-PWM) and Space Vector PWM (SVPWM). The comparison between them is made in terms of the compensated currents THD%, implementation complexity, necessary CPU time and SAPF efficiency. To perform this comparison are presented and analyzed several experimental results, obtained with a 20 kVA Shunt Active Power Filter prototype, specially developed for this purpose. The control system of the developed SAPF is based in the p-q Theory with a grid synchronization algorithm p-PLL.

Multithreading RTOS processor design

Tese de Doutoramento Plano Doutoral em Engenharia Eletrónica e de Computadores.

Phylogenetic Code in the Cloud - Can it Meet the Expectations?

Cloud computing has recently become very popular, and several bioinformatics applications exist already in that domain. The aim of this article is to analyse a current cloud system with respect to usability, benchmark its performance and compare its user friendliness with a conventional cluster job submission system. Given the current hype on the theme, user expectations are rather high, but current results show that neither the price/performance ratio nor the usage model is very satisfactory for large-scale embarrassingly parallel applications. However, for small to medium scale applications that require CPU time at certain peak times the cloud is a suitable alternative.

Fast docking using the CHARMM force field with EADock DSS.

The prediction of binding modes (BMs) occurring between a small molecule and a target protein of biological interest has become of great importance for drug development. The overwhelming diversity of needs leaves room for docking approaches addressing specific problems. Nowadays, the universe of docking software ranges from fast and user friendly programs to algorithmically flexible and accurate approaches. EADock2 is an example of the latter. Its multiobjective scoring function was designed around the CHARMM22 force field and the FACTS solvation model. However, the major drawback of such a software design lies in its computational cost. EADock dihedral space sampling (DSS) is built on the most efficient features of EADock2, namely its hybrid sampling engine and multiobjective scoring function. Its performance is equivalent to that of EADock2 for drug-like ligands, while the CPU time required has been reduced by several orders of magnitude. This huge improvement was achieved through a combination of several innovative features including an automatic bias of the sampling toward putative binding sites, and a very efficient tree-based DSS algorithm. When the top-scoring prediction is considered, 57% of BMs of a test set of 251 complexes were reproduced within 2 Å RMSD to the crystal structure. Up to 70% were reproduced when considering the five top scoring predictions. The success rate is lower in cross-docking assays but remains comparable with that of the latest version of AutoDock that accounts for the protein flexibility. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011.

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer-set, andthe firm decides the best subset to offer at any given moment to maximize expected revenue. The resultingdynamic program for the firm is intractable and approximated by a deterministic linear programcalled the CDLP which has an exponential number of columns. However, under the choice-set paradigmwhen the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has beenproposed but finding an entering column has been shown to be NP-hard. In this paper, starting with aconcave program formulation based on segment-level consideration sets called SDCP, we add a class ofconstraints called product constraints, that project onto subsets of intersections. In addition we proposea natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methodson the benchmark data sets in the literature. Both the product constraints and the ?SDCP method arevery simple and easy to implement and are applicable to the case of overlapping segment considerationsets. In our computational testing on the benchmark data sets in the literature, SDCP with productconstraints achieves the CDLP value at a fraction of the CPU time taken by column generation and webelieve is a very promising approach for quickly approximating CDLP when segment consideration setsoverlap and the consideration sets themselves are relatively small.

Heterogeneity and event dependence in the analysis of sickness absence

Sickness absence (SA) is an important social, economic and public health issue. Identifying and understanding the determinants, whether biological, regulatory or, health services-related, of variability in SA duration is essential for better management of SA. The conditional frailty model (CFM) is useful when repeated SA events occur within the same individual, as it allows simultaneous analysis of event dependence and heterogeneity due to unknown, unmeasured, or unmeasurable factors. However, its use may encounter computational limitations when applied to very large data sets, as may frequently occur in the analysis of SA duration. To overcome the computational issue, we propose a Poisson-based conditional frailty model (CFPM) for repeated SA events that accounts for both event dependence and heterogeneity. To demonstrate the usefulness of the model proposed in the SA duration context, we used data from all non-work-related SA episodes that occurred in Catalonia (Spain) in 2007, initiated by either a diagnosis of neoplasm or mental and behavioral disorders. As expected, the CFPM results were very similar to those of the CFM for both diagnosis groups. The CPU time for the CFPM was substantially shorter than the CFM. The CFPM is an suitable alternative to the CFM in survival analysis with recurrent events,especially with large databases.

The role of van der Waals interactions in the case of H2 adsorption on ruthenium (0001) surface

Computational material science with the Density Functional Theory (DFT) has recently gained a method for describing, for the first time the non local bonding i.e., van der Waals (vdW) bonding. The newly proposed van der Waals-Density Functional (vdW-DF) is employed here to address the role of non local interactions in the case of H2 adsorption on Ru(0001) surface. The later vdW-DF2 implementation with the DFT code VASP (Vienna Ab-initio Simulation Package) is used in this study. The motivation for studying H2 adsorption on ruthenium surface arose from the interest to hydrogenation processes. Potential energy surface (PES) plots are created for adsorption sites top, bridge, fcc and hcp, employing the vdW-DF2 functional. The vdW-DF yields 0.1 eV - 0.2 eV higher barriers for the dissociation of the H2 molecule; the vdW-DF seems to bind the H2 molecule more tightly together. Furthermore, at the top site, which is found to be the most reactive, the vdW functional suggests no entrance barrier or in any case smaller than 0.05 eV, whereas the corresponding calculation without the vdW-DF does. Ruthenium and H2 are found to have the opposite behaviors with the vdW-DF; Ru lattice constants are overestimated while H2 bond length is shorter. Also evaluation of the CPU time demand of the vdW-DF2 is done from the PES data. From top to fcc sites the vdW-DF computational time demand is larger by 4.77 % to 20.09 %, while at the hcp site it is slightly smaller. Also the behavior of a few exchange correlation functionals is investigated along addressing the role of vdW-DF. Behavior of the different functionals is not consistent between the Ru lattice constants and H2 bond lengths. It is thus difficult to determine the quality of a particular exchange correlation functional by comparing equilibrium separations of the different elements. By comparing PESs it would be computationally highly consuming.

Calculation of nondifferential properties for atomic ground states /

A new method for sampling the exact (within the nodal error) ground state distribution and nondiflPerential properties of multielectron systems is developed and applied to firstrow atoms. Calculated properties are the distribution moments and the electronic density at the nucleus (the 6 operator). For this purpose, new simple trial functions are developed and optimized. First, using Hydrogen as a test case, we demonstrate the accuracy of our algorithm and its sensitivity to error in the trial function. Applications to first row atoms are then described. We obtain results which are more satisfactory than the ones obtained previously using Monte Carlo methods, despite the relative crudeness of our trial functions. Also, a comparison is made with results of highly accurate post-Hartree Fock calculations, thereby illuminating the nodal error in our estimates. Taking into account the CPU time spent, our results, particularly for the 8 operator, have a relatively large variance. Several ways of improving the eflSciency together with some extensions of the algorithm are suggested.