Additional CPU Time Research Articles

On the Implementation of a Preconditioned Riccati Recursion based Primal-Dual Interior-Point Algorithm for Input Constrained Optimal Control Problems⋆

We present a preconditioned interior-point algorithm tailored for input constrained quadratic programmings (QPs) arising in optimal control problems (OCPs). The implicit approach to OCPs results in large sparse QPs, which we utilized by a tailored Riccati recursion algorithm. The Riccati recursion algorithm requires the solution of a set of small dense linear sub-systems of equations. The proposed preconditioner is an easily invertible diagonal matrix, which we apply in every linear sub-system of equations. We solve a target tracking OCP for a linearized modified quadruple tank system in Matlab. The computational results indicate that ill-conditioning in the sub-systems are reduced and that the additional CPU time for preconditioning is negligible. Additionally, the paper presents a detailed description of the proposed algorithm and serves as an implementation guide for the algorithm.

Divergence-free turbulence inflow conditions for large-eddy simulations with incompressible flow solvers

Synthetic turbulence for inflow conditions formulated on a 2-D plane generally produces unphysically large pressure fluctuations in direct numerical and large-eddy simulations. To reduce such artificial fluctuations a divergence-free method is developed with incompressible flow solvers. The procedure of the velocity–pressure solvers is slightly modified on a vertical plane near (rather than at) the inlet by inserting the synthetic turbulence on that plane during the procedure. Simple analytic and numerical error estimations are used to show that the impact of the modified solvers on solution accuracy is small. The final synthetic turbulence satisfies the divergence-free condition. No additional CPU time is required to achieve this condition. The method was tested via simulations of a plane channel flow with Reτ=395. Reynolds stresses, wall skin friction and power spectra of velocity fluctuations are compared with those obtained from using periodic inlet–outlet boundary conditions. In particular, the variances and power spectra of pressure fluctuations are shown to be accurately predicted only when the divergence-free inlet condition is used.

Radiative heat transfer modelling in a concentrated solar energy bubbling fluidized bed receiver using the Monte Carlo Method

According to recent studies in the solar energy community, a promising ways of solar energy conversion seems to be the beam down concentration technology associated to a fluidized bed receiver. The advantage of this system is its ability to heat air at temperature reaching 1000 K in a receiver directly exposed to a concentrated solar beam and integrated in a thermodynamic cycle. This paper focus on the modelling of radiative heat transfer from the optical concentrator to the receiver by taking into account absorption and multiple scattering of light in the particles bed. To achieve this objective, we develop in this work an efficient tool based on an algorithm solving the integral formulation of the Radiative Transfer Equation by the Monte Carlo Method. This algorithm is implemented in EDStaR environment where computer graphics libraries, parallel computing and specific functionalities to produce statistical quantities and their associated derivatives are available. One of the main advantage of the proposed radiative transfer modelling is the determination of the sensitivities (derivatives) of the physical quantities to any physical or geometrical parameter without significant additional CPU time.

On the boundary immobilization and variable space grid methods for transient heat conduction problems with phase change: Discussion and refinement

Explicit numerical schemes obtained using variable space grid (VSGM) and boundary immobilization (BIM) methods are considered for the solution of the transient heat conduction problem with phase change. This article briefly reviews different approaches developed to track the phase change front with a particular interest to those tracking explicitly the moving boundary. The analysis shows that both methods lead to identical computational algorithm, then considers the modified numerical scheme developed by Kutluay et al. (J. Comput. Appl. Math. 81 (1997) 135–144) and proposes a refinement procedure for the scheme without any additional CPU time. Two Stefan-like problems, having exact solutions, are studied and numerical results are assessed with respect to their performances.

Finite-Volume Formulation and Solution of the P3 Equations of Radiative Transfer on Unstructured Meshes

Abstract The method of spherical harmonics (or PN) is a popular method for approximate solution of the radiative transfer equation (RTE) in participating media. A rigorous conservative finite-volume (FV) procedure is presented for discretization of the P3 equations of radiative transfer in two-dimensional geometry—a set of four coupled, second-order partial differential equations. The FV procedure presented here is applicable to any arbitrary unstructured mesh topology. The resulting coupled set of discrete algebraic equations are solved implicitly using a coupled solver that involves decomposition of the computational domain into groups of geometrically contiguous cells using the binary spatial partitioning algorithm, followed by fully implicit coupled solution within each cell group using a preconditioned generalized minimum residual solver. The RTE solver is first verified by comparing predicted results with published Monte Carlo (MC) results for two benchmark problems. For completeness, results using the P1 approximation are also presented. As expected, results agree well with MC results for large/intermediate optical thicknesses, and the discrepancy between MC and P3 results increase as the optical thickness is decreased. The P3 approximation is found to be more accurate than the P1 approximation for optically thick cases. Finally, the new RTE solver is coupled to a reacting flow code and demonstrated for a laminar flame calculation using an unstructured mesh. It is found that the solution of the four P3 equations requires 14.5% additional CPU time, while the solution of the single P1 equation requires 9.3% additional CPU time over the case without radiation.

Classifying under computational resource constraints: anytime classification using probabilistic estimators

In many online applications of machine learning, the computational resources available for classification will vary from time to time. Most techniques are designed to operate within the constraints of the minimum expected resources and fail to utilize further resources when they are available. We propose a novel anytime classification algorithm, anytime averaged probabilistic estimators (AAPE), which is capable of delivering strong prediction accuracy with little CPU time and utilizing additional CPU time to increase classification accuracy. The idea is to run an ordered sequence of very efficient Bayesian probabilistic estimators (single improvement steps) until classification time runs out. Theoretical studies and empirical validations reveal that by properly identifying, ordering, invoking and ensembling single improvement steps, AAPE is able to accomplish accurate classification whenever it is interrupted. It is also able to output class probability estimates beyond simple 0/1-loss classifications, as well as adeptly handle incremental learning.

Consensus sequences improve PSI-BLAST through mimicking profile–profile alignments

Sequence alignments may be the most fundamental computational resource for molecular biology. The best methods that identify sequence relatedness through profile–profile comparisons are much slower and more complex than sequence–sequence and sequence–profile comparisons such as, respectively, BLAST and PSI-BLAST. Families of related genes and gene products (proteins) can be represented by consensus sequences that list the nucleic/amino acid most frequent at each sequence position in that family. Here, we propose a novel approach for consensus-sequence-based comparisons. This approach improved searches and alignments as a standard add-on to PSI-BLAST without any changes of code. Improvements were particularly significant for more difficult tasks such as the identification of distant structural relations between proteins and their corresponding alignments. Despite the fact that the improvements were higher for more divergent relations, they were consistent even at high accuracy/low error rates for non-trivially related proteins. The improvements were very easy to achieve; no parameter used by PSI-BLAST was altered and no single line of code changed. Furthermore, the consensus sequence add-on required relatively little additional CPU time. We discuss how advanced users of PSI-BLAST can immediately benefit from using consensus sequences on their local computers. We have also made the method available through the Internet (http://www.rostlab.org/services/consensus/).

Model Of The Smoothed Motion Of Interacting Particles In LES Of TurbulentDispersed Two-phase Channel Flow

By analogy with kinetic approach, the gas-solid turbulent flow was considered as an ensemble of interacting both stochastic liquid and solid particles, and then the motion equation for the solid particle along a partially averaged trajectory has been derived. Pushing further this analogy with kinetic approach, the statistical temperature has been introduced for both the solid particle and for the stochastic liquid particle with relaxation-type relation between these two temperatures. The smoothed particles dynamics was then computed along LES of turbulent channel gas flow with two-way coupling of momentum. The calculated results are compared with the experiment of Kulick et. al. (1994) and with the devoted to this experiment LESIparticle computation of Yamomoto et. al. (2001), where the inter-particle interaction was deterministically considered in the framework of hard-sphere collisions with prescribed efficiency. The computation with smoothed motion of particle is relatively in agreement with experiment. At the same time, this model has an advantage: it, practically, does not require an additional CPU time to account for stochastic inter-particle interactions. 1 Motivation and objective The experimental study [ l ,2] of dispersed two-phase developed turbulent flow in the vertical channel motivated to validate in [3] the LES approach with Lagrangian tracking of particles. The computed mean and r.m.s. velocity of flow and particles showed that while the gas flow has been predicted relatively well, the computed particle velocity differed from measurements. In the framework of discrete particles [4, S ] and continuum [6] approaches, this discrepancy motivated the further developments with inter-particle collisions. For example, Transactions on Engineering Sciences vol 42, © 2003 WIT Press, www.witpress.com, ISSN 1743-3533

Problems in practical finite element analysis using Preisach hysteresis model

An efficient which is called the distribution function method, for calculating the magnetic field strength H from the flux density B through the Preisach model is developed. By using the H can be directly obtained without iteration from B which is calculated by the usual FEM, with the magnetic vector potential as an unknown variable. The effects of the dimension n of the inverse distribution function on the CPU time and the memory requirements are investigated through a numerical example by increasing the dimension n of the inverse distribution function. It is shown that the additional CPU time for taking account of hysteresis is negligible when n is less than about 200.

The inside-outside contact search algorithm for finite element analysis

A new contact search algorithm (Inside–Outside Algorithm) for the sheet forming simulation has been developed and implemented in the dynamic explicit FE code: ‘DYNAMIC’. The inside–outside algorithm is derived based on the feature of the inside–outside status of a nodal ‘mesh normal vector’ in respect to a surface segment for the judgment of the contact of FE nodes with the tool surface. This new algorithm includes local search, local track and penetration calculation processes. Almost no additional CPU time is required for the local search process, because the calculations for both global and local search are combined. Moreover, the problems of conventional contact searching algorithms, such as iterations for local search and the deadzone problem, are resolved. Therefore, the quick, robust contact searching and accurate evaluation of penetration have been achieved. The numerical results show that the new contact searching algorithm is more cost effective and robust than conventional ones. © 1997 John Wiley & Sons, Ltd.

Combining consecutive short arcs into long arcs for precise and efficient GPS Orbit Determination

The final products of theCODE Analysis Center (Center for Orbit Determination in Europe) of theInternational GPS Service for Geodynamics (IGS) stem fromoverlapping 3-day-arcs. Until 31 December, 1994 these long arcs were computedfrom scratch, i.e. by processing three days of observations of about 40 stations (by mid 1995 about 60 stations were used) of the IGS Global Network in our parameter estimation program GPSEST. Becauseone-day-arcs have to be produced first (for the purpose of error detection etc.) the actual procedure was rather time-consuming. In the present article we develop the mathematical tools necessary to form long arcs based on the normal equation systems of consecutive short arcs (one-day-solutions in the case of CODE). The procedure in its simplest version is as follows: From the point of view of the result the new procedure iscompletely equivalent to an actual re-evaluation of all observations pertaining to the long arc. It is much more efficient and flexible, however because it allows us to construct 2-day-arcs, 3-day-arcs, etc. based on the previously stored daily normal equation systems without requiring much additional CPU time. The theory is developed in the first four sections. Technical aspects are dealt with in appendices A and B. The actual implementation into the Bernese GPS Software system and test results are given in section 5.

Coarse grid correction scheme for implicit multiblock Euler calculations

A coarse grid correction scheme is used to bring global influence to implicit multiblock calculations. Compared to using only explicit coupling between the blocks, a considerable reduction in the number of time steps needed to reach steady state has been observed for transonic and subsonic flows. The additional CPU time per time step associated with the method is small, resulting in a highly efficient parallel implicit scheme.

A new method for incorporating solvent effect into the classical, ab initio molecular orbital and density functional theory frameworks for arbitrary shape cavity

A new method for calculating the solvation energy of an arbitrary shape solute is presented. In this method, the solvents is treated as a homogeneous dielectric medium with a cavity. The solvation energy is presented in the Hartee-Fock-Roothaan form, which can be incorporated into both molecular orbital and density functional theories, as well as in the classical theory using the distributed monopole approach. We found that this approach yields on the average of 10% additional CPU time compared to the gas-phase calculations and an accuracy of better than 2.0 kcal/mol for neutral polar solutes but somewhat larger for ions.

モンテカルロ法による表面線量当量率分布の計算手法

A technique for Monte Carlo codes to obtain surface dose rate profiles of cask surfaces within a reasonable CPU time is presented in this paper. This technique does not use a huge number of actual small detectors defined by additional geometry input data, but uses imaginary detectors. To demonstrate this technique, SAS4 in the SCALE code system is chosen. The estimator is a surface crossing estimator (SXE). The technique is very simple and easy. In the Monte Carlo calculation, the contribution to the dose by a particle across the surface estimator is stored separately according to the coordinate of the surface crossing point of the particle as if there were a series of small surface estimators. After the Monte Carlo calculation has been done, the post processing procedure is made to produce dose rate profiles at the cask surface using the data from a series of small surface estimators. The additional CPU time required for introducing the new technique to the original CPU time is very small. The proposed technique using SXE is confirmed to be a very efficient and cost-saving method for getting dose rate profiles around a cask.

A formulation of multiple-reference CI with terms linear in the interelectronic distances

A formulation of the extension of the method of Kutzelnigg and Klopper, to include terms that are linear in the interelectronic distances in the Ansatz for the wavefunction, to general multiple-referece CI ( r 12-MR-CI) with the same basis set requirements as in the closed-shell single reference case, is presented. The implementation into existing direct CI programs is straightforward. The additional CPU time needed by the r 12 part should be negligible. r 12-MR-CI is readily extended to r 12-MR-ACPF, which allows for accurate approximations of full-CI energies. This implies the possibility of accurately solving the electronic Schrödinger equation for medium-sized atoms and molecules.

Combined Penalty Multiplier Optimization Methods to Enforce Integral Invariants Conservation

Abstract An augmented Lagrangian multiplier-penalty method is applied for the first time to solving the problem of enforcing simultaneous conservation of the nonlinear integral invariants of the shallow water equations on a limited-area domain. The method approximates the nonlinearly constrained minimization problem by solving a series of unconstrained minimization problems. The computational efficiency and accuracy of the method is tested using two finite-difference solvers of the nonlinear shallow water equations on a β-plane. The method is also compared with a pure quadratic penalty approach. The updating of the Lagrangian multipliers and the penalty parameters is done using procedures suggested by Bertsekas. The method yielded satisfactory results in the conservation of the integral constraints while the additional CPU time required did not exceed 15% of the total CPU time spent on the numerical solution of the shallow water equations. The methods proved to be simple in their implementation and they h...