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Computational Savings (computational + savings)

Distribution by Scientific Domains

Chemistry	50%
Engineering	37%

Selected Abstracts

Reducing dimensionality in topology optimization using adaptive design variable fields

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2010
James K. Guest
Abstract Topology optimization methodologies typically use the same discretization for the design variable and analysis meshes. Analysis accuracy and expense are thus directly tied to design dimensionality and optimization expense. This paper proposes leveraging properties of the Heaviside projection method (HPM) to separate the design variable field from the analysis mesh in continuum topology optimization. HPM projects independent design variables onto element space over a prescribed length scale. A single design variable therefore influences several elements, creating a redundancy within the design that can be exploited to reduce the number of independent design variables without significantly restricting the design space. The algorithm begins with sparse design variable fields and adapts these fields as the optimization progresses. The technique is demonstrated on minimum compliance (maximum stiffness) problems solved using continuous optimization and genetic algorithms. For the former, the proposed algorithm typically identifies solutions having objective functions within 1% of those found using full design variable fields. Computational savings are minor to moderate for the minimum compliance formulation with a single constraint, and are substantial for formulations having many local constraints. When using genetic algorithms, solutions are consistently obtained on mesh resolutions that were previously considered intractable. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Two-dimensional anisotropic Cartesian mesh adaptation for the compressible Euler equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2004
W. A. Keats
Abstract Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This paper discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this paper, the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Separable approximations of space-time covariance matrices

ENVIRONMETRICS, Issue 7 2007
Marc G. Genton
Abstract Statistical modeling of space-time data has often been based on separable covariance functions, that is, covariances that can be written as a product of a purely spatial covariance and a purely temporal covariance. The main reason is that the structure of separable covariances dramatically reduces the number of parameters in the covariance matrix and thus facilitates computational procedures for large space-time data sets. In this paper, we discuss separable approximations of nonseparable space-time covariance matrices. Specifically, we describe the nearest Kronecker product approximation, in the Frobenius norm, of a space-time covariance matrix. The algorithm is simple to implement and the solution preserves properties of the space-time covariance matrix, such as symmetry, positive definiteness, and other structures. The separable approximation allows for fast kriging of large space-time data sets. We present several illustrative examples based on an application to data of Irish wind speeds, showing that only small differences in prediction error arise while computational savings for large data sets can be obtained. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Two-dimensional anisotropic Cartesian mesh adaptation for the compressible Euler equations

A new approach to response surface development for detailed gas-phase and surface reaction kinetic model optimization

INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 2 2004
Scott G. Davis
We propose a new method for constructing kinetic response surfaces used in the development and optimization of gas-phase and surface reaction kinetic models. The method, termed as the sensitivity analysis based (SAB) method, is based on a multivariate Taylor expansion of model response with respect to model parameters, neglecting terms higher than the second order. The expansion coefficients are obtained by a first-order local sensitivity analysis. Tests are made for gas-phase combustion reaction models. The results show that the response surface obtained with the SAB method is as accurate as the factorial design method traditionally used in reaction model optimization. The SAB method, however, presents significant computational savings compared to factorial design. The effect of including the partial and full third order terms was also examined and discussed. The SAB method is applied to optimization of a relatively complex surface reaction mechanism where large uncertainty in rate parameters exists. The example chosen is laser-induced fluorescence signal of OH desorption from a platinum foil in the water/oxygen reaction at low pressures. We introduce an iterative solution mapping and optimization approach for improved accuracy. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 94,106, 2004 [source]

Simple yet powerful techniques for optimization of horizontal recursion steps in Gaussian-type two-electron integral evaluation algorithms

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2007
Marcin Makowski
Abstract Simple heuristic rules are given that allow optimization of the performance of horizontal recursion steps present in schemes for calculation of two electron integrals are given. The number of floating point operations and computer timings are compared with the other algorithmic approaches to the problem. It is shown that the presented rules lead to substantial computational savings when compared with the standard implementation and may be also used succesfully instead of the algorithms based on full tree search techniques. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]

Hartree,Fock exchange fitting basis sets for H to Rn ,

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 2 2008
Florian Weigend
Abstract For elements H to Rn (except Lanthanides), a series of auxiliary basis sets fitting exchange and also Coulomb potentials in Hartree,Fock treatments (RI-JK-HF) is presented. A large set of small molecules representing nearly each element in all its common oxidation states was used to assess the quality of these auxiliary bases. For orbital basis sets of triple zeta valence and quadruple zeta valence quality, errors in total energies arising from the RI-JK approximation are below ,1 meV per atom in molecular compounds. Accuracy of RI-JK-approximated HF wave functions is sufficient for being used for post-HF treatments like Møller,Plesset perturbation theory, MP2. Compared to nonapproximated treatments, RI-JK-HF leads to large computational savings for quadruple zeta valence orbital bases and, in case of small to midsize systems, to significant savings for triple zeta valence bases. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008 [source]

An improved algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory: Application to alanine tetrapeptide conformational analysis

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 5 2007
Robert A. Distasio JR.
Abstract We present a new algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory (RI-MP2) and thoroughly assess its computational performance and chemical accuracy. This algorithm addresses the potential I/O bottlenecks associated with disk-based storage and access of the RI-MP2 t -amplitudes by utilizing a semi-direct batching approach and yields computational speed-ups of approximately 2,3 over the best conventional MP2 analytical gradient algorithms. In addition, we attempt to provide a straightforward guide to performing reliable and cost-efficient geometry optimizations at the RI-MP2 level of theory. By computing relative atomization energies for the G3/99 set and optimizing a test set of 136 equilibrium molecular structures, we demonstrate that satisfactory relative accuracy and significant computational savings can be obtained using Pople-style atomic orbital basis sets with the existing auxiliary basis expansions for RI-MP2 computations. We also show that RI-MP2 geometry optimizations reproduce molecular equilibrium structures with no significant deviations (>0.1 pm) from the predictions of conventional MP2 theory. As a chemical application, we computed the extended-globular conformational energy gap in alanine tetrapeptide at the extrapolated RI-MP2/cc-pV(TQ)Z level as 2.884, 4.414, and 4.994 kcal/mol for structures optimized using the HF, DFT (B3LYP), and RI-MP2 methodologies and the cc-pVTZ basis set, respectively. These marked energetic discrepancies originate from differential intramolecular hydrogen bonding present in the globular conformation optimized at these levels of theory and clearly demonstrate the importance of long-range correlation effects in polypeptide conformational analysis. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [source]