| |||

## Accurate Computation (accurate + computation)
## Selected Abstracts## Simulation of multiple shock,shock interference using implicit anti-diffusive WENO schemes INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2010Tsang-Jen HsiehAbstract Accurate computations of two-dimensional turbulent hypersonic shock,shock interactions that arise when single and dual shocks impinge on the bow shock in front of a cylinder are presented. The simulation methods used are a class of lower,upper symmetric-Gauss,Seidel implicit anti-diffusive weighted essentially non-oscillatory (WENO) schemes for solving the compressible Navier,Stokes equations with Spalart,Allmaras one-equation turbulence model. A numerical flux of WENO scheme with anti-diffusive flux correction is adopted, which consists of first-order and high-order fluxes and allows for a more flexible choice of first-order dissipative methods. Experimental flow fields of type IV shock,shock interactions with single and dual incident shocks by Wieting are computed. By using the WENO scheme with anti-diffusive flux corrections, the present solution indicates that good accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Computed surface pressure distribution and heat transfer rate are also compared with experimental data and other computational results and good agreement is found. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## A hypersingular time-domain BEM for 2D dynamic crack analysis in anisotropic solids INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2009M. WünscheAbstract A hypersingular time-domain boundary element method (BEM) for transient elastodynamic crack analysis in two-dimensional (2D), homogeneous, anisotropic, and linear elastic solids is presented in this paper. Stationary cracks in both infinite and finite anisotropic solids under impact loading are investigated. On the external boundary of the cracked solid the classical displacement boundary integral equations (BIEs) are used, while the hypersingular traction BIEs are applied to the crack-faces. The temporal discretization is performed by a collocation method, while a Galerkin method is implemented for the spatial discretization. Both temporal and spatial integrations are carried out analytically. Special analytical techniques are developed to directly compute strongly singular and hypersingular integrals. Only the line integrals over an unit circle arising in the elastodynamic fundamental solutions need to be computed numerically by standard Gaussian quadrature. An explicit time-stepping scheme is obtained to compute the unknown boundary data including the crack-opening-displacements (CODs). Special crack-tip elements are adopted to ensure a direct and an accurate computation of the elastodynamic stress intensity factors from the CODs. Several numerical examples are given to show the accuracy and the efficiency of the present hypersingular time-domain BEM. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## On computing the forces from the noisy displacement data of an elastic body INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2008A. Narayana ReddyAbstract This study is concerned with the accurate computation of the unknown forces applied on the boundary of an elastic body using its measured displacement data with noise. Vision-based minimally intrusive force-sensing using elastically deformable grasping tools is the motivation for undertaking this problem. Since this problem involves incomplete and inconsistent displacement/force of an elastic body, it leads to an ill-posed problem known as Cauchy's problem in elasticity. Vision-based displacement measurement necessitates large displacements of the elastic body for reasonable accuracy. Therefore, we use geometrically non-linear modelling of the elastic body, which was not considered by others who attempted to solve Cauchy's elasticity problem before. We present two methods to solve the problem. The first method uses the pseudo-inverse of an over-constrained system of equations. This method is shown to be not effective when the noise in the measured displacement data is high. We attribute this to the appearance of spurious forces at regions where there should not be any forces. The second method focuses on minimizing the spurious forces by varying the measured displacements within the known accuracy of the measurement technique. Both continuum and frame elements are used in the finite element modelling of the elastic bodies considered in the numerical examples. The performance of the two methods is compared using seven numerical examples, all of which show that the second method estimates the forces with an error that is not more than the noise in the measured displacements. An experiment was also conducted to demonstrate the effectiveness of the second method in accurately estimating the applied forces. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## The parameterization and validation of generalized born models using the pairwise descreening approximation JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 14 2004Julien MichelAbstract Generalized Born Surface Area (GBSA) models for water using the Pairwise Descreening Approximation (PDA) have been parameterized by two different methods. The first method, similar to that used in previously reported parameterizations, optimizes all parameters against the experimental free energies of hydration of organic molecules. The second method optimizes the PDA parameters to compensate only for systematic errors of the PDA. The best models are compared to Poisson,Boltzmann calculations and applied to the computation of potentials of mean force (PMFs) for the association of various molecules. PMFs present a more rigorous test of the ability of a solvation model to correctly reproduce the screening of intermolecular interactions by the solvent, than its accuracy at predicting free energies of hydration of small molecules. Models derived with the first method are sometimes shown to fail to compute accurate potentials of mean force because of large errors in the computation of Born radii, while no such difficulties are observed with the second method. Furthermore, accurate computation of the Born radii appears to be more important than good agreement with experimental free energies of solvation. We discuss the source of errors in the potentials of mean force and suggest means to reduce them. Our findings suggest that Generalized Born models that use the Pairwise Descreening Approximation and that are derived solely by unconstrained optimization of parameters against free energies of hydration should be applied to the modeling of intermolecular interactions with caution. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1760,1770, 2004 [source] ## Ab initio quality one-electron properties of large molecules: Development and testing of molecular tailoring approach JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 4 2003K. BabuAbstract The development of a linear-scaling method, viz. "molecular tailoring approach" with an emphasis on accurate computation of one-electron properties of large molecules is reported. This method is based on fragmenting the reference macromolecule into a number of small, overlapping molecules of similar size. The density matrix (DM) of the parent molecule is synthesized from the individual fragment DMs, computed separately at the Hartree,Fock (HF) level, and is used for property evaluation. In effect, this method reduces the O(N3) scaling order within HF theory to an n·O(N,3) one, where n is the number of fragments and N,, the average number of basis functions in the fragment molecules. An algorithm and a program in FORTRAN 90 have been developed for an automated fragmentation of large molecular systems. One-electron properties such as the molecular electrostatic potential, molecular electron density along with their topography, as well as the dipole moment are computed using this approach for medium and large test chemical systems of varying nature (tocopherol, a model polypeptide and a silicious zeolite). The results are compared qualitatively and quantitatively with the corresponding actual ones for some cases. This method is also extended to obtain MP2 level DMs and electronic properties of large systems and found to be equally successful. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 484,495, 2003 [source] ## Computing projections via Householder transformations and Gram,Schmidt orthogonalizations NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 7 2004Achiya DaxAbstract Let x* denote the solution of a linear least-squares problem of the form where A is a full rank m × n matrix, m > n. Let r*=b - Ax* denote the corresponding residual vector. In most problems one is satisfied with accurate computation of x*. Yet in some applications, such as affine scaling methods, one is also interested in accurate computation of the unit residual vector r*/,r*,2. The difficulties arise when ,r*,2 is much smaller than ,b,2. Let x, and r, denote the computed values of x* and r*, respectively. Let ,denote the machine precision in our computations, and assume that r, is computed from the equality r, =b - Ax,. Then, no matter how accurate x, is, the unit residual vector ű =r,/,r,,2 contains an error vector whose size is likely to exceed ,,b,2/,r*,2. That is, the smaller ,r*,2 the larger the error. Thus although the computed unit residual should satisfy ATű=0, in practice the size of ,ATű,2 is about ,,A,2,b,2/,r*,2. The methods discussed in this paper compute a residual vector, r,, for which ,ATr,,2 is not much larger than ,,A,2,r,,2. Numerical experiments illustrate the difficulties in computing small residuals and the usefulness of the proposed safeguards. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Numerical accuracy of a Padé-type non-reflecting boundary condition for the finite element solution of acoustic scattering problems at high-frequency INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005R. KechroudAbstract The present text deals with the numerical solution of two-dimensional high-frequency acoustic scattering problems using a new high-order and asymptotic Padé-type artificial boundary condition. The Padé-type condition is easy-to-implement in a Galerkin least-squares (iterative) finite element solver for arbitrarily convex-shaped boundaries. The method accuracy is investigated for different model problems and for the scattering problem by a submarine-shaped scatterer. As a result, relatively small computational domains, optimized according to the shape of the scatterer, can be considered while yielding accurate computations for high-frequencies. Copyright © 2005 John Wiley & Sons, Ltd. [source] |