Home  About us  Contact
 

Spatial Grid (spatial + grid)

Distribution by Scientific Domains
Mathematics and Statistics40%
Chemistry40%

Selected Abstracts

On accuracy of the finite-difference and finite-element schemes with respect to P -wave to S -wave speed ratio

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2010
Peter Moczo
SUMMARY Numerical modelling of seismic motion in sedimentary basins often has to account for P -wave to S -wave speed ratios as large as five and even larger, mainly in sediments below groundwater level. Therefore, we analyse seven schemes for their behaviour with a varying P -wave to S -wave speed ratio. Four finite-difference (FD) schemes include (1) displacement conventional-grid, (2) displacement-stress partly-staggered-grid, (3) displacement-stress staggered-grid and (4) velocity,stress staggered-grid schemes. Three displacement finite-element schemes differ in integration: (1) Lobatto four-point, (2) Gauss four-point and (3) Gauss one-point. To compare schemes at the most fundamental level, and identify basic aspects responsible for their behaviours with the varying speed ratio, we analyse 2-D second-order schemes assuming an elastic homogeneous isotropic medium and a uniform grid. We compare structures of the schemes and applied FD approximations. We define (full) local errors in amplitude and polarization in one time step, and normalize them for a unit time. We present results of extensive numerical calculations for wide ranges of values of the speed ratio and a spatial sampling ratio, and the entire range of directions of propagation with respect to the spatial grid. The application of some schemes to real sedimentary basins in general requires considerably finer spatial sampling than usually applied. Consistency in approximating first spatial derivatives appears to be the key factor for the behaviour of a scheme with respect to the P -wave to S -wave speed ratio. [source]

Quantum wave packet dynamics on multidimensional adaptive grids: Applications of the moving boundary truncation method

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2007
Lucas R. Pettey
Abstract Recently, we reported a novel method for integrating the time dependent Schrödinger equation which used hydrodynamic quantum trajectories to adapt the boundaries of a fixed spatial grid. The moving boundary truncation (MBT) method significantly reduced the number of grid points needed to perform accurate calculations while maintaining stability during the time propagation. In this work, the method is extended to multidimensional examples. The application of MBT to scattering on 2D and 3D potential energy surfaces shows a greater decrease in the number of grid points needed compared with full fixed grids while maintaining excellent accuracy and stability, even for very long propagation times. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]

SPACE,TIME MODELLING OF SYDNEY HARBOUR WINDS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 1 2005
Edward Cripps
Summary This paper develops a space-time statistical model for local forecasting of surface-level wind fields in a coastal region with complex topography. The statistical model makes use of output from deterministic numerical weather prediction models which are able to produce forecasts of surface wind fields on a spatial grid. When predicting surface winds at observing stations, errors can arise due to sub-grid scale processes not adequately captured by the numerical weather prediction model, and the statistical model attempts to correct for these influences. In particular, it uses information from observing stations within the study region as well as topographic information to account for local bias. Bayesian methods for inference are used in the model, with computations carried out using Markov chain Monte Carlo algorithms. Empirical performance of the model is described, illustrating that a structured Bayesian approach to complicated space-time models of the type considered in this paper can be readily implemented and can lead to improvements in forecasting over traditional methods. [source]

A fourth-order accurate, Numerov-type, three-point finite-difference discretization of electrochemical reaction-diffusion equations on nonuniform (exponentially expanding) spatial grids in one-dimensional space geometry

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 12 2004
aw K. Bieniasz
Abstract The validity for finite-difference electrochemical kinetic simulations, of the extension of the Numerov discretization designed by Chawla and Katti [J Comput Appl Math 1980, 6, 189,196] for the solution of two-point boundary value problems in ordinary differential equations, is examined. The discretization is adapted to systems of time-dependent reaction-diffusion partial differential equations in one-dimensional space geometry, on nonuniform space grids resulting from coordinate transformations. The equations must not involve first spatial derivatives of the unknowns. Relevant discrete formulae are outlined and tested in calculations on two example kinetic models. The models describe potential step chronoamperometry under limiting current conditions, for the catalytic EC, and Reinert-Berg CE reaction mechanisms. Exponentially expanding space grid is used. The discretization considered proves the most accurate and efficient, out of all the three-point finite-difference discretizations on such grids, that have been used thus far in electrochemical kinetics. Therefore, it can be recommended as a method of choice. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1515,1521, 2004 [source]

An Eulerian-Lagrangian method for option pricing in finance

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2007
Zheng Wang
Abstract This article is devoted to the development and application of an Eulerian-Lagrangian method (ELM) for the solution of the Black-Scholes partial differential equation for the valuation of European option contracts. This method fully utilizes the transient behavior of the governing equations and generates very accurate option's fair values and their derivatives also known as option Greeks, even if coarse spatial grids and large time steps are used. Numerical experiments on two standard option contracts are presented which show that the ELM method (favorably) compares in terms of accuracy and efficiency to many other well-perceived methods. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 293,329, 2007 [source]