Computational and Applied Mathematics (18070302)37(2)pp. 978-995
Numerical methods in approximation of derivatives on regular or irregular gridded and scattered data points are of significance in the study of numerous problems in engineering and geoscience. A mathematically accurate and stable method is assessed to compute the differential quantities, while being flexible and easy to implement. Strain-invariant parameters in deformation analysis and curvature attributes in geometrical analysis of approximated surfaces are independent quantities which could be derived numerically through radial basis functions (RBFs) for scattered data points. Approximation of a function or its derivatives through RBFs is highly correlated to its shape parameter which depends on the number and distribution of the particles on the support domain. A procedure to find the optimal shape parameter for RBFs in the influence domain of each nodal point together with the presentation of a manner of calculating the curvature attributes and strain parameters through Gaussian RBFs is proposed here. Results indicate a significant improvement in the approximation accuracy of strain parameters and curvature attributes, while this approximation is more stable when RBFs with optimal shape parameter are implemented rather than the traditional moving least squares. © 2016, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.
Engineering Analysis with Boundary Elements (09557997)58pp. 119-128
The meshless moving least squares (MLS) is expanded here based on recursive least squares (RLS) where the outcome is the newly developed recursive moving least squares (RMLS) approximation method. In RMLS method each nodal point has its own size of the support domain; accordingly, the number of field points on the influence domain varies from node to node. This method makes it possible to select the optimal size of the support domain by imposing any arbitrary measures such as precision or convergence of the unknown parameters on the support domain. Moreover, the possibility of applying the statistical test in removing any undesired outliers of function values is provided. Another feature of this newly developed method is providing the possibility of revealing the significant break-lines and faults diagnosis on the surface. In RMLS the radius of the support domain would become extended to a point where the optimal precision of unknown parameters is achieved or reach the discontinuous or high gradient interfaces. The numerical results indicate that this method improves the accuracy of approximated surface more than 50%, especially for rough surfaces or the contaminated particles by random or gross errors, with no significant increase in time. © 2015 Elsevier Ltd. All rights reserved.
Journal of Geodetic Science (20819943)4(1)
Precision, reliability and cost are the major criteriaapplied in optimization and design of geodetic networks.The terrestrial networks are being replaced quicklyby permanent and campaign Global Positioning System(GPS) networks. These networks must be optimized usingthe same three criteria. In this article the optimization ofthe observational plan of local GPS networks (Second OrderDesign (SOD)) is considered using the precision criterion.This study is limited to the selection of optimal numbersand the best distribution of the non-trivial baselinesthroughout the network. This objective is accomplishedbased on the SOD solution through the analytical methodin operational research by the means of quadratic programmingalgorithm. This presented method is tested ona real GPS network and appears to be a useful techniquein terms of cost reduction in the field work by the providedobservational plan and optimal distribution of thebaselines throughout the network. Results indicate thatweights of almost 36% of the baselines are negligiblewhencompared to the weights of the rest of the baselines; therefore,they could be eliminated fromthe observational plan,resulting in a 36% saving in the fieldwork cost. © 2014 H. Mehrabi, B. Voosoghi.
