Volume 4, Issue 4
Local Hermite-RBF based Grid-Free Scheme with a Variable (Optimal) Shape Parameter for Steady Convec

Y. V. S. S. SANYASIRAJU AND CH. SATYANARAYANA

Int. J. Numer. Anal. Mod. B, 4 (2013), pp. 382-393

Published online: 2013-04

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  • Abstract
In this work, a local algorithm is proposed to optimize the shape parameter of the infinitely smooth Radial Basis Function (RBF) in the local Hermite-RBF (LHRBF) grid free scheme which has been developed to the solve the partial differential equations, in particular, steady Convection Diffusion Equations (CDE), more accurately. The algorithm is based on the re-construction of the forcing term and its (differential) operator value over the centers in the local support domain. A cost function which has similar variation as RMS error function is obtained and the same is minimized to generate a variable shape parameter for each reference center. The LHRBF scheme with the obtained variable (optimal) shape parameter is tested over one and two dimensional steady CDEs to demonstrate its robustness.
  • AMS Subject Headings

76R99 78M50 78M25

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COPYRIGHT: © Global Science Press

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@Article{IJNAMB-4-382, author = {Y. V. S. S. SANYASIRAJU AND CH. SATYANARAYANA}, title = {Local Hermite-RBF based Grid-Free Scheme with a Variable (Optimal) Shape Parameter for Steady Convec}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2013}, volume = {4}, number = {4}, pages = {382--393}, abstract = {In this work, a local algorithm is proposed to optimize the shape parameter of the infinitely smooth Radial Basis Function (RBF) in the local Hermite-RBF (LHRBF) grid free scheme which has been developed to the solve the partial differential equations, in particular, steady Convection Diffusion Equations (CDE), more accurately. The algorithm is based on the re-construction of the forcing term and its (differential) operator value over the centers in the local support domain. A cost function which has similar variation as RMS error function is obtained and the same is minimized to generate a variable shape parameter for each reference center. The LHRBF scheme with the obtained variable (optimal) shape parameter is tested over one and two dimensional steady CDEs to demonstrate its robustness.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/264.html} }
TY - JOUR T1 - Local Hermite-RBF based Grid-Free Scheme with a Variable (Optimal) Shape Parameter for Steady Convec AU - Y. V. S. S. SANYASIRAJU AND CH. SATYANARAYANA JO - International Journal of Numerical Analysis Modeling Series B VL - 4 SP - 382 EP - 393 PY - 2013 DA - 2013/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/264.html KW - grid-free scheme KW - radial basis function KW - convection-diffusion KW - multiquadric KW - optimal shape parameter and Hermite-RBF scheme AB - In this work, a local algorithm is proposed to optimize the shape parameter of the infinitely smooth Radial Basis Function (RBF) in the local Hermite-RBF (LHRBF) grid free scheme which has been developed to the solve the partial differential equations, in particular, steady Convection Diffusion Equations (CDE), more accurately. The algorithm is based on the re-construction of the forcing term and its (differential) operator value over the centers in the local support domain. A cost function which has similar variation as RMS error function is obtained and the same is minimized to generate a variable shape parameter for each reference center. The LHRBF scheme with the obtained variable (optimal) shape parameter is tested over one and two dimensional steady CDEs to demonstrate its robustness.
Y. V. S. S. SANYASIRAJU AND CH. SATYANARAYANA. (2013). Local Hermite-RBF based Grid-Free Scheme with a Variable (Optimal) Shape Parameter for Steady Convec. International Journal of Numerical Analysis Modeling Series B. 4 (4). 382-393. doi:
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