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