TY - JOUR

T1 - An efficient accurate Local Method of Approximate Particular Solutions for solving convection-diffusion problems

AU - Bustamante, C. A.

AU - Power, H.

AU - Florez, W. F.

PY - 2014/10

Y1 - 2014/10

N2 - An efficient accurate Local Method of Approximate Particular Solutions (LMAPS) using Multiquadric Radial Basis Functions (RBFs) for solving convection-diffusion problems is proposed. It consists in adding auxiliary points to the local interpolation stencil at which the governing PDE is enforced, known as PDE points, besides imposing the boundary condition at the stencil in contact with the problem boundary. Two convection-diffusion problems are considered as test problems and solved with two previous local direct RBF collocation schemes (with and without PDE points) and two LMAPS (with and without PDE points), as well as the Global MAPS, in order to compare accuracy, convergence order and their behaviour in terms of the shape parameter. If PDE points are added, the result accuracy is improved as well as the convergence rate when using both local direct and MAPS formulations.

AB - An efficient accurate Local Method of Approximate Particular Solutions (LMAPS) using Multiquadric Radial Basis Functions (RBFs) for solving convection-diffusion problems is proposed. It consists in adding auxiliary points to the local interpolation stencil at which the governing PDE is enforced, known as PDE points, besides imposing the boundary condition at the stencil in contact with the problem boundary. Two convection-diffusion problems are considered as test problems and solved with two previous local direct RBF collocation schemes (with and without PDE points) and two LMAPS (with and without PDE points), as well as the Global MAPS, in order to compare accuracy, convergence order and their behaviour in terms of the shape parameter. If PDE points are added, the result accuracy is improved as well as the convergence rate when using both local direct and MAPS formulations.

KW - Convection-diffusion equation

KW - Meshless methods

KW - Particular solutions

KW - Radial basis functions

UR - http://www.scopus.com/inward/record.url?scp=84903990874&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2014.06.004

DO - 10.1016/j.enganabound.2014.06.004

M3 - Artículo

AN - SCOPUS:84903990874

SN - 0955-7997

VL - 47

SP - 32

EP - 37

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

IS - 1

ER -