Non-overlapping Domain Decomposition Scheme For The Symmetric Radial Basis Function Meshless Approach With Double Collocation At The Sub-domain Interfaces
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H. Power, A. Hernandez & A. La Rocca
In the particular case of solving large-scale boundary value problems, the computational cost derived as a result of the application of any numerical scheme represents a determinant factor in the determination of its computational efficiency. The present work studies the influence of the non-overlapping domain decomposition on the symmetric radial basis collocation method, as a way to improve its efficiency under high demanding numerical conditions. Due to the Hermitian character of the symmetric scheme at each of the collocations points of the sub-domain interfaces it is possible to impose simultaneously all the corresponding matching conditions. A multi-zone problem is considered as a test example, comparison between the numerical result and the analytical solution for two set of different physical parameters are presented. Keywords: symmetric RBF meshless approach, domain decomposition and double collocation. 1 Introduction The use of a mesh is a basic characteristic of traditional numerical approaches for the solution of partial differential equations, as is the case of the finite difference, element, volume and the boundary element methods. In the first cases, assumptions are made for the local approximation, which require internal mesh to support them. On the other hand, in the case on boundary methods, a
symmetric RBF meshless approach, domain decomposition and double collocation.