Multi-level meshless methods based on direct multi-elliptic interpolation

Authors:
C. Gáspár
Affiliations:
Széchenyi István University, P.O. Box 701, H-9007 Györ, Hungary
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

A short overview on the direct multi-elliptic interpolation and the related meshless methods for solving partial differential equations is given. A new technique is proposed which produces a biharmonic interpolation along the boundary and solves the original problem inside the domain. An error estimation is also derived. To implement the method, quadtree-based multi-level methods are used. The approach avoids the use of large, dense and ill-conditioned matrices and significantly reduces the computational cost.