Nonisoparametric formulations for the three-dimensional boundary element method

• Published in: Engineering analysis Vol. 5; no. 4; pp. 198 - 204
• Main Authors: Aliabadi, M.H, Hall, W.S
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1988
• Subjects: boundary element method; iso-parametric; potential problems; quadrilateral elements; shape functions; sub-parametric; super-parametric; quadrilateral elements; boundary element method; shape functions; sub-parametric; super-parametric; iso-parametric; potential problems
• ISSN: 0264-682X
• DOI: 10.1016/0264-682X(88)90017-2

The paper investigates the inaccuracies arising from discretization procedures in the three-dimensional Boundary Element Method for potential problems, particularly from the representation of the surface and unknown function by interpolating shape functions. Nonisoparametric formulations are considered; that is, sub-parametric in which the surface is not as well represented as the unknown function, and super-parametric in which the surface is better represented than the unknown function. These nonisoparametric formulations are based on 8-node and 9-node quadrilaterals which are also used to provide two different levels of isoparametric formulations. Numerical results based on the various formulations are presented for some problems for which exact solutions are known. Firstly, Dirichlet problems of finding the surface charge for a unit sphere with given uniform and nonuniform potentials corresponding to first and second order harmonics; secondly, a Neuman problem of finding the velocity potential on a sphere placed in a uniform stream. The results show that there is an advantage in accuracy and reduced calculation time for the super-parametric formulation compared to iso-parametric formulations. The sub-parametric formulation in which the unknown function is better represented than the surface is less accurate and offers no time reduction. It also presents special difficulties in defining the position of any extra unknown function node not corresponding to a surface node.