Hermite curves in the modification of integral equations for potential boundary‐value problems
Abstract
This paper presents a modification of the classical boundary integral equation method (BIEM) for two‐dimensional potential boundary‐value problem. The proposed modification consists in describing the boundary geometry by means of Hermite curves. As a result of this analytical modification of the boundary integral equation (BIE), a new parametric integral equation system (PIES) is obtained. The kernels of these equations include the geometry of the boundary. This new PIES is no longer defined on the boundary, as in the case of the BIE, but on the straight line for any given domain. The solution of the new PIES does not require boundary discretization as it can be reduced merely to an approximation of boundary functions. To solve this PIES a pseudospectral method has been proposed and the results obtained compared with exact solutions.
Keywords
Citation
Zieniuk, E. (2003), "Hermite curves in the modification of integral equations for potential boundary‐value problems", Engineering Computations, Vol. 20 No. 2, pp. 112-128. https://doi.org/10.1108/02644400310465272
Publisher
:MCB UP Ltd
Copyright © 2003, MCB UP Limited