Abstract
It is well known that homogeneous elliptic field problems may be alternatively posed as infinite systems of boundary integral equations obtained by using a suitable family of kernel functions and integration by parts [1], [2]. A determinate system of non-homogeneous linear algebraic equations is obtained therefrom by discretizing the system, using elements defined after the manner of finite elements and a finite member of Kernel functions [1]. The result is a practical and powerful numerical method for the solution of elliptic field problems which may easily be generalized to rival the finite element method in its range of applicability.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Brebbia, C. A., The Boundary Element Method for Engineers. Pentech Press, London 1978
Watson, J. O., Advanced implementation of the boundary element method for two and three-dimensional elastostatics, In: Developments in Boundary Element Methods — 1. Eds. Banerjee, P. K. & Butterfield, R., Applied Science Publishers, London, Chapt. 3, pp. 31–63, 1979
Patterson, C., Sufficient conditions for convergence in the finite element method for any solution of finite energy. In: Mathematics of Finite Elements & Applications. Ed. Whiteman, J. R., Academic Press, London, pp. 213–224, 1973
Lachat, J. C., A Further Development of the Boundary Integral Technique for Elastostatics. Ph.D. Thesis, University of Southampton 1975
Patterson, C., Sheikh, M. A., A regular boundary elementmethod for fluid flow. In: Int. J. Num. Methods in Fluids, 2, pp. 239–251, 1982
Patterson, C., Sheikh, M. A., Regular boundary integral equations for stress analysis. In: Boundary Element Methods. Ed. Brebbia, C. A., Springer-Verlag, Berlin, pp. 85 —104, 1981
Patterson, C., Sheikh, M. A., A regular boundary element method for coupled sub-domains. In: Numerical Methods for Coupled Problems. Eds. Lewis, R. W., Bettess, P., and Hinton, E., Pineridge Press, Swansea, pp. 115 —126, 1981
Patterson, C., Sheikh, M. A., A higher order boundary element method for fluid flow. In: Finite Element Flow Analysis. Ed. Kawai, T., Tokyo University Press, Tokyo, pp. 907–913, 1982
Ergatoudis, J., Isoparametric Finite Elements in Two and Three-Dimensional Analysis. Ph.D. Thesis, University of Wales, Swansea 1968
Brebbia, C. A., Walker S., Boundary Element Techniques in Engineering. Newnes-Butterworths, London 1980
Patterson, C., Sheikh, M. A., Discontinuous boundary elements for heat conduction. In: Numerical Methods in Thermal Problems — II. Eds. Lewis, R. W., Morgan, K., and Schrefler, B. A., Pineridge Press, Swansea, pp. 25–34, 1981
Chaudonneret, M., On the discontinuity of the stress vector in the boundary integral equation method for elastic analysis. In: Recent Advances in Boundary Element Methods. Ed. Brebbia, C. A., Pentech Press, London, pp. 185–194, 1978
Wardle, L. J., Crotty, J. M., Two-dimensional boundary integral equation analysis for non-homogeneous mining applications. In: Recent Advances in Boundary Element Methods. Ed. Brebbia, C. A., Pentech Press, London, pp. 233–251, 1978
Milne-Thompson, L. M., Theoretical Hydrodynamics. Macmillan, London 1968
Peterson, R. E., Stress Concentration Factors. John Wiley & Sons, New York 1974
Patterson, C., Sheikh, M. A., Non-conforming boundary elements for stress analysis. In: Boundary Element Methods. Ed. Brebbia, C. A., Springer-Verlag, Berlin, pp. 137 —152 1981
Patterson, C., El-Sebai, N. A. S., A regular boundary method using non-conforming elements for potential problems in three dimensions, In: Boundary Element Methods in Engineering. Ed. Brebbia, C. A., Springer-Verlag, Berlin, pp. 112–126, 1982
El-Sebai, N. A. S., An Investigation of the Regular Boundary Element Method in Three Dimensions. Ph.D. Thesis, University of Sheffield 1982
Danson, D. J., BEASY, A boundary element analysis system. In: Boundary Element Methods in Engineering. Ed. Brebbia, C. A., Springer-Verlag, Berlin, pp. 557–557, 1982
Aypaci, V. S., Conduction Heat Transfer. Addison-Welsey, USA 1966
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Patterson, C., Sheikh, M.A. (1984). Interelement Continuity in the Boundary Element Method. In: Brebbia, C.A. (eds) Topics in Boundary Element Research. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2877-1_7
Download citation
DOI: https://doi.org/10.1007/978-1-4899-2877-1_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-13097-2
Online ISBN: 978-1-4899-2877-1
eBook Packages: Springer Book Archive