A one-sweep method for the numerical solution of finite-element equations is presented. This procedure is especially efficient in computing time and storage when the solution is required at only a few nodes of the finite-element mesh. Furthermore, the method is particularly useful in dealing with problems on infinite or semi-infinite domains. Artificial boundaries must be introduced in such cases, and the one-sweep method affords an extremely efficient algorithm by which the dependence of the solution on the location of these boundaries can be assessed. An application of the method to the vibration of a half-submerged circular cylinder in a heavy fluid is presented.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Distéfano, N.,Invariant Imbedding and the Solution of Finite Element Equations, Journal of Mathematical Analysis and Applications, Vol. 46, No. 2, 1974.
Distéfano, N., andSamartin, A.,A Dynamic Programming Approach to the Formulation and Solution of Finite Element Equations, Computer Methods in Applied Mechanics and Engineering, Vol. 5, No. 1, 1975.
Chiu, H.,Solution of the Boundary - Value Potential Problems by a Finite Element Method with Invariant Imbedding, University of California, Berkeley, California, Department of Naval Architecture, PhD Dissertation, 1975.
Godunov, S. K., andRyabenki, V. S.,Theory of Difference Schemes, Appendix II, North-Holland Publishing Company, Amsterdam, Holland, 1964.
Angel, E., andBellman, R.,Dynamic Programming and Partial Differential Equations, Academic Press, New York, New York, 1972.
Lamb, H.,Hydrodynamics, Dover Publications, New York, New York, 1945.
The second author wishes to express his thanks to Professor J. L. Sackman for reviewing this work.
Communicated by G. Leitmann
About this article
Cite this article
Distéfano, N., Chiu, H. A one-sweep method in the solution of finite-element equations: An application to the vibration of structures in heavy fluids. J Optim Theory Appl 23, 27–40 (1977). https://doi.org/10.1007/BF00932295
- One-sweep method
- invariant imbedding
- fluid-structure interaction