Bordering method for solving systems of linear equations generated by the finite element method in the plate bending problem
A combined iteration algorithm based on the bordering and conjugate gradient methods is proposed to solve systems of linear equations generated by the finite element method in the plate bending problem. The numerical results for the analysis of the convergence rate of the iterative process are presented in the solution of model problems using a classical and modified algorithm of the method of conjugate gradients. The possibility of acceleration of the iterative algorithm is shown.
Keywordsfinite element method bordering method method of conjugate gradients iterative process convergence accuracy
Unable to display preview. Download preview PDF.
- 1.G. Meurant, Computer Solution of Large Linear Systems. Studies in Mathematics and Its Applications, Amsterdam; Lausanne; New York; Oxford; Shannon; Singapore; Tokyo (1999).Google Scholar
- 2.A. George and J. Lew, Numerical Solution of Large Sparse Systems of Equations [ Russian translation], Mir, Moscow (1984).Google Scholar
- 3.S. Pissanetsky, Sparse Matrix Technology [Russian translation], Mir, Moscow (1988).Google Scholar
- 4.L. Heigeman and D. Yang, Applied Iterative Methods [Russian translation], Mir, Moscow (1986).Google Scholar
- 5.M. Hestens and E. Stiefel, “Methods of conjugate gradients for solving linear systems,” Nat. Bur. Std. J. Res., 49, 409–436 (1952).Google Scholar
- 6.J. K. Reid, “On the method of conjugate gradients for the solution of large sparse systems of linear equations,” in: Large Sparse Sets of Linear Equations, Academic Press, London; New York (1971), pp. 231–252.Google Scholar
- 7.E. G. D’yakonov, “About some direct and iterative methods based on the matrix bordering,” in: G. I. Marchuk (Ed.), Numerical Methods in the Mathematical Physics [in Russian], Siberian Department of the Ac. Sci. USSR, Novosibirsk (1979), pp. 45–68.Google Scholar
- 8.A. M. Matsokin and S. V. Nepomnyashchikh, “Application of the bordering in the solution of mesh systems of equations,” in: Computational Algorithms in Problems of the Mathematical Physics [in Russian], Siberian Department of the Ac. Sci. USSR, Novosibirsk (1983), pp. 99–109.Google Scholar
- 9.S. P. Timoshenko and S. Woinowsky-Krieger, Theory Plates and Shells, McGraw-Hill, New York (1959).Google Scholar
- 11.A. Jennings, “A compact storage scheme for the solution of symmetric linear simultaneous equations,” Comput. J., 9, 281–285 (1966).Google Scholar
- 12.E. Cuthill and J. McKee, “Reducing the bandwidth of sparse symmetric matrices,” in: Proc 24th Nat. Conf. Assoc. Comput. Mach., ACM Publ. (1969), pp. 157–172.Google Scholar
- 13.A. Chang, “Application of sparse matrix methods in electric power system analysis,” Willoughby, 113–122 (1969).Google Scholar