×

zbMATH — the first resource for mathematics

The method of fundamental solutions for the numerical solution of the biharmonic equation. (English) Zbl 0618.65108
The method of fundamental solutions for second order elliptic partial differential equations (and particularly for the biharmonic equation) together with test problems (elasticity, fluid flow) is presented. A particular attention is devoted to the nonlinear least-squares method for fitting of boundary conditions.
Reviewer: J.Šmíd

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
35J25 Boundary value problems for second-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aleksidze, M.A., Differential equations, 2, 515, (1966)
[2] Banerjee, P.K.; Butterfield, R., Boundary element methods in engineering science, (1981), McGraw-Hill U.K · Zbl 0499.73070
[3] Bézine, G., Mech. res. comm., 5, 197, (1978)
[4] Black, J.R.; Denn, M.M.; Hsiao, G.C., (), 3
[5] Bogomolny, A., SIAM J. numer. anal., 22, 644, (1985)
[6] Burgess, G.; Mahajerin, E., Comput. & structures, 19, 697, (1984)
[7] Burgess, G.; Mahajerin, E., Comput. fluids, 12, 311, (1984)
[8] Coleman, C.J., Quart. J. mech. appl. math., 34, 453, (1981)
[9] DeMey, G., Comput. & structures, 8, 113, (1978)
[10] Fairweather, G.; Rizzo, F.J.; Shippy, D.J.; Wu, Y.S., J. comput. phys., 31, 96, (1979)
[11] Fairweather, G.; Johnston, R.L., (), 349
[12] Gospodinov, G.; Ljutskanov, D., Appl. math. modelling, 6, 237, (1982)
[13] Heise, U., Comput. & structures, 8, 199, (1978)
[14] Ho-Tai, S.; Johnston, R.L.; Matron, R., ()
[15] Ingber, M.S.; Mitra, A.K., Int. J. numer. methods eng., 23, 2121, (1985)
[16] Jaswon, M.A.; Maiti, M.; Symm, G.T., Int. J. solids and structures, 3, 309, (1967) · Zbl 0148.19403
[17] Jaswon, M.A.; Maiti, M., J. eng. math., 2, 83, (1968)
[18] Jaswon, M.A.; Symm, G.T., Integral equation methods in potential theory and elastostatics, (1977), Academic Press New York · Zbl 0414.45001
[19] Johnston, R.L.; Matron, R., Int. J. numer. methods eng., 14, 1739, (1979)
[20] Johnston, R.L.; Fairweather, G., Appl. math. modelling, 8, 265, (1984)
[21] Karageorghis, A., ()
[22] Kelmanson, M.A., Comput. fluids, 11, 307, (1983)
[23] Kelmanson, M.A., J. comput. phys., 51, 139, (1983)
[24] Keshavarzi, M., Comput. methods appl. mech. eng., 16, 1, (1978)
[25] Kupradze, V.D., Potential methods in the theory of elasticity, (1965), Israel Program for Scientific Translations Jerusalem · Zbl 0188.56901
[26] Kupradze, V.D., Russian math. surveys, 22, 58, (1967)
[27] Kupradze, V.D.; Aleksidze, M.A., U.S.S.R. comput math. math. phys., 4, No. 4, 82, (1964)
[28] MacDonell, M., ()
[29] Maiti, M.; Chakrabarti, S.K., Int. J. eng. sci., 12, 793, (1974)
[30] Matron, R., ()
[31] Matron, R.; Johnston, R.L., SIAM J. numer. anal., 14, 638, (1977)
[32] Murashima, S.; Nonaka, Y.; Nieda, H., (), 75
[33] Oliveira, E.R., (), 79
[34] Richter, G.R., (), 41
[35] Segedin, C.M.; Brickell, D.G.A., (), 41
[36] Stern, M., Int. J. solids and structures, 15, 769, (1979)
[37] Symm, G.T., ()
[38] Timoshenko, S.; Woinowsky-Krieger, S., Theory of plates and shells, (1959), McGraw-Hill New York · Zbl 0114.40801
[39] Tottenham, H., (), 173
[40] Wu, B.C.; Altiero, N.J., Comput. structures, 10, 703, (1979)
[41] Bhargava, R.D., (), 571
[42] Bhattacharyya, P.K.; Symm, G.T., Comput. math. appl., 6, 443, (1980)
[43] Bhattacharyya, P.K.; Symm, G.T., Appl. math. modelling, 8, 226, (1984)
[44] Redekop, D., Appl. math. modelling, 6, 390, (1982)
[45] Redekop, D.; Thompson, J.C., Comput. & structures, 17, 485, (1983)
[46] Paris, F.; De León, S., Int. J. numer. methods eng., 23, 173, (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.