The method of fundamental solutions for Signorini problems. (English) Zbl 0901.73017

Poullikkas, A.; Karageorghis, A.; Georgiou, G.

IMA J. Numer. Anal. 18, No. 2, 273-285 (1998).

Summary: We investigate the use of the mehod of fundamental solutions (MFS) for the numerical solution of Signorini boundary value problems. The MFS is an ideal candidate for solving such problems because inequality conditions alternating at unknown points of the boundary can be incorporated naturally into the least-squares minimization scheme associated with the MFS. To demonstrate its efficiency, we apply the method to two Signorini problems. The first is a groundwater flow problem related to percolation in gently sloping beaches, and the second is an electropainting application. For both problems, the results are in close agreement with previously reported numerical solutions.

MSC:

74B99	Elastic materials
74H99	Dynamical problems in solid mechanics
35R35	Free boundary problems for PDEs
86A05	Hydrology, hydrography, oceanography
78A55	Technical applications of optics and electromagnetic theory

Keywords:

boundary value problems; inequality conditions; least-squares minimization scheme; groundwater flow problem; percolation; electropainting