Method of Fundamental Solution (MFS) coupled with Particle Swarm Optimization (PSO) to determine optimal phreatic line in uncon ned seepage problem

In this research, Method of Fundamental Solution (MFS) is coupled with Particle Swarm Optimization (PSO) technique to determine the optimal phreatic line in unconned seepage problems. To model the unconned boundary (phreatic line), a formulation with oating geometry is derived. Regarding the use of fundamental solution of the Laplace equation, expressed in the Radial Basis Functions (RBF), a boundary type of the mesh-free method can be established. In this research, an objective function, based on principle of minimum potential energy, is formed to control the position of unconned boundary. MFS and PSO are utilized simultaneously to t the phreatic line, using 4th degree polynomials, satisfying the ow continuity and energy principle. Eciency and accuracy of the proposed method are veried through examples. The obtained results are in a good agreement with other numerical and experimental models.