Method of Fundamental Solution (MFS) coupled with particle swarm optimization (PSO) to determine optimal phreatic line in unconfined seepage problem


1 Civil Engineering Department, Vali-e-Asr University of Rafsanjan, Rafsanjan, P.O. Box: 518, Iran

2 Kerman Graduate University of Technology, Kerman, P.O. Box: 76315-117, Iran


In this research, Method of Fundamental Solution (MFS) is coupled with Particle Swarm Optimization (PSO) technique to determine the optimal phreatic line in unconfined seepage problems. To model the unconfined boundary (phreatic line), a formulation with floating 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 unconfined boundary. MFS and PSO are utilized simultaneously to fit the phreatic line using 4thdegree polynomials, satisfying the flow continuity and energy principle. Efficiency and accuracy of the proposed method are verified through examples. The obtained results are in a good agreement with other numerical and experimental models.