Boundary element method with particle swarm optimization for solving potential problems

Abstract

In this paper, the boundary element method (BEM) based on the particle swarm optimization (PSO) algorithm is proposed for solving potential problems. At present, the traditional Gaussian elimination method still needs to improve for computing results accuracy. The PSO algorithms with substantial accuracy used to improve the accuracy of potential problems. So it is introduced the PSO to solve the system of matrix equations derived from the boundary integral equation (BIE). For the presented method, unknown solutions to the system of matrix equations are considered particles, and the optimal solution is sought through group collaboration. Some parameters in this model play a vital role, so confirming them and initializing the positions and velocities of the particles are needed. Then, the positions of the particles are constantly updated with the iteration formula until obtained the optimum solutions. Furthermore, the optimum solution are arrived at in which the cycle is jumped when meeting the conditions (i. e. given the maximum number of iterations or the fitness value). There are examples with constant element and linear element and quadratic element types of boundary, in turn. The three numerical models of 2D potential problems are analyzed and discussed. They certified that the PSO algorithm has feasibility and good convergence. Most importantly, it is proved that the PSO applied in BEM has higher accuracy compared with the Gaussian elimination method for solving potential problems.