Study on Complex Geometric Boundary Problems in Hamiltonian system

Based on the Hamiltonian system, a numerical method of boundary integral is proposed for solving the problems of mechanical boundary conditions, especially those with complex geometric boundary. This method is based on the eigensolution of analytic form and realizes the solution of the problem through twice integration. On the one hand, the eigenvalue equation is established by directly integrating the eigenvalues of analytic form on the boundary, and the eigenvalues corresponding to the eigenvalues can meet the boundary conditions in an average sense; on the other hand, taking the eigenvalues of each order as the weight function, through the weighted integration on the boundary, the algebraic equations on the expansion of the eigenvalues are established to realize the Effective handling.