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Solving waveguide eigenvalue problem by using radial basis function method

Traditional mesh-based methods achieve poor eigenvalue accuracy at high order modes in waveguide. A meshless method based on radial basis function was introduced to settle such issue. Collocation principles of RBF coupled with polynomials were expounded. Ideas on how to solve eigenvalue problems with RBF were presented and corresponding discrete equations were founded. Numerical experiments on rectangle, ridge and cylindrical waveguides were carried out both with FEM and RBF method. All the experiments show that RBF method not only obtains more accurate eigenvalues at high order modes, but also acquires higher precision results with fewer nodes than FEM. Moreover, RBF method is insensitive to spatial dimension and can be realized easily.