Algorithm Research On Cavity Electromagnetic Scattering

In this paper,several related problems in the field of cavity electromagnetic scattering are studied.Using the idea of a high-order fast algorithm proposed for single cavity electromagnetic scattering calculation,this paper proposes a multi-cavity electromagnetic scattering fast algorithm and a fast solution method for three-dimensional Helmholtz equation.For the regular rectangular multi-cavity problem,by introducing transparent boundary conditions,the boundaryless scattering problem is transformed into a problem that internally satisfies the Helmholtz equation and couples non-local boundary conditions on the aperture surfaces of multiple cavities.This method can deal with the violent oscillation of numerical solutions under large wave numbers.Numerical experiments are carried out to verify the effectiveness of the proposed algorithm.For the three-dimensional problem,we propose a fourth-order fast algorithm for solving the three-dimensional Helmholtz equation,and deduced the Dirichlet boundary condition and the Neumann boundary condition respectively.By introducing the Fourier sine transform operator,the large system is disassembled into a series of small independent systems,which greatly speeds up the solution.In addition,the method also has a good structure corresponding to the coefficient matrix of the linear system,which enables us to easily use the parallel processor to accelerate the solution of the equation.This implementation is very effective for solving numerical solutions on a particular surface within a domain.A large number of numerical experiments have shown that the algorithm has fourth-order accuracy,and the fast algorithm is effective for two different boundary conditions.