Hybrid combinations of global and local operators for solving Helmholtz and Poisson equations

This paper addresses hybrid methods which employ analytic or asymptotic approaches as global operators and which employ numerical algorithms as local operators for studying physical phenomena in complex environments governed by Helmholtz and Poisson equations. Specifically, a ray-mode-boundary elements-finite elements method for analyzing wave scattering from a scatterer embedded in a waveguid is shown. This hybrid method can also be employed to analyze static problems as the source frequency becomes zero. Numerical results show smooth transition between static and dynamic responses.