The Finite Ray Element Method For The Helmholtz Equation Of Scattering: First Numerical Experiments

Introduction. A new numerical method for the Helmholtz equation of scattering is presented. The method uses as basis function plane waves in a set of directions at every mesh node, multiplied by standard linear finite element basis functions. The motivation is that potentially one can use only a few basis functions with directions close to the dominant wave propagation directions, and with element size larger than the wavelength. This property was confirmed in our experiments and we have obtained high accuracy in a model problem using only few such directions. We have introduced an efficient criterion to identify dominant directions in a coarse approximation to the solution obtained by only few uniformly distributed directions present in the Finite Ray Element basis. The potential significance of the Finite Ray Element Method is that it allows to approximate the scattered field with a complexity that depends on the complexity of the field itself rather than on the wave number