An improved solution of open-region scattering problems using the finite element method

A method for reducing the total number of unknowns while enhancing the radiation boundary condition is introduced in connection with the use of the finite-element method to solve open-range scattering problems. The asymptotic form of the scattering field, described as an outgoing spherical wave or cylindrical wave modulating a scattering amplitude, is extended inward throughout the scattering region. The general scattering amplitude may vary with radial distance, although it is mainly nonoscillatory. The Helmholtz equation is rewritten in terms of scattering amplitude and is solved by the finite-element method. Due to the smooth nature of the scattering amplitude, the density of the finite-element mesh can be greatly reduced in the radial direction, decreasing the total number of unknowns. As a result, with this method the use of local boundary conditions becomes more attractive.<>