Boundary element method based on preliminary discretization

The final publication is available at Springer via http://dx.doi.org/10.1134/S2070048214020082A new numerical method for solving wave diffraction problems is given. The method is based on the concept of boundary elements; i.e., the unknown values are the field values on the surface of the scatterer. An analog of a boundary element method rather than a numerical approximation of the initial (continuous) problem is constructed for an approximate statement of the problem on the discrete lattice. Although it reduces the accuracy of the method, it helps to simplify the implementation significantly since the Green functions of the problem are no longer singular. In order to ensure the solution to the diffraction problem is unique (i.e., to suppress fictitious resonances), a new method is constructed similarly to the CFIE approach developed for the classical boundary element method.Peer Reviewe