The method of summary representation developed by G. N. Polozhii is a quasi-analytical method for solving self-adjoint, finite-difference boundary value problems expressed on regular meshes. In principle, the method should allow considerable savings in computing time as well as improved accuracy when compared to commonly used finite-difference schemes. We have used summary representation as the basis for a new hybrid scheme to solve the two-dimensional Helmholtz equation for electromagnetic modeling. The theory behind this hybrid scheme is presented. Preliminary results for the two-dimensional problem show that substantial computing time and storage savings can be made.

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