SLIM - A SLENDER TECHNIQUE FOR UNBOUNDED-FIELD PROBLEMS

Electrostatic- and electromagnetic-field problems in unbounded regions are often solved using finite differences (FD's) or finite elements ( FE) combined with approximate boundary conditions. Inversion of the sp arse FD or FE matrix is then required. First-order or higher order abs orbing boundary conditions may be used, or one can use more accurate b oundary conditions obtained by the measured equation of invariance (ME I) or by iteration. The more accurate boundary conditions are helpful because they permit reduction of the size of the mesh and, thus, the n umber of unknowns. In this paper, we show that the process can be carr ied to a maximally simple limit in which the mesh is reduced to a sing le layer and the matrix-inversion step disappears entirely. This resul ts in the single layer iterative method (SLIM), an unusually simple te chnique for unbounded-field problems. Computational experiments demons trate the effectiveness of SLIM in electrostatics, and also in electro dynamic examples, such as scattering of TM plane waves from a perfectl y conducting cylinder. The technique is most likely to be useful in la rge or complex problems where simplification is helpful, or in repetit ive calculations such as scattering of radiation from many angles of i ncidence.