On matrix partitioning and the “add-on” technique

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For large scatterers whose operator is discretized by a prohibitively large matrix. It may be advisable to build the solution in a gradual manner while relying on previously known information on a portion of the body. In this way, rather than analyzing the large composite body, a succession of calculations of small additions is carried out, starting at the point where the partial solution is known. The “Add On” method, introduced recently, has done this successfully for a number of large planar problems. The method reconstructs the matrix solution without building the entire matrix up and without inverting It. A companion formulation, based on matrix partitioning, is used in this work to compare the “Add-On” technique with the matrix formulation. It is shown that the two formulations yield the same results. However, the numerical advantages of the “Add On” technique are clearly shown, especially with regard to storage problems, since the full N × N matrix need not be generated and stored. Instead, the responses to P sources are handled, making the storage requirements similar to an N × P matrix, where P is typically much smaller than N. Speed advantage is also seen In this method, where the maximum amount of computations, assuming no previously known Information, is proportional to N2 or N2.5, depending on the problem at hand. Examples with up to 6000 unknowns have been worked out and are presented below.

Original languageEnglish
Pages (from-to)331-344
Number of pages14
Issue number3
StatePublished - 1 Jan 1989


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