Technique and program code constituting use of local-global solution (LOGOS) modes for sparse direct representations of wave-like phenomena

摘要

A technique for implementation employing a computerized device and associated computer executable program code, for obtaining a direct solution of a linear system of equations, comprising a unique routine. The method can be employed for characterizing wave phenomena—of the electromagnetic and acoustic type—to aid in the design of a structure around which the wave phenomena will scatter; the method is useful for linear system of equations consisting of a plurality of sparse matrix equations, and a plurality of compressed representations of full matrix equations. The routine includes: using a plurality of solution modes, J, that are localized to a subdomain of a larger simulation domain, the plurality of solution modes also satisfying an original system equation of the form: ZJ=Eⁱ, where Z represents an impedance matrix, and Eⁱ represents a forcing vector. Using a basis of local solutions that satisfy the original system equation, ZJ=Eⁱ, a plurality of compressed representations of solution operators can be obtained comprising a product of matrices, (A₁ A₂ . . . A_n), wherein each A_i represents a matrix having been derived from information taken from the matrix Z, such that J=(A₁ A₂ . . . A_n) Eⁱ; the plurality of solution modes, J, having been obtained from a plurality of forcing vectors, Eⁱ. Both ‘non-radiating’ and ‘radiating’ scenarios are contemplated.