Efficient Iterative and Direct Solvers for Electromagnetic Simulations

Grants and Contracts Details


The development of efficient and stable algorithms for numerical simulations of large-scale electromagnetic radiation and scattering problems is proposed. The core of the proposed research program is the integration and extension of two recent and complementary developments in integral equation methods. The Simply Sparse method (SSM) is a general, physically-motivated compression algorithm for integral equation formulations of electromagnetic phenomena. An important feature of the algorithm is the ease with which it can be applied to diverse scattering and radiation configurations. Because the algorithm relies on unitary transformations to obtain a sparse representation, the SSM permits the relatively efficient application of both iterative and direct solution methods to the transformed linear system. Independently of the SSM, recent progress has also been made in developing new integral equation formulations for electromagnetic interactions with penetrable and impenetrable targets. Unlike the integral equations of classical electromagnetic theory, these new formulations yield matrix equations which are stable with respect to changes in frequency, discretization mesh, and material properties (e.g., dielectric constant, conductivity). The new integral equations also provide a more direct incorporation of the underlying physical phenomena. For example, Neumann iteration of the new formulations reproduces the physical optics series in the high frequency limit, including shadowing through multiple boundaries, for both penetrable and impenetrable targets. The improved computational efficiencies provided by both the Simply Sparse compression algorithm and the new physics-based integral equations are a result of developing numerical algorithms which mimic essential properties of the underlying physical processes. By combining the insights provided by each set of techniques, we propose to develop new algorithms which will provide significant computational savings relative to those provided by either the Simply Sparse method or the new integral equations in isolation.
Effective start/end date5/1/045/15/11


  • Office of Naval Research: $1,139,820.00


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