## Grants and Contracts Details

### Description

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.

Status | Finished |
---|---|

Effective start/end date | 5/1/04 → 5/15/11 |

### Funding

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

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