A theoretical proof on the error-bounded low-rank representation of integral operators for large-scale 3-D electrodynamic analysis

We theoretically prove that the minimal rank of the interaction between two separated geometry blocks in an integral-equation based analysis of general 3-D objects, for a prescribed error bound, scales linearly with the electric size of the block diameter. We thus prove the existence of the error-bounded low-rank representation of both surface and volume based integral operators for electrodynamic analysis, irrespective of electric size and scatterer shape. Numerical experiments have verified its validity. This work provides a theoretical basis for employing and further developing the low-rank matrix algebra to accelerate the computation of large-scale electrodynamic problems.