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We present an e cient, stable, recursive T-matrix algorithm to calculate the scattered eld from a heterogeneous collection of spatially separated objects. The algorithm is based on the use of higher-order multipole expansions than those typically employed in recursive T-matrix techniques. The use of these expansions introduces instability in the recursions developed in 5, 6] speci cally in the case of near-eld computations. By modifying the original recursive algorithm to avoid these instabilities we arrive at a exible and e cient forward solver appropriate for a variety of scattering calculations. The algorithm can be applied when the objects are dielectric, metallic, or a mixture of both. We verify this method for cases where the scatterers are electrically small (fraction of a wavelength) or relatively large (1-2). While developed for near-eld calculation, this approach is applicable for far-eld problems as well. Finally, we demonstrate that the computational complexity of this approach compares favorably with comparable recursive algorithms.

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