Multiple multipole method for simulating EM problems involving biological studies

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Abstract
The three-dimensional implementation of the multiple multipole (MMP) method, based on the generalized multipole technique (GMT), is presented. Its performance in simulating electromagnetic problems involving biological bodies is analyzed. In particular, the step-by-step simulation technique and the built-in procedures to validate the solution on numerical basis are discussed and demonstrated in two examples. A comparison is made with other numerical techniques often applied in this field. The advantages of the MMP method are shown to be in its validation capability, in its efficiency for smoothly shaped bodies and in the achievable accuracy, in particular near boundaries. The method is especially suited to handle high-gradient fields in the vicinity of biological bodies. On the other hand, finite difference (FD) techniques are superior for scatterers with complicated angular shapes or inhomogeneous bodies, for which MMP shows rather strong practical limitations. However, in most cases the inhomogeneities of biological bodies modify the field distribution only locally beyond the uncertainties of models. In these cases, inhomogeneities can be stimulated efficiently and with high accuracy by MMP applying the block iterative technique. Other methods are not general enough to compete with FD or MMP in solving EM problems involving biological tissues.

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