Application of the matrix perturbation theory in the computation of internal fields in a three dimensional arbitrarily shaped biological body

A novel matrix perturbation theory for the matrix equation [A] [u] = [b] is presented. One of its applications, the computation of internal fields in a three-dimensional arbitrarily shaped heterogeneous biological body illuminated by a plane wave, is investigated. If we consider a normal biological body as the basic model and store its computation results, when the shape and/or the internal properties of the body change little, the internal fields in the changed body can be rapidly computed by using the normal results, which have been stored, from the matrix perturbation theory. Compared with the usual moment methods, the new theory not only has an equivalent precision, but can save some 70 times the execution time. This theory is especially suitable for the case when the biological body changes many times (for example, the body experiences many diseases).<>