Introduction: In hyperthermia treatment planning cancerous tissue is elevated in temperature. This elevation must be targeted. If too low, nothing happens, if too high good tissue is also burnt. At the right temperature, around 42^oC, cancerous tissue is burnt.

A finite element program models the exciting coils surrounding the diseased human body part such as the thigh afflicted by cancer. The problem is to optimize the shape  and location of the exterior exciting coils so as to accomplish the desired temperature in the afflicted part.

Methods and Results: This paper describes the two-part optimization problem to determine the shape and location of the exciting coils. The first finite element problem solves for the electric filed E which gives the Joule heating in the various parts of the body. This Joule heating then sources the second finite element problem of determining the resulting temperature distribution.

Conclusions/implications: The challenge is that the object function is in the temperature problems, while the parameters being optimized are in the first electric field problem. Material properties are adjusted as the temperature changes. Excellent results are obtained for the coil distribution to obtain the desired temperature distribution in a human thigh.