Inversion of Heavy Current Electroheat Problems on a Graphics Processing Unit (GPU)

The inversion of electroheat problems is important in electrical machine design, metallurgical processes of mixing, and hyperthermia treatment in oncology. One of the important computations involves synthesizing the electromagnetic arrangement of coils so as to accomplish a desired heat distribution to achieve mixing, reduce machine heat or burn cancerous tissue. Two finite element problems need to be solved, first for the magnetic fields and the joule heat that the associated eddy currents generate and then, based on these heat sources, the second finite element problem for heat distribution. This two part problem needs to be iterated on to obtain the desired thermal distribution by optimization. This represents a heavy computational load associated with long wait-times before results are ready. The graphics processing unit (GPU) has recently been demonstrated to enhance the efficiency of the finite element field computations and cut down solution times. In this paper, given the heavy computational load from the two-part problem and the optimization, we use the GPU to perform the electroheat optimization by the genetic algorithm to achieve computational efficiencies better than those reported for a single finite element problem. The feasibility of the method is established through the simple problem of shaping a current carrying conductor so as to yield a constant temperature along a line. Submitted to journal Mathematics Problems in Engineering