The inversion of electro-heat problems is important in areas such as electrical machine design, the metallurgical processes of mixing, and hyperthermia treatment in oncology. One of the important computations involves synthesizing the electromagnetic arrangement of coils to accomplish a desired heat distribution to achieve mixing and reduce machine heat, or to 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 optimizing the shape of the current source. 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 finite element field computations and to cut down solution times. In our work, given the heavy computational load from the two-part problem and the attendant optimization, we use the GPU to perform the electro-heat optimization by the genetic algorithm launched on several parallel threads to achieve computational efficiencies. To avoid the complexities of a two-physics problem, we first develop the shaping algorithms on a single physics problem for nondestructive evaluation. This shape optimizing concept is developed for defect characterization in a steel plate. When a steel plate in a ground vehicle is found to be defective, it is usually taken out of service for repair without determining if the defect warrants withdrawal. We investigate and establish a procedure so that a decision to withdraw a vehicle may be justifiable and ensures the safety of the vehicle and its passengers. To test our algorithms and seek novel use, they were employed in a semester’s course on finite elements and optimization with true device design. Flip-teaching was introduced to tackle the challenges of time. The traditional order of a) delivering theory b) programming ancillary tools (mesh generators, solvers) is flipped to do real design. After the algorithms were understood from use in NDE and the flip-teaching experience, we successfully developed them for the two-physics system with reduced computational time with the speedup (CPU Time to GPU time ratio) of 28 and increased accuracy established through the problem of shaping a current carrying conductor so as to yield a constant temperature along a line. Finally we applied the electro-thermal software to hyperthermia treatment planning by a numerical model of a human thigh with a tumor treated by current carrying conductors to be shaped to produce the desired temperature at the tumor. The bio-heat equations under steady state condition are solved and the heat removal due to blood perfusion is also taken into account to determine the shape yielding the desired temperature profile. An efficient methodology for multi-physics systems has been developed with applications in flip-teaching, NDE and hyperthermia.
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