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A method for the solution of the equations of electromagnetics and heat transfer for high-power electric arc furnaces by means of a parallel computer network is outlined. The numerical scheme chosen to solve the electromagnetic problem is based on a generalized control-volume scheme. The approach taken is an attempt to ensure compatibility of the analysis as it extends to incorporate the equations of fluid mechanics and heat transfer. The system is cast into a concurrent computational framework that allows the inclusion of related systems without the degradation of computational effort associated with segregated serial numerical algorithms. Typical results relating to the behavior of six electrode arc furnaces are included.