A three-dimensional (3D) non-overlapping domain decomposition method for analyzing electrical-thermal contact problems is presented. The computational domain is subdivided into non-overlapping regions discretized according to the Cell Method. Voltage and temperature drops at the contact interfaces are modeled by means of boundary constitutive operators. Continuity between sub-domains is enforced with Lagrange multipliers. The coupled non-linear problem is cast into a saddle-point form ensuring existence and uniqueness to the solution.
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