A three-dimensional (3D) 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 modelled by means of boundary constitutive operators. Continuity between sub-domains is enforced with Lagrange multipliers. The final non-linear algebraic system is solved by an iterative Newton procedure combined to a Schur's complement approach in order to reduce the problem size and improve the condition number. Potential and temperature jumps across the contact interface depend on the local surface conditions according to Holm's theory. Surface roughness and a-spot density in the contact area are modelled by means of statistical parameters that can be easily embedded into a CM formulation. The developed code has been validated by a 3D FEM commercial software package.
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