Holistic / Monolithic Time Integration

This chapter discusses a number of techniques to solve the discrete systems of equations that result from the coupling of the circuit and electromagnetic field equations. We briefly summarize the modified nodal analysis for the lumped modeling of circuits. Then we discuss the coupling relations for including EM models into the circuit simulation systems and combine them with the spatially discretized Maxwell equations. Finally, we apply an adaptive time stepping scheme to the resulting coupled differential-algebraic equation system and in particular focus on a number of technical steps to find the solutions of the discretized coupled equations.