Analytical validation of time‐step interpolation in transient insular nodal analysis

Abstract

The transient insular nodal analysis method (TINA) combines elements from the finite differences (FD) and transmission‐matrix methods (TLM) in one unified approach. In contrast to existing TLM‐FD methods, TINA uses time‐decoupled cells, avoiding the need for solving large system matrices. The time‐decoupled cells allow for easy parallelisation, and the solution of large systems in detail. Due to the use of an exact transmission‐line model in the cells, wave propagation can be computed without the need for discretisation of the equations, nor the use of prediction, yielding an unconditionally stable method. Boundary conditions are implicit, and are solely defined by the wave speed and characteristic impedance of the medium. One key difference with the TLM method is how cells whose transmission time is not an integer multiple of the simulation time step are integrated in the simulation. These mismatches occur due to the the varying wave speeds of the different media in the cells. In TINA, the match is obtained through interpolation, as opposed to the stub‐matching methodology employed in TLM. In this paper, we will demonstrate the validity of the interpolation approach analytically, as well as compare the TINA method to a theoretical case.