Solution of resistive meshes by deterministic and Monte Carlo transmission-line modelling

The conventional random-walk and conventional adjoint random-walk processes for the solution of general resistive networks are summarised. Particular attention is paid to resistive meshes which model potential and diffusion fields. The paper proceeds to introduce a new single-step simultaneous-displacements method for general resistive networks through the concept of transmission-line modelling (TLM). A demonstration of the method is given for a potential problem. The Monte Carlo method implied by deterministic TLM is then defined for general resistive networks. This new statistical process is evaluated and discussed in the context of potential and diffusion fields.