Generating stable and sparse reluctance/inductance matrix under insufficient conditions

This paper presents generating stable and sparse reluctance/inductance matrix from the inductance matrix which is extracted under insufficient discretization. So far, to generate the sparse reluctance matrix with guaranteed stability, this matrix has to be diagonally dominant M matrix. Hence, the repeated inductance extractions are necessary using a smaller grid size, in order to obtain the well-defined matrix. Alternatively, this paper provides some ideas for generating the sparse reluctance matrix, even if the extracted reluctance matrix is not diagonally dominant M matrix, precisely, the positive off-diagonal elements are even found. This eases the extraction tasks greatly. Furthermore, the sparse inductance matrix is also generated by using the practical and sophisticated double inverse methods, which is useful for the SPICE simulation, since reluctance components are not still supported in SPICE- like simulators.