Diacoptic basis function grouping techniques applied to the Method of Moment solution of (M)MIC-Structures

For the analysis and design process of (M)MIC structures, electromagnetic simulators based on the method of moments (MoM) are widely used due to their high accuracy and good modeling capabilities. For the standard MoM using an explicit system matrix, many improvements could be achieved for a faster and more accurate computation of the matrix entries. The solution of the linear systems of equations typically remains the most cumbersome part of the MoM. An important class of methods to improve the solution process was initialized by the diacoptic theory of linear antennas. This theory is based on a component decomposition and is therefore not restricted to the analysis of wire antennas but is particularly well suited for (M)MIC structures with its typical circuit component subdivision. Diacoptic strategies are mainly based on the use of so-called macro basis functions (MBs). leading to multilevel MoM implementations. In our contribution, we first compare different versions of the two-level approach in S. Ooms and D. De Zutter (IEEE Trans. Microwave Theory and Tech., vol. 46, no. 3, pp. 280-291, 1998), combined with an advanced description of the macro basis function decomposition. Furthermore it is shown that the derived matrix decomposition can be used for a very effective preconditioning strategy applied to Krylov subspace methods. It results in excellent convergence properties without the explicit current profile determination of the MBs, which is cumbersome or not reasonable in many cases.