ABSTRACT
This chapter covers direct decomposition-based methods. Two main types of circuit decomposition can be distinguished: nodal decomposition and branch decomposition. Both can be viewed as a decomposition of the circuit graph or circuit equations. Decomposition of linear equations can be formally represented as partitioning of graphs or a system of equations. The bordered block diagonal structure equations are the foundation of decomposition-based methods. Timing simulation algorithms for large-scale circuits give time-profiles of signals about a few hundreds of times faster than direct methods. However, they suffer from limitations introduced by relaxation methods. In the classification of concurrent simulation techniques, the relaxation techniques are essential. They use decoupling of equations, and the separate solution of each part. Decoupling into individual equations is known as nodal decoupling. Decoupling can be applied to different levels of equation transformation. Three such levels are: the algebraic-differential equations level; the discretized nonlinear algebraic equations level; and the linearized discretized algebraic equations level.
