Matrix Order Reduction by Nodal Analysis Formulation and Relaxation-Based Fast Simulation for Power/Ground Plane

Block-Latency Insertion Method (Block-LIM) for Fast Transient Simulation of Tightly Coupled Transmission Lines

“…This is because the difference equations (1) and (2) include respectively only one variable, and therefore, these equations are not solved implicitly by the matrix solver but solved explicitly and result in the explicit forms of the updating formulas. This scheme is analogous to the relaxation-based method for the circuit simulations, which separates the simultaneous equation into several individual equations and solves them individually [5]. In fact, it is noted in [8] that the basic LIM formulation introduced in II is a scalar version of the FDTD-like formulation.…”

“…The topology of the transformed branch is the one completely required for the block-LIM formulation. Since the value of the CCCS is defined as (11) and multiplied by R m to transform to the voltage source, the nonzero elements associated with the CCCS are stamped in the off-diagonal parts of the resistance matrix R ab in (5). Actually, the updating formula of the currents in the branch block with CCCSs is derived by replacing R ab in (5) with the resistance matrix…”

“…Our recent research indicates that the latency insertion method (LIM) in [1] could be one of the important methods for the fast simulation of large networks [2]- [4]. Ultimately, a method which circumvents the matrix operation such as LIM and the relaxation-based method in [5] are imperative for the simulation of recent extremely highspeed and high-density circuits.…”

Block latency insertion method (Block-LIM) for fast transient simulation of tightly coupled transmission lines

“…This is because the difference equations (1) and (2) include respectively only one variable, and therefore, these equations are solved by only transformations of the equations and result in the explicit forms of the updating formulas. This is analogous to the relaxation-based method which separates the variables in a circuit equation and solves for them individually [4]. In fact, it is referred in [7] that the basic LIM formulation introduced in II is a scalar version of the FDTD-like formulation.…”

“…Our recent researches indicated that the latency insertion method (LIM) in [1] could be one of the noticeable methods for the fast simulation of large networks [2], [3]. Ultimately, the method which circumvents the matrix operation such as LIM and the relaxation-based method in [4] is imperative for the simulation of the recent extremely high-speed and high-density circuits.…”