A novel subgridding scheme for the distributed TLM modeling of thin layers - Isele, Bertram; Mangold, Tobias; Weigel, Robert; Russer, Peter (Progress in Electromagnetics Research Symposium, 1997)
The present work arose from a requirement of accurate time domain modeling of inter- connections in multichip modules (MCM's). As is the case with similar methods, the Transmission-Line-Matrix (TLM) method provides the feasibility to handle nearly any geometry and is not restricted to planar geometries. However, the modeling of circuits consisting of elements with strongly varying geometrical dimensions such as thin layers is not suitable for a conventional discretization due to limited computational resources. Also the use of graded meshes is very limited since the dispersion characteristic of these meshes becomes worse. For metalic layers surface-impedance models may be used which yield accurate broadband frequency characteristics [3]. In general, a local mesh refinement is required to increase the spatial resolution. Such subgridding techniques enable the mesh to carry for details, which could not be resolved by a coarse mesh. The combining of fine and coarse meshes requires for a careful investigation at the interface. In [1] the following conditions are postulated for the coarse mesh/fine mesh interface: energy conservation (i), charge conservation (ii), zero reflection (iii) and zero delay (iv). In the subgridding model, proposed by [1] the wave amplitudes incident from the coarse mesh to the fine mesh are kept constant during the time step within the coarse mesh. This introduces some lag in the interfering of the sub meshes. In contrary, we use a recursive description, in which also the incident pulses from the coarse mesh are adjusted to the updated field situation on the fine mesh. In this improved subgridding model additional transforma- tions between the wave amplitudes and the field quantities are necessary, which can be done exactly only at the cell boundaries of the TLM nodes. Our algorithm is completely embedded in a TLM simulation package utilizing distributed computing making best use of the available resources [2]. We use the Parallel Virtual Ma- chine (PVM) as an environment for the distributed computing. The simulations are done within clusters of interconnected workstations and parallel computers. The subgridding model was tested for several scenarios and has been approved to satisfy the previously mentioned conditions. The method was applied to the simulation of interconnections in multichip modules, where the thickness of some intermediate layers was more than one order of magnitude smaller than the transversal dimensions of the remaining elements. The improved subgridding approach opens a wide range of applications for the TLM method and benefits inherently from the flexibility of distributed computing.
elib2cris::1512001600,isele1997