The measured equation of invariance (MEI) is a new concept in computational electromagnetics. It has been demonstrated that the MEI technique can be used to terminate the meshes very close to the object boundary and still strictly preserves the sparsity of the finite-difference (FD) equations. Therefore, the final system matrix encountered by the MEI is a sparse matrix with a size similar to that of integral equation methods. However complicated the Green's function, disagreeable Sommerfeld integrals, and very difficult umbilical meshes for multiconductors make the traditional MEI very difficult (if not impossible) to be applied to analyze multilayer and multiconductor interconnects. In this paper, the authors propose the geometry independent MEI (GIMEI) which substantially improves the original MEI method. The authors use GIMEI for capacitance extraction of general two-dimensional (2-D) and three-dimensional (3-D) very large scale integration (VLSI) interconnect. numerical results are in good agreement with published data and those obtained by using FASTCAP from Massachusetts Institute of Technology (MIT) and some other commercial tools, while GIMEIs are generally an order of magnitude faster than FASTCAP with much less memory usage.

Fast parameter extraction of general interconnects using geometry independent measured equation of invariance

In this paper, the domain-decomposition method (DDM) has been used to extract the capacitance matrices of multilayered three-dimensional (3-D) interconnects in very-large-scale integration (VLSI) circuits. Different subdomains are analyzed separately, so the most efficient method can be chosen for every subdomain. Therefore, the DDM can greatly reduce the algorithm complexity and provide a good platform for the development of combining methods. Numerical results show that the computing time and memory size used by the DDM are more than ten times less than those used by Ansoft's Maxwell SpiceLink-and more importantly, they are unrelated to the thickness of the pure dielectric layers.

An efficient algorithm for the parameter extraction of 3-D interconnect structures in the VLSI circuits: domain-decomposition method

In this study, the method of lines (MOL) has been applied to solve two-dimensional vertically integrated shallow water equations in Cartesian coordinates for the prediction of water levels due to a storm surge along the coast of Bangladesh. In doing so, the partial derivatives with respect to the space variables were discretized by the finite difference (central) method to obtain a system of ordinary differential equations (ODEs) with time as independent variable. The classical fourth-order Runge–Kutta method was used to solve the obtained system of the ODEs. We used a nested finite difference scheme, where a high resolution fine grid model (FGM) capable of incorporating all major islands along the coastal region of Bangladesh was nested into a coarse grid model (CGM) covering up to 15°N latitude of the Bay of Bengal. The boundaries of the coast and islands were approximated through proper stair step. Appropriate tidal condition over the model domain was generated by forcing the sea level to be oscillatory with the constituent M
 2 along the southern open boundary of the CGM omitting wind stress. Along the northeast corner of the FGM, the Meghna River discharge was taken into account. The developed model was applied to estimate water levels along the coast of Bangladesh due to the interaction of tide and surge associated with the April 1991 storm. We also computed our results employing the standard finite difference method (FDM). Simulated results show the MOL performs well in comparison with the FDM with regard to CPU time and stability, and ensures conformity with observations.

Implementation of method of lines to predict water levels due to a storm along the coastal region of Bangladesh

Computation of capacitance matrix for integrated circuit interconnects using semi-analytic Green's function method

An efficient approach to forecast water levels owing to the interaction of tide and surge associated with a storm along the coast of Bangladesh

A new technique is implemented in the method of lines to extract the capacitance and inductance matrices of a multiconductor interconnection embedded in a multilayered lossy dielectric region. Using the concept of equivalent transmission lines the electromagnetic problem is turned into a simple network problem. This technique avoids the problem associated with Green's function in the multilayered region and makes the deduction process almost independent of the number of dielectric layers and conductors. Based on the extracted parameters a bilevel waveform relaxation method is used to compute the transient response of such a system terminated in arbitrary loads.

http://ieeexplore.ieee.org/iel1/2196/12032/00553644.pdf

Electromagnetic modelling and transient simulation of interconnects in high speed VLSI circuits

In this paper, one type of waveguide three-dimension discontinuity, rectangular waveguide inserted by a metallic sheet of arbitray shape with zero thickness, is firstly analysed by using the Method of Lines. This waveguide discontinuity can be regarded as basic unit of microwave and MMW passive components and active circuits. Numerical results are in good agreement with physical meanings and other published data. Numerical results of several characteristics are presented at the end of the paper, including convergent characteristic of which the scattering parameters are depended on the number of discretization lines, dependence of scattering parameters on the size of metallic sheet and frequency response of scattering parameters.

Analysis of waveguide inserted by a metallic sheet of arbitrary shape with the method of lines

A new technique is implemented in the method of lines to calculate the static parameters of a multilayered multiconductor system. Every dielectric layer is equivalent to a transmission line and every interface with conductors is equivalent to a current source, thus the whole structure is equivalent to a series of cascading two port networks. A bilevel waveform relaxation method is then used to compute the transient response of such a system terminated in arbitrary loads. All these are integrated into a software specially for the interconnect problems and one of its typical applications is presented.

Electromagnetic modeling and transient simulation of interconnects in high speed VLSI

In this paper we have presented a novel approach for active antenna optimization. The results from our work have demonstrated the feasibility and efficiency of the combination of PHB and the neural network.

Analysis of active antenna by using piecewise harmonic balance technique and neural network

In this paper, the scattering parameters of a waveguide cross junction loaded with a metallic post in the center are analyzed for the first time by using the Method of Lines. The homogeneous boundary condition of the third kind and curved boundary are introduced in the formulation. Numerical results are in good agreement with the experimental data. The scattering parameters at Ka-band and W-band of the cross junctions loaded with metallic posts of different radii are presented. It is shown from the numerical results that loaded with metallic posts is an effective means for adjusting the network parameters of the waveguide cross junction to satisfy some special requirements in the design of millimeter wave components.

Yun-Yi Wang

Papers

Electromagnetic modelling and transient simulation of interconnects in high speed VLSI circuits

Analysis of waveguide inserted by a metallic sheet of arbitrary shape with the method of lines

Electromagnetic modeling and transient simulation of interconnects in high speed VLSI

Analysis of active antenna by using piecewise harmonic balance technique and neural network

Scattering parameters of a waveguide cross junction loaded with a metallic post in the center