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Using an H2 matrix as the mathematical framework, we compactly represent a dense system matrix by a reduced set of parameters, thus enabling a significant reduction in computational complexity. The error bound of the H2-matrix-based representation of an electrodynamic problem was derived. We show that exponential convergence with respect to the number of interpolation points can be achieved irrespective of the electric size. In addition, we show that a direct application of H2 -matrix-based techniques to electrodynamic problems would result in a complexity greater than O(N), with N being the matrix size, due to the need of increasing the rank when ascending an inverted tree in order to keep a constant order of accuracy. A rank function was hence developed to maintain the same order of accuracy in a wide range of electric sizes without compromising computational complexity. With this rank function, we demonstrate that given a range of electric sizes which lead to a range of N, the dense system of O(N2) parameters can be compactly stored in O(N) units, and the dense matrix-vector multiplication can be performed in O(N) operations. Moreover, the same order of accuracy can be kept across this range. The method is kernel independent, and hence is suitable for any integral-equation-based formulation. In addition, it is applicable to arbitrary structures. Numerical experiments from small electric sizes to 64 wavelengths have demonstrated the performance of the proposed method. [ABSTRACT FROM AUTHOR]

A fast-marching time-domain layered finite-element reduction-recovery (LAFE-RR) method is proposed for high-frequency modeling and simulation of large-scale integrated circuits. This method increases the time step of the LAFE-RR method by three orders of magnitude. In addition, it preserves the computational efficiency of the LAFE-RR method, i.e., the matrix reduction is achieved analytically from a three-dimensional layered system to a single-layer one regardless of the original problem size, and the sparsity of the reduced single-layer system matrix is the same as that of the original system matrix. The method applies to any arbitrarily-shaped multilayer structure. Numerical and experimental results are given to demonstrate its validity. [ABSTRACT FROM AUTHOR]

A fast and high-capacity electromagnetic solution, time-domain layered finite element reduction recovery (LAFE-RR) method, is proposed for high-frequency modeling and simulation of large-scale on-chip circuits. This method rigorously reduces the matrix of a multilayer system to that of a single-layer system, regardless of the problem size. More importantly, the matrix reduction is achieved analytically, and hence the CPU and memory overheads are minimal. The recovery of solutions in all other layers involves only forward and backward substitution of matrices of single-layer size. The memory cost is also modest-requiring only the memory needed for the factorization of two sparse matrices of half-layer size. The superior performance applies to any arbitrarily shaped multilayer structure. Numerical and experimental results are presented to demonstrate the accuracy, efficiency, and capacity of the proposed method. [ABSTRACT FROM AUTHOR]

A high-capacity electromagnetic solution, layered finite element method, is proposed for high-frequency modeling of large-scale three-dimensional on-chip circuits. In this method, first, the matrix system of the original 3-D problem is reduced to that of 2-D layers. Second, the matrix system of 2-D layers is further reduced to that of a single layer. Third, an algorithm of logarithmic complexity is proposed to further speed up the analysis. In addition, an excitation and extraction technique is developed to limit the field unknowns needed for the final circuit extraction to a single layer only, as well as keep the right-hand side intact during the matrix reduction process. The entire procedure is numerically rigorous without making any theoretical approximation. The computational complexity only involves solving a single layer irrespective of the original problem size. Hence, the proposed method is equipped with a high capacity to solve large-scale IC problems. The proposed method was used to simulate a set of large-scale interconnect structures that were fabricated on a test chip using conventional Si processing techniques. Excellent agreement with the measured data has been observed from dc to 50 GHz. [ABSTRACT FROM AUTHOR]

An effective algorithm to construct perfectly matched layers (PMLs) for truncating time-domain finite-element meshes used in the simulation of three-dimensional (3-D) open-region electromagnetic scattering and radiation problems is presented. Both total- and scattered-field formulations are described. The proposed algorithm is based on the time-domain finite-element solution of the vector wave equation in an anisotropic and dispersive medium. The algorithm allows for the variation of the PML parameters within each element, which facilitates the efficient use of higher order vector basis functions. The stability of the resultant numerical procedure is analyzed, and it is shown that unconditionally stable schemes can be obtained. Numerical simulations of radiation and scattering problems based on both the zeroth- and higher order vector bases are presented to validate the proposed PML scheme. [ABSTRACT FROM AUTHOR]

This paper presents a general approach for the stability analysis of the time-domain finite-element method (TDFEM) for electromagnetic simulations. Derived from the discrete system analysis, the approach determines the stability by analyzing the root-locus map of a characteristic equation and evaluating the spectral radius of the finite element system matrix. The approach is applicable to the TDFEM simulation involving dispersive media and to various temporal discretization schemes such as the central difference, forward difference, backward difference, and Newmark methods. It is shown that the stability of the TDFEM is determined by the material property and by the temporal and spatial discretization schemes. The proposed approach is applied to a variety of TDFEM schemes, which include: 1) time-domain finite-element modeling of dispersive media; 2) time-domain finite element-boundary integral method; 3) higher order TDFEM; and 4) orthogonal TDFEM. Numerical results demonstrate the validity of the proposed approach for stability analysis. [ABSTRACT FROM AUTHOR]

An algorithm is presented to implement perfectly matched layers (PMLs) for the time-domain finite-element (TDFE) simulation of two-dimensional open-region electromagnetic scattering and radiation problems. The proposed algorithm is based on the TDFE solution of a special vector wave equation similar to the one in an anisotropic and dispersive medium. The impact of the PML on the stability of the resultant TDFE solution is studied for a variety of temporal discretization schemes, and it is shown that the proposed algorithm for implementing PML can support unconditionally stable TDFE schemes. Both the totaland the scattered-field formulations are described, and numerical simulations of radiation and scattering problems are presented to validate the proposed PML algorithm for the mesh truncation of the TDFE solution. [ABSTRACT FROM AUTHOR]

A novel hybrid time-domain finite element-boundary integral method for analyzing three-dimensional (3-D) electromagnetic scattering phenomena is presented. The method couples finite element and boundary integral field representations in a way that results in a sparse system matrix and solutions that are devoid of spurious modes. To accurately represent the unknown fields, the scheme employs higher-order vector basis functions defined on curvilinear tetrahedral elements. To handle problems involving electrically large objects, the multilevel plane-wave time-domain algorithm is used to accelerate the evaluation of the boundary integrals. Numerical results demonstrate the accuracy and versatility of the proposed scheme. [ABSTRACT FROM AUTHOR]

Presents a finite element-boundary integral (FE-BI) scheme for analyzing transient electromagnetic scattering from freestanding inhomogeneous objects. Description of the FE-BI scheme; Evaluation of boundary integrals; Accuracy of the FE-BI scheme.