Jin Fa Lee

Optimization of subgridding schemes for FDTD

A procedure to optimize the coupling coefficients between fine and coarse mesh regions for two-dimensional (2-D) finite-difference time-domain (FDTD) subgridding algorithms is introduced. The coefficients are optimized with respect to different angles and expanded in a form suitable for FDTD computation.

An approach for automatic grid generation in three-dimensional FDTD simulations of complex geometries

The finite-different time-domain (FDTD) method has become a popular method in computational electromagnetics because of its simplicity, flexibility, and efficiency. However, the process of generating a three-dimensional (3D) FDTD grid can be time-consuming and error-prone when manually manipulating complex geometries. In order to expedite the generation of FDTD grids, computer-graphics-based methods can alternatively be used. Starting from the geometric description of the problem domain given by a CAD file, an FDTD grid with a specific spatial resolution can be automatically produced. A simple algorithm to this end is discussed, along with sample results.

Filtering schemes for dispersion-optimized FDTD algorithms

IGH order FDTD methods have been proven to be an effective way of reducH ing numerical dispersion error [1]-[7]. Traditional high order methods can be improved upon in different ways. In some cases, it is important to optimize the method to allow for reduced dispersion only around a pre-assigned angular sector (i.e., in the case of highly elongated FDTD domains). In other cases, the dispersion error should be minimized around a pre-assigned frequency band, but not necessarily for low frequencies. The so-called Angle-Optimized FDTD (AO-FDTD) [SI and Dispersion-Relation-Preserving FDTD (DPR-FDTD) [9] have been recently proposed to optimize (high order) FDTD methods with these respective objectives in mind. In this paper, we shall describe the use of filtering schemes to further improve the performance of those techniques in a wide band of frequencies. For simplicity, we shall restrict ourselves here to 2-D cases with homogenous cell size h.

Single level dual rank SVD algorithm for volume integral equations of electromagnetic scattering

Electromagnetic scattering from arbitrarily shaped inhomogeneous dielectric bodies has been an interesting topic due to its importance in problems that include propagation through inhomogeneities. This paper presents a novel single level dual rank SVD algorithm that efficiently compresses the system matrix to reduce the memory requirement and CPU time for both matrix assembly and matrix-vector multiplication to O(N/sup N2/). The dual rank SVD algorithm is based on the rank deficiency feature of the integral equation for well-separated groups of basis functions. The algorithm forms the Q-R factorization of rank deficient local matrices due to non-self group interactions by ranking the most linearly independent basis functions in the transmitting (source) group and the most significant ones in the receiving (observation) group.

An O(N) multilevel solver for dense method of moment systems in electrostatic applications

Integral equation methodologies applied to extract parasitics at the board, package and on-chip levels involve solving a dense system of equations. In this paper, we present a multilevel matrix compression algorithm that reduces both computational complexity and memory requirement to O(N) for N number of unknowns. The approach is based on the adaptive cross approximation method that exploits the rank deficiency of matrix blocks for physically separated groups of basis functions without explicitly dealing with the integral equation kernel. Hence the proposed method is practical for large-scale problems and can be implemented in a wide range of applications with a few or no modifications.

Automatic grid generation of complex geometries for 3D FDTD simulations

The application of the finite-difference time-domain (FDTD) method for solving problems in complex geometries usually requires a costly and time-consuming process of manually creating the FDTD grid. We introduce an automatic grid generation technique to produce three-dimensional (3D) FDTD grids of complex geometries directly from the input CAD data files. This technique reduces the cost and the time associated with a manual grid generation, and minimizes possible errors on the geometric depiction of the objects. The focus of our automatic FDTD grid generation algorithms is for 3D applications. In the implementation of this algorithm, we assume that the objects within the problem domain are bounded, and the cells in the FDTD grid are uniform. The approach uses methods adapted from computer graphics applications, and results in a robust and efficient algorithm for automatic FDTD grid generation. The benefits are in the increasing speed of the process and the reduction of the complexity in manually creating the FDTD grids. Even though the main focus of approach is for finite volume objects, infinitely thin surfaces can also be represented by the algorithm with few modifications.

Multi-scale structures analysis using automatic h-refinement and Discontinuous Galerkin Integral Equation.

This work describes an automatic tool able to estimate the error in the Integral Equation solution in order to refine the mesh where the error is higher than the chosen threshold. The local refinement is performed through a hierarchical dyadic subdivision on the selected triangles to reach the desired error. As the resulting mesh is non-conformal, a Discontinous Galerkin scheme is applied.

Determining the uncertainty of computational electromagnetics simulations

In real-world problems of interest, inputs to computational electromagnetics (CEM) codes are never known with 100% certainty. However, the methodologes currently employed by the CEM community presume that a single deterministic solution (often using the mean values of the uncertain input parameters) is sufficient. This is certainly an overly optimistic assumption, and perhaps, at times, dangerous. All inputs to CEM codes are potentially uncertain: it is not possible to manufacture geometry exactly to the required specifications, results of material measurement systems have errors and uncertainty, and the frequency of operation and angles of observation will not be perfect in measurement systems. The goal of this effort is to devise a general approach that incorporates these “uncertainties” on top of standard deterministic CEM code predictions.