Accurate and efficient three-dimensional electrostatics analysis using singular boundary elements and Fast Fourier Transform on Multipole (FFTM)

Ph.DDOCTOR OF PHILOSOPH

Modeling multi-layer via structure using PEEC method

In this dissertation, a new integral equation formulation for via structures is developed for the capacitance extraction between vias and planes. The proposed method can be used to calculate the shared-antipad via structure which is widely used in highspeed differential signal interconnects. In addition, we use the image theory to handle inhomogeneous media. Further, a new technique is given to reduce computational resources for via-to-plane structures based on properties of the matrix coefficient. The extracted capacitance is also incorporated into the physics-based circuit model to characterize the overall performance of the via transition. In the second paper, a rigorous modeling of the shared-antipad via structure is developed using surface partial element equivalent circuit (PEEC). The cavity Green\u27s function is used to evaluate the equivalent circuit elements, thereby requiring fewer cells for numerical computation. The non-orthogonal, quadrilateral cell is used in the mesh to better accommodate the non-rectangular shape of the via and the antipad. A novel wave port excitation method is applied to the equivalent circuit to obtain the network parameters of the via transition. The Z-parameters of the via structure are calculated using the proposed method, and the results are validated with the finite element solution obtained from commercial software. In the third paper, an effective methodology is proposed to estimate the RF interference received by an antenna due to near-field coupling using divide-and-conquer based on reciprocity. The proposed methodology fits well with engineering practice, and is particularly suitable for pre-layout wireless system design and planning --Abstract, page iv

Rapid solution of potential integral equations in complicated 3-dimensional geometries

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (p. 133-137).by Joel Reuben Phillips.Ph.D

A meshless, high-order integral equation method for smooth surfaces, with application to biomolecular electrostatics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 87-97).In this thesis, we develop methods for efficient simulation of biomolecular electrostatics based on Poisson-Boltzmann equation. Current techniques using finite-difference solution of differential formulation have many drawbacks. We present an integral formulation that resolves these difficulties and enables an efficient implementation using a recently developed fast solver. The new approach can solve practical engineering problems with good accuracy, but only with an aid of a high quality mesh generator, and sometimes require a large number of panels to discretize a surface. To this end, a novel approach to discretize singular integral equations is proposed. Unlike the traditional boundary element method using panel discretization, the new method is meshless and capable of achieving spectral convergence: numerical errors decrease exponentially fast with increasing size of basis set. We will describe a number of techniques in our approach, including the use of global, high order basis, quadrature-based panel integration, and innovative surface representation. The biomolecular problem is particularly suited for this method because molecular surfaces are typically smooth and can be represented globally using spherical harmonics.(cont.) The use of flat panels in the traditional approach would incur significant geometrical distortion, in addition to much slower convergence rate. Computational results demonstrate that for a practical problem at engineering accuracy (a tolerance of 10¡3) this new approach requires one to two orders of magnitude fewer unknowns than a flat panel method. For a more stringent tolerance of 10¡6, a comparison to an analytically solvable problem reveals that an improvement more than three orders of magnitude has been achieved.by Shih-Hsien Kuo.Ph.D

Efficient integral equation based algorithms for parasitic extraction of interconnects with smooth or rough surface

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 187-198).This thesis describes a few efficient parasitic extraction algorithms based on integral equation methods. It has two parts. Part one describes the algorithms used in FastImp, a program for accurate analysis of wide-band electromagnetic effects in very complicated geometries of conductors. The program is based on a recently developed surface integral formulation and a Pre-corrected FFT accelerated iterative method, but includes a new piecewise quadrature panel integration scheme, a new scaling and preconditioning technique as well as a generalized grid interpolation and projection strategy. Computational results are given on a variety of integrated circuit interconnect structures to demonstrate that FastImp is robust and can accurately analyze very complicated geometries of conductors. Part two describes an efficient Stochastic Integral Equation (SIE) Method for computing the mean value and variance of the capacitance of interconnects with random surface roughness in O(Nlog2Ì(N)) time. An ensemble average Green's function is used to account for the surface roughness. A second-order correction scheme is used to improve the accuracy. A sparsification technique based on the Hierarchical Matrix method is proposed to significantly reduce the computational cost. The SIE method avoids the time-consuming Monte Carlo simulations and the discretization of rough surfaces. Numerical experiments show that the results of the new method agree very well with those of Monte Carlo simulations.by Zhenhai Zhu.Ph.D

Fast Isogeometric Boundary Element Method based on Independent Field Approximation

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology is demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.Comment: 32 pages, 27 figure

Mobile array designs with ANSERLIN antennas and efficient, wide-band PEEC models for interconnect and power distribution network analysis

A mobile, wide-band antenna system has been developed around the ANSERLIN antenna element and a 3-dB splitter design. The size of the antenna elements was reduced over previous versions by introducing dielectric substrates. Additionally, new variations of the antenna were designed to influence radiation characteristics. To further reduce the number of components in the array, a very low profile splitter was designed and mounted below one of the antenna elements, doubling as the return plane for the antenna. The partial-element equivalent circuit (PEEC) method has been used for 3D interconnect analysis and numerous other applications. Being based on the same ideas as the method of moments, the PEEC method generates dense matrices for its cell interactions. This thesis contains research focused on efficiently using a limited number of cells for accurate results. This has been approached with a hybrid method and also with grid refinements. Additionally, the accuracy of PEEC coupling over electrically long distances has been addressed using wide-band accurate partial parameter calculations --Abstract, page iii