Swagato Chakraborty

Evaluation of Green's function integrals in conducting media

This work presents an accurate integration method for computing Greens function operators related to lossy conducting media. The presented approach is ultrawideband, i.e., the integration schemes cover the entire range of frequency behavior, from high frequencies where skin current is prevalent to low frequencies where volume current flow dominates. The scheme is a step toward permitting exact ultrawide-band frequency domain surface-only-based integral-equation simulation of arbitrarily-shaped three-dimensional conductors, and toward obviating the need for volume-based explicit frequency-dependent skin effect modeling. This work deals specifically with the computation of Greens functions and not with the unrelated but important low-frequency conditioning issue associated with the standard electric field integral equation.

Polar Integration for Exact Space-Time Quadrature in Time-Domain Integral Equations

A space-time polar quadrature technique for numerical integration of Greens function interactions in time-domain integral equations is presented. The method transforms 2-D surface space-time integrals associated with vector and scalar potentials to a 1-D integral that is performed using Gauss-Legendre integration. The advantage of the presented technique compared to standard 2-D Gaussian quadrature is that time delays between each section of the source basis function and the observation point are accounted for exactly in an analytic manner. This ensures highly accurate temporal behavior of the Greens function interactions thereby contributing to the stability of the overall time-domain integral equations

A three-stage preconditioner for geometries with multiple holes and handles in integral equation-based electromagnetic simulation of integrated packages

A novel three-stage approach for preconditioner including loop-tree, basis function rearrangement and incomplete LU is presented. In particular a new technique for construction of loop-tree basis functions for arbitrary-shaped geometries consisting of any number of holes and handles is described. This preconditioner enables fast iterative solution of integral modeling of electromagnetic components in integrated packages.

A surface equivalence-based method to enable rapid design and layout iterations of coupled electromagnetic components in integrated packages

A novel methodology is presented that expedites the electromagnetic analysis in the design cycle of individual layout components in close proximity to other radiating and electromagnetic structures. The proposed method retains all the advantages of a surface based moment method technique, but avoids explicit modeling of the interactions between the object under design and the neighboring ones, without compromising on the accuracy of capturing the electromagnetic coupling between them. As a result, the simulation time in an individual design cycle is greatly reduced.

Towards system-level electromagnetic field simulation on computing clouds

Cloud computing is a potential paradigm-shifter for system-level electronic design automation tools for chip-package-board design. However, exploiting the true power of on-demand scalable computing is as yet an unmet challenge. We examine electromagnetic (EM) field simulation on cloud platforms.

A Framework And Simulator for Parallel Fast Integral Equation Simulation of Microelectronic Structures

As a part of IBMs special session, this paper presents a framework and integral equation-based 3D electromagnetic simulator for parallel simulation of microelectronic structures including those of interest to IBM. The translators, mesher, and simulator is described and is validated for initial cases. Progress on the IBM benchmark is reported

A parallel low-rank multilevel matrix compression algorithm for parasitic extraction of electrically large structures

Simulation of distributed electromagnetic effects of electrically large structures is no longer a luxury but a necessity in the accurate prediction of modern day circuit performance. In this regard, integral equation based methods have steadily gained in popularity but suffer from the time and memory bottlenecks arising from the resultant dense matrix. Fast linear complexity solvers have been introduced in the past but with the growing complexity of circuit layouts parallel implementations are the only viable options in addressing practical circuit layouts. In this paper, we present a parallel implementation of the low-rank compression based fast solver with linear cost reduction capacity with respect to the number of processors. The main problems in parallelizing a hierarchical algorithm are discussed and the advantages of the implemented scheme are highlighted. The new solver enables the simulation of full-chip problems consisting of millions of unknowns with acceptable accuracy and modest time and memory requirements

System-level SoC near-field (NF) emissions: Simulation to measurement correlation

As System-on-Chip (SoC) designs migrate to 28nm process node and beyond, the electromagnetic (EM) co-interactions of the Chip-Package-Printed Circuit Board (PCB) becomes critical and require accurate and efficient characterization and verification. In this paper a fast, scalable, and parallelized boundary element based integral EM solutions to Maxwell equations is presented. The accuracy of the full-wave formulation, for complete EM characterization, has been validated on both canonical structures and real-world 3-D system (viz. Chip + Package + PCB). Good correlation between numerical simulation and measurement has been achieved. A few examples of the applicability of the formulation to high speed digital and analog serial interfaces on a 45nm SoC are also presented.

Next-generation three-dimensional full-wave electromagnetic solver hybridization for large-scale signal integrity, power integrity, and EMI modeling

This paper introduces a new methodology and conceptual framework for implementation of automated hybrid solver technology. Specifically, it addresses the challenges and approaches to automated solver hybridization, whereby a three-dimensional full-wave simulation technology may adapt automatically to geometric redundancies and significantly reduce cost while maintaining high accuracy. The proposed method is one step towards the grand goal of an adaptive error-controllable solver that embodies all aspects of 3D full-wave, 3D quasi-static, 2D solvers, and various semi-analytic and analytic approximations within a unified automated framework.

Combined multilevel FMM-QR algorithm for broadband applications

This paper presents a combined multilevel FMM-QR approach applicable to three-dimensional scattering problems of widely varying electrical sizes. The classic MLFMA suffers breakdown at low frequencies (I. Bogaert et al., 2005), while QR based methods become inefficient at high frequencies (D. Gope and V. Jandhyala, 2005). The presented algorithm combines these two methods to achieve stability at all frequencies, and at the same time preserves the O(NlogN) complexity of setup, memory and matrix-vector products. Examples demonstrating time and memory requirements are presented, and the efficient nature of the overall method at all frequencies is also demonstrated