Fast algorithms for ill-conditioned dense matrix problems in VLSI interconnect and substrate modeling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (leaves 131-135).by Mike Chuan Chou.Ph.D

When self-consistency makes a difference

Compound semiconductor power RF and microwave device modeling requires, in many cases, the use of selfconsistent electrothermal equivalent circuits. The slow thermal dynamics and the thermal nonlinearity should be accurately included in the model; otherwise, some response features subtly related to the detailed frequency behavior of the slow thermal dynamics would be inaccurately reproduced or completely distorted. In this contribution we show two examples, concerning current collapse in HBTs and modeling of IMPs in GaN HEMTs. Accurate thermal modeling is proved to be be made compatible with circuit-oriented CAD tools through a proper choice of system-level approximations; in the discussion we exploit a Wiener approach, but of course the strategy should be tailored to the specific problem under consideratio

Computational Prototyping Tools and Techniques

Contains reports on five research projects.Industry Consortium (Mobil, Statoil, DNV Software, Shell, OTRC, Petrobras, NorskHydro, Exxon, Chevron, SAGA, NSWC)U.S. Navy - Office of Naval ResearchAnalog DevicesDefense Advanced Research Projects Agency Contract J-FBI-95-215Cadence Design SystemsHarris SemiconductorMAFET ConsortiumMotorola SemiconductorDefense Advanced Research Projects AgencyMultiuniversity Research InitiativeSemiconductor Research CorporationIBM Corporatio

Joint CARE-ELAN, CARE-HHH-APD, and EUROTEV-WP3 Workshop on Electron Cloud Clearing

This report contains the Proceedings of the joint CARE-HHH-APD, CARE-ELAN, and EUROTEV-WP3 Mini-Workshop on 'Electron Cloud Clearing - Electron Cloud and Technical Consequences', "ECL2", held at CERN in Geneva, Switzerland, 1-2 March 2007). The ECL2 workshop explored novel technological remedies against electron-cloud formation in an accelerator beam pipe. A primary motivation for the workshop was the expected harmful electron-cloud effects in the upgraded LHC injectors and in future linear colliders, as well as recent beam observations in operating facilities like ANKA, CESR, KEKB, RHIC, and SPS. The solutions discussed at ECL2 included enamel-based clearing electrodes, slotted vacuum chambers, NEG coating, and grooves. Several of the proposed cures were assessed in terms of their clearing efficiency and the associated beam impedance. The workshop also reviewed new simulation tools like the 3D electron-ion build-up 'Faktor', modeling assumptions, analytical calculations, beam experiments, and laboratory measurements. Several open questions could be identified. The workshop reinforced inter-laboratory collaboration on electron-cloud suppression, and it concluded with a discussion of the next steps to be taken

Fast methods for extraction and sparsification of substrate coupling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 107-111).Substrate coupling effects have had an increasing impact on circuit performance in recent years. As a result, there is strong demand for substrate simulation tools. Past work has concentrated on fast substrate solvers that are applied once per contact to get the dense conductance matrix G. We develop a method of using any underlying substrate solver a near-constant number of times to obtain a sparse approximate representation G [approximately equal to] QGwtQ' in a new basis. This method differs from previous matrix sparsification techniques in that it requires only a "black box" which can apply G quickly; it doesn't need an analytical representation of the underlying kernel or access to individual entries of G. The change-of-basis matrix Q is also sparse. For our largest example, with 10240 contacts, we obtained a Gwt with 130 times fewer nonzeros than the dense G (and Q more than twice as sparse as Gwt), with 20 times fewer solves than the naive method, and fewer than 4 percent of the QGwtQ' entries had relative error more than 10% compared to the exact G.by Joseph Daniel Kanapka.Ph.D

Potential-based Formulations of the Navier-Stokes Equations and their Application

Based on a Clebsch-like velocity representation and a combination of classical variational principles for the special cases of ideal and Stokes flow a novel discontinuous Lagrangian is constructed; it bypasses the known problems associated with non-physical solutions and recovers the classical Navier-Stokes equations together with the balance of inner energy in the limit when an emerging characteristic frequency parameter tends to infinity. Additionally, a generalized Clebsch transformation for viscous flow is established for the first time. Next, an exact first integral of the unsteady, three-dimensional, incompressible Navier-Stokes equations is derived; following which gauge freedoms are explored leading to favourable reductions in the complexity of the equation set and number of unknowns, enabling a self-adjoint variational principle for steady viscous flow to be constructed. Concurrently, appropriate commonly occurring physical and auxiliary boundary conditions are prescribed, including establishment of a first integral for the dynamic boundary condition at a free surface. Starting from this new formulation, three classical flow problems are considered, the results obtained being in total agreement with solutions in the open literature. A new least-squares finite element method based on the first integral of the steady two-dimensional, incompressible, Navier-Stokes equations is developed, with optimal convergence rates established theoretically. The method is analysed comprehensively, thoroughly validated and shown to be competitive when compared to a corresponding, standard, primitive-variable, finite element formulation. Implementation details are provided, and the well-known problem of mass conservation addressed and resolved via selective weighting. The attractive positive definiteness of the resulting linear systems enables employment of a customized scalable algebraic multigrid method for efficient error reduction. The solution of several engineering related problems from the fields of lubrication and film flow demonstrate the flexibility and efficiency of the proposed method, including the case of unsteady flow, while revealing new physical insights of interest in their own right

Efficient numerical methods for capacitance extraction based on boundary element method

Fast and accurate solvers for capacitance extraction are needed by the VLSI industry in order to achieve good design quality in feasible time. With the development of technology, this demand is increasing dramatically. Three-dimensional capacitance extraction algorithms are desired due to their high accuracy. However, the present 3D algorithms are slow and thus their application is limited. In this dissertation, we present several novel techniques to significantly speed up capacitance extraction algorithms based on boundary element methods (BEM) and to compute the capacitance extraction in the presence of floating dummy conductors. We propose the PHiCap algorithm, which is based on a hierarchical refinement algorithm and the wavelet transform. Unlike traditional algorithms which result in dense linear systems, PHiCap converts the coefficient matrix in capacitance extraction problems to a sparse linear system. PHiCap solves the sparse linear system iteratively, with much faster convergence, using an efficient preconditioning technique. We also propose a variant of PHiCap in which the capacitances are solved for directly from a very small linear system. This small system is derived from the original large linear system by reordering the wavelet basis functions and computing an approximate LU factorization. We named the algorithm RedCap. To our knowledge, RedCap is the first capacitance extraction algorithm based on BEM that uses a direct method to solve a reduced linear system. In the presence of floating dummy conductors, the equivalent capacitances among regular conductors are required. For floating dummy conductors, the potential is unknown and the total charge is zero. We embed these requirements into the extraction linear system. Thus, the equivalent capacitance matrix is solved directly. The number of system solves needed is equal to the number of regular conductors. Based on a sensitivity analysis, we propose the selective coefficient enhancement method for increasing the accuracy of selected coupling or self-capacitances with only a small increase in the overall computation time. This method is desirable for applications, such as crosstalk and signal integrity analysis, where the coupling capacitances between some conductors needs high accuracy. We also propose the variable order multipole method which enhances the overall accuracy without raising the overall multipole expansion order. Finally, we apply the multigrid method to capacitance extraction to solve the linear system faster. We present experimental results to show that the techniques are significantly more efficient in comparison to existing techniques