Abstract: Significant improvement is achieved in the analysis of IC layout by utilizing the fact that IC designs exhibit a large amount of regularity. By employing a unique mesh generation approach that takes advantage of the regularity, combined with the use of a limited number of different shapes for the majority of the IC geometry greatly increases the speed of processing. Additionally, by employing a unique approach for specifying the different mesh elements—based on the parameters that define the relative difference between one shape and another—provides significant additional reductions in the necessary calculations, and a corresponding increase in speed of IC simulations. Yet another improvement is realized by simplifying the inductive influence calculations by employing averages that permit using dot products of vectors rather than integrations of non-constant vectors.

Abstract: Significant improvement is achieved in the analysis of IC layout by utilizing the fact that IC designs exhibit a large amount of regularity. By employing a unique mesh generation approach that takes advantage of the regularity, combined with the use of a limited number of different shapes for the majority of the IC geometry greatly increases the speed of processing. Additionally, by employing a unique approach for specifying the different mesh elements—based on the parameters that define the relative difference between one shape and another—provides significant additional reductions in the necessary calculations, and a corresponding increase in speed of IC simulations. Yet another improvement is realized by simplifying the inductive influence calculations by employing averages that permit using dot products of vectors rather than integrations of non-constant vectors.

Abstract: For use in an integral equation formulation of capacitance, a system for, and method of, generating a representation of charge distribution for a given capacitive structure (which may be an integrated circuit). In one embodiment, the system includes: (1) a charge variation function generator that creates a multidimensional charge variation function that is not directly dependent on a conductive geometry of the structure and (2) a conductive geometry generator, associated with the charge variation generator, that creates a conductive geometry that is independent of charge variation in the structure, the charge variation function and the conductive geometry employable in the integral equation formulation to reduce a complexity thereof.

Abstract: Apparatus and method for simulating a component, where the component is conducting a current density, are disclosed. In one embodiment, the method includes discretizing the component into a plurality of triangular elements, and computing Green's functions descriptive of the relationship of the elements discretizing the component. In addition, the method includes computing basis functions relating to the elements, where the basis functions decompose the current density into divergence free and curl free parts, and the curl free parts are computed using a spanning tree. The method further includes combining the Green's functions and the basis functions to calculate a value representing a current density of said component. In one embodiment, the apparatus includes components configured to discretize the components, process Green's functions, compute basis functions, and combine the Green's functions and the basis functions to arrive at the value.

Abstract: The element to be simulated is divided into regions, and each region is further divided into a plurality of quadrature nodes. Pairs are formed for all the quadrature nodes. Green's functions are computed and stored for the pairs. Each of the pairs is allocated to either the far field or the near field for purposes of simulation in accordance with a criterion. A Gaussian quadrature is computed for the pairs allocated to the far field while a high order quadrature is computed for those allocated in the near field. The component simulation is arrived after combining information derived from the Gaussian quadrature and the high order quadrature into a matrix which is then solved to obtain the charge distribution. Summation of the charges thus obtained yields the capacitance of the element. The high order quadrature is computed using a plurality of basis functions. The basis functions, denoted &psgr;ik(r′), are 1,x,y,x2,xy,y2. The basis functions are used to compute a set of weights vjk.

Abstract: A component design tool extracts a parameter associated with a component defined in a model of a physical system. The design tool discretizes the component and generates a matrix representative of a specified parameter. By subdividing the matrix into a hierarchy of submatrices and iteratively compressing and blending the submatrices, the design tool produces a compressed matrix. The compressed matrix is efficiently solved using iterative techniques. From the solution of the matrix, the design tool calculates the specified parameter.

Abstract: A layered structure is divided into a plurality of regions. Transmission line equivalents (Green's functions) in the spectral domain are formed between all regions within the layered structure. The spectral domain Greens' function are converted to the spatial domain using a near field and a far field computed for those regions part of a component within the layered structure. The far field is extracted from a compressed database computed from the transmission line equivalents and descriptive of the layered structure. The near field is computed using a prioritization mechanism. Priority is assigned in accordance with the amplitude of a source and the length of the path between regions of interest.Once the physical characteristics of the layers used in the fabrication process of the IC are identified, the database used for computation of the far field is compiled and compressed, and remains unchanged for each new parameter extraction.