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: Methods and apparatus for performing non-linear analysis using preconditioners to reduce the computation and storage requirements associated with processing a system of equations. A circuit, system or other device to be analyzed includes n unknown waveforms, each characterized by N coefficients in the system of equations. A Jacobian matrix representative of the system of equations is generated. The Jacobian matrix may be in the form of an n×n sparse matrix of dense N×N blocks, such that each block is of size N2. In an illustrative embodiment, a low displacement rank preconditioner is applied to the Jacobian matrix in order to provide a preconditioned linear system. The preconditioner may be in the form of an n×n sparse matrix which includes compressed blocks which can be represented by substantially less than N2 elements.

Abstract: A frequency-domain analysis method computes noise power spectral densities (PSDs) in nonlinear circuits. The method uses harmonic components of the periodic time-varying PSD of cyclostationary noise, i.e., harmonic power spectral densities which are deterministic functions that describe the time-varying second-order statistics of cyclostationary noise. A block-structured matrix equation is used which relates output noise statistics to input noise statistics. By exploiting Toeplitz block structure, an efficient noise calculation method requires O(nN log N) computation time and O(nN) memory, where n is the circuit size and N is the number of significant harmonics in the circuit's steady state. The method successfully treats device noise sources with arbitrarily shaped PSDs (including thermal, shot, and flicker noises), handles noise input correlations and computes correlations between different outputs.

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.

Abstract: Methods and apparatus for performing frequency domain analysis using compressed matrix storage to reduce the computation and storage requirements associated with processing a system of harmonic balance equations. A nonlinear circuit, system or other device to be analyzed includes n unknown node spectra, each characterized by N spectral coefficients in the system of harmonic balance equations. A compressed version of a Jacobian matrix J representing the system of harmonic balance equations is generated by forming m sequences of length N using one or more block-diagonal matrices associated with the Jacobian matrix J, converting each of the m sequences to the frequency domain using a discrete Fourier transform, such that a set of Fourier coefficients are generated for each of the m sequences, and storing only those Fourier coefficients which exceed a threshold as the compressed version of the Jacobian matrix J.