Adaptive transient solution of nonuniform multiconductor transmission lines using wavelets

Wavelet-based high-order adaptive modeling of lossy interconnects

“…The latter is based on a fit of the convolution kernel with exponential functions giving rise to recursive convolution terms. We omit here the standard derivation (see, e.g., [22], [25] for the FDTD case), leading to the final expression where the auxiliary arrays are computed through the following recursion rule (15) The coefficients represent the -term Prony approximation of according to (16) We have found that setting allows to cover with negligible error at least three decades for the parameter . The corresponding values of and are listed in Table I.…”

“…For the interested reader, we point to [4]- [6] for general wavelet theory and [7], [8]. and [15] for some details on the sparse approximations that will be used in this paper. In the following paragraphs, we detail the main results that are essential for the presentation of the main algorithm.…”

“…Otherwise, the effectiveness of the adaptive algorithm would be wasted in case of ac losses. It turns out that the recurrence rule (15) relates each of these vectors to the time derivative of the unknowns. The time derivatives are large exactly where the fast variations of the solution occur.…”

“…It is then natural to resort to some more advanced representation allowing mesh coarsening and refinement on the basis of the structure of the solution. Wavelets are the most appropriate mathematical tool to be employed in such cases [9], [10], [15]. We will show how a simple change of basis in the representation of the solution allows to work with wavelet coefficients instead of nodal values.…”

Analysis of Nonuniform Transmission Lines With an Iterative and Adaptive Perturbation Technique

“…parameters [2], finite-difference time domain methods [3], [5], Chebyshev interpolations [31], [32], waveform relaxation [33], the method of characteristics [34], full-wave simulations [35], rational approximations [36], wavelets theory [37], [38], the differential quadrature method [39], or congruence transforms [40]. These methods, however, rely on specific assumptions, idealizations or approximations, and they often turn out to be rather time consuming and/or cumbersome to implement.…”