Method of Characteristics

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The Experts below are selected from a list of 267 Experts worldwide ranked by ideXlab platform

A. Dounavis - One of the best experts on this subject based on the ideXlab platform.

Q Xu - One of the best experts on this subject based on the ideXlab platform.

  • Transmission line modeling by modified Method of Characteristics
    Proceedings of the IEEE International Conference on VLSI Design, 2001
    Co-Authors: Q Xu, Pinaki Mazumder, Zhongcheng Li
    Abstract:

    In this paper a new model of lossy transmission lines is presented for the time-domain simulation of high-speed interconnects. This model is based on Modified Method of Characteristics (MMC). The characteristic functions are first approximated by applying lower-order Taylor series in the frequency domain, and then a set of simple recursive formulas are obtained in the time domain. The formulas, which involve tracking performance between two ends of the transmission line, are similar to those derived by the Method of Characteristics (MC) for lossless or undistorted lossy transmission lines. The algorithm based on the model can efficiently evaluate transient responses of high-speed interconnects. It only uses the quantities at two ends of the lines, requiring less computation time and less memory than other Methods. Examples indicate that the new Method is having high accuracy and is very efficient for the time-domain simulation of interconnects in high-speed integrated circuits.

  • Time-domain modeling of high-speed interconnects by modified Method of Characteristics
    IEEE Transactions on Microwave Theory and Techniques, 2000
    Co-Authors: Q Xu
    Abstract:

    In this paper, a new model of lossy transmission lines is\npresented for the time-domain simulation of high-speed interconnects.\nThis model is based on the modified Method of Characteristics (MMC). The\ncharacteristic functions are first approximated by applying lower order\nTaylor series in the frequency domain, and then a set of simple\nrecursive formulas are obtained in the time domain. The formulas, which\ninvolve tracking performances between two ends of a transmission line,\nare similar to those derived by the Method of Characteristics for\nlossless and undistorted lossy transmission lines. The algorithm, based\non the proposed MMC model, can efficiently evaluate transient responses\nof high-speed interconnects. It only uses the quantities at two ends of\nthe lines, requiring less computation time and less memory space than\nrequired by other Methods. Examples indicate that the new Method has\nhigh accuracy and is very efficient for the time-domain simulation of\ninterconnects in high-speed integrated circuits

Shu-ichiro Inutsuka - One of the best experts on this subject based on the ideXlab platform.

  • Smoothed particle magnetohydrodynamics with a Riemann solver and the Method of Characteristics
    Monthly Notices of the Royal Astronomical Society, 2011
    Co-Authors: Kazunari Iwasaki, Shu-ichiro Inutsuka
    Abstract:

    In this paper, we develop a new Method for magnetohydrodynamics (MHD) using smoothed particle hydrodynamics (SPH). To describe MHD shocks accurately, the Godunov Method is applied to SPH instead of artificial dissipation terms. In the interaction between particles, we solve a nonlinear Riemann problem with magnetic pressure for compressive waves and apply the Method of Characteristics for Alfv{\'e}n waves. An extensive series of MHD test calculations is performed. In all test calculations, we compare the results of our SPH code with those of a finite-volume Method with an approximate Riemann solver, and confirm excellent agreement.

V.a. Pothiwala - One of the best experts on this subject based on the ideXlab platform.

  • Passive Closed-Form Transmission Line Macromodel Using Method of Characteristics
    IEEE Transactions on Advanced Packaging, 2008
    Co-Authors: A. Dounavis, V.a. Pothiwala
    Abstract:

    This paper presents an efficient passive time-domain macromodeling algorithm for distributed lossy transmission lines based on the generalized Method of Characteristics (MoC). A new theorem is described that specifies sufficient conditions to guarantee the passivity of the MoC by construction. A key feature of the proposed Methodology is that the curve fitting to realize the MoC depends only on the per-unit-length (p.u.l.) parameters and not on the discretization of the macromodel. Thus, with the knowledge of the rational functions derived from the p.u.l. parameters, the MoC can be formulated in a closed-form manner for any line length while ensuring passivity.

  • Efficient passive transmission line macromodeling algorithm using Method of Characteristics
    2006 IEEE International Symposium on Circuits and Systems, 2006
    Co-Authors: V.a. Pothiwala, A. Dounavis
    Abstract:

    This paper presents an efficient passive macro-modeling algorithm for distributed lossy transmission lines based on Method of Characteristics (MoC). A new theorem is described that specifies sufficient conditions to guarantee the passivity of the MoC macromodel by construction

Laurent Pilon - One of the best experts on this subject based on the ideXlab platform.

  • EUROTHERM 82 - Modified Method of Characteristics for Solving the Transient Radiation Transfer Equation
    2020
    Co-Authors: Kamal M. Katika, Laurent Pilon
    Abstract:

    This paper presents the modified Method of Characteristics f or simulating multidimensional transient radiation transfer in absorbing and scattering media. The modified Method of Characteristics transforms the integro-differential equation for radiative transfer expressed in terms of both space and time into four ordinary differential equations with respect to time. It ma kes use of an arbitrary set of points and, unlike the conventional Method of Characteristics follows the photons backward in space along their Characteristics curves (or pathline). First, the principle and ad vantages of the numerical scheme are presented. Then, test problems for diffuse and collimated irradiation in one- and three-dimensional participating media with various boundary conditions are considered. The numerical results show good agreement with analytical and numerical solutions reported in litera ture. The scheme is fast and able to capture the sharp discontinuities associated with the propagation of a radiation front in transient radiation transport.

  • Modified Method of Characteristics in transient radiation transfer
    Journal of Quantitative Spectroscopy & Radiative Transfer, 2006
    Co-Authors: Kamal M. Katika, Laurent Pilon
    Abstract:

    This paper presents the modified Method of Characteristics for simulating multidimensional transient radiative transfer in emitting, absorbing and scattering media. The Method is based on the Method of Characteristics that follows photons along their pathlines. It makes use of a fixed set of points, and unlike the conventional Method of Characteristics, it follows the photons backward in space. Test problems involving diffuse irradiation in 1-D and 3-D participating media and collimated irradiation in 1-D participating media were considered. The results show good agreement with analytical and numerical solutions reported in literature. The scheme is fast and was able to capture the sharp discontinuities associated with the propagation of a radiation front in transient radiation transport.

  • Modified Method of Characteristics for solving population balance equations
    International Journal for Numerical Methods in Fluids, 2003
    Co-Authors: Laurent Pilon, Raymond Viskanta
    Abstract:

    SUMMARY This paper presents a new numerical Method for solving the population balance equation using the modied Method of Characteristics. Aggregation and break-up are neglected but the density function variations in the three-dimensional space and its dependence on the externalelds are accounted for. The Method is an interpretation of the Lagrangian approach. Based on a pre-specied grid, it follows the particles backward in time as opposed to forward in the case of traditional Method of Characteristics. Unlike the direct marching Method, the inverse marching Method uses axed grid thus, making it compatible with other numerical schemes (e.g. �nite-volume, �nite elements) that may be used to solve other coupled equations such as the mass, momentum, and energy conservation equations. The numerical solutions are compared with the exact analytical solutions for simple one-dimensionalow cases. Very good agreement between the numerical and the theoretical solutions has been obtained conrming the validity of the numerical procedure and the associated computer program. Copyright ? 2003 John Wiley & Sons, Ltd.

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