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MVHAM: An Extension of the Homotopy Analysis Method for Improving Convergence of the Multivariate Solution of Nonlinear Algebraic Equations as Typically Encountered in Analog Circuits

Jain, Divyanshu
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1194974755

Abstract Details

2007, MS, University of Cincinnati, Engineering : Computer Engineering.
Most real world systems, including analog electronic circuits, express themselves formally as a set of nonlinear differential algebraic equations. Such systems are typically modeled in languages such as VHDL-AMS. As applications grow, the size and complexity of these equations also increases. Achieving convergence in an efficient manner in these situations has become a real challenge. Additional demands such as the desire to find multiple solutions from a single starting point force us to explore alternatives to the traditional method used for finding linear approximations of nonlinear algebraic equations-the Newton Raphson (NR) method. Homotopy methods provide theoretical promise of global convergence [55]. The Homotopy Analysis Method (HAM) [12] is a recently proposed and promising method based on homotopy theory. This thesis presents an efficient iterative numerical algorithm based on HAM for the solution of a multivariate system of nonlinear algebraic equations (MVHAM). The proposed method is experimentally characterized according to a set of determined parameters which affect the system. The experimental results highlight the potential and limitations of the new method and imply directions for future work. The method can handle most types of algebraic equations, is accurate and simple, and integrates well into the direct method of circuit simulation. It is shown to have significant advantages over the traditional Newton-Raphson method in terms of flexibility, convergence, ability to find multiple solutions and possibly speed. MVHAM is also shown to exhibit significantly improved convergence performance in comparison with the classical homotopy theory.
Dr. Harold Carter (Advisor)
162 p.
Homotopy Analysis Method; Solution of Nonlinear Algebraic Equations; Convergence

Recommended Citations

Citations

  • Jain, D. (2007). MVHAM: An Extension of the Homotopy Analysis Method for Improving Convergence of the Multivariate Solution of Nonlinear Algebraic Equations as Typically Encountered in Analog Circuits [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1194974755

    APA Style (7th edition)

  • Jain, Divyanshu. MVHAM: An Extension of the Homotopy Analysis Method for Improving Convergence of the Multivariate Solution of Nonlinear Algebraic Equations as Typically Encountered in Analog Circuits. 2007. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1194974755.

    MLA Style (8th edition)

  • Jain, Divyanshu. "MVHAM: An Extension of the Homotopy Analysis Method for Improving Convergence of the Multivariate Solution of Nonlinear Algebraic Equations as Typically Encountered in Analog Circuits." Master's thesis, University of Cincinnati, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1194974755

    Chicago Manual of Style (17th edition)

ucin1194974755
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© 2007, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.