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      Numerical analysis of multidomain systems: coupled nonlinear PDEs and DAEs with noise

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      Author(s)
      Demir, A.
      Hanay, Selim
      Date
      2018
      Source Title
      IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
      Print ISSN
      0278-0070
      Publisher
      Institute of Electrical and Electronics Engineers
      Volume
      37
      Issue
      7
      Pages
      1445 - 1458
      Language
      English
      Type
      Article
      Item Usage Stats
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      200
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      Abstract
      We present a numerical modeling and simulation paradigm for multidomain, multiphysics systems with components modeled both in a lumped and distributed manner. The lumped components are modeled with a system of differential-Algebraic equations (DAEs), whereas the possibly nonlinear distributed components that may belong to different physical domains are modeled using partial differential equations (PDEs) with associated boundary conditions. We address a comprehensive suite of problems for nonlinear coupled DAE-PDE systems including 1) transient simulation; 2) periodic steady-state (PSS) analysis formulated as a mixed boundary value problem that is solved with a hierarchical spectral collocation technique based on a joint Fourier-Chebyshev representation, for both forced and autonomous systems; 3) Floquet theory and analysis for coupled linear periodically time-varying DAE-PDE systems; 4) phase noise analysis for multidomain oscillators; and 5) efficient parameter sweeps for PSS and noise analyses based on first-order and pseudo-Arclength continuation schemes. All of these techniques, implemented in a prototype simulator, are applied to a substantial case study: A multidomain feedback oscillator composed of distributed and lumped components in two physical domains, namely, a nano-mechanical beam resonator operating in the nonlinear regime, an electrical delay line, an electronic amplifier and a sensor-Actuator for the transduction between the two physical domains.
      Keywords
      Chebyshev and Fourier representations and collocation
      Differential-Algebraic equations (DAEs)
      Mixed boundary value problems
      Multidomain systems
      Multiphysics simulation
      Nano electro-mechanical systems (NEMS)
      Noise
      Oscillators
      Partial differential equations (PDEs)
      Phase noise
      Spectral methods
      Permalink
      http://hdl.handle.net/11693/50247
      Published Version (Please cite this version)
      https://doi.org/10.1109/TCAD.2017.2753699
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      • Department of Electrical and Electronics Engineering 3863
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