Numerical analysis of multidomain systems: coupled nonlinear PDEs and DAEs with noise
Date
2018Source 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
ArticleItem Usage Stats
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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 collocationDifferential-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