Numerical Simulation and Modelling of Electronic and Biochemical Systems

Abstract

Numerical simulation and modelling have been growing in importance and seeing steadily increasing practical application. The proliferation of applications and physical domains for which simulation technologies are now needed, compounded by generally increased complexity, has expanded the scope of numerical simulation and modelling within CAD and spurred new research directions. Numerical Simulation and Modelling of Electronic and Biochemical Systems provides an introduction to the fundamentals of numerical simulation, and to the basics of modelling electronic circuits and biochemical reactions. The emphasis is on capturing a minimal set of important concepts succinctly, but concretely enough that the reader will be left with an adequate foundation for further independent exploration. Starting from mathematical models of basic electronic elements, circuits are modelled as nonlinear differential-algebraic equation (DAE) systems. Two basic techniques - quiescent steady state and transient - for solving these differential equations systems are then developed. It is then shown how biochemical reactions can also be modelled deterministically as DAEs. Following this, frequency domain techniques for finding sinusoidal steady states of linear DAEs are developed, as are direct and adjoint techniques for computing parameter sensitivities and the effects of stationary random noise. For readers interested in a glimpse of topics beyond these basics, an introduction to nonlinear periodic steady state methods (harmonic balance and shooting) and the multitime partial differential equation formulation is provided. Also provided is an overview of model order reduction, an important topic of current research that has roots in numerical simulation algorithms. Finally, sample applications of nonlinear oscillator macromodels - in circuits (PLLs), biochemical reaction-diffusion systems and nanoelectronics - are presented.