Interdisciplinary Applied Mathematics

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Such “best-fits” are tabulated and are used in the simulation according to the specific structure considered, without the need for solving the partial differential equations governing the dynamics of the structure.


One of the simplest approaches for reduced-order modeling is to recast mechanical systems into electrical systems, so that mechanical systems can be integrated into SPICE. This can be understood more clearly by considering the analogy of a mass-spring-damper system driven by an external force with a parallel-connected RLC circuit with a current source. In this example, mass corresponds to capacitance, dampers to resistors, springs to inductive elements, and forces to currents. An effort has already been made to produce equivalent RLC circuits for microflows such as the squeezed gas film in silicon accelerometers, which we discuss in detail in Chapter 18. A variety of other sophisticated and complicated approaches, such as generalized Kirchhoffian networks, black box models, and Galerkin techniques, can be used for generation of reduced-order models and these are discussed in detail in Chapter 17. The application of various reduced-order methods for simulation of microflows is presented in Chapter 18.

1.7.2 Coupled Circuit/Device Modeling


For highly nonlinear behavior of microsystems, the development of simple, easy-to-use, and accurate reduced-order models can be challenging. In such cases, simulation based on full-physics models of all the energy domains contained in the microsystem may become necessary. Coupled circuit/device modeling refers to the simultaneous simulation of different functional units of the microsystem. The concept of a coupled circuit and device simulator has proved to be extremely beneficial in the domain of integrated circuits. Since the first of such simulators, MEDUSA (Engl et al., 1982), became available in the early 1980s, there has been significant work addressing coupled simulation. These activities have focused on improved algorithms, faster execution speeds, and applications. Today, commercial CAD vendors also support a mixed circuit-device simulation capability (Technology Modeling Associates, 1997; Silvaco International, 1995).

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