For a wide variety of micromachined devices, designers need accurate analysis of fluid drag forces for complicated three-dimensional (3-D) problems. This paper describes FastStokes, a recently developed 3-D fluid analysis program. FastStokes rapidly computes drag forces on complicated structures by solving an integral formulation of the Stokes equation using a precorrected fast Fourier transform (PFFT)-accelerated boundary element method (BEM). The specializations of the PFFT algorithm to the Stokes flow problem are described, and computational results are presented. Timing results are used to demonstrate that FastStokes scales almost linearly with problem complexity, can easily analyze structures as complicated as an entire comb drive in under an hour, and can produce results that accurately match measured data.

We propose an efficient approach, namely the hybrid BIE/Poisson/Schrodinger approach, for electrostatic analysis of nanowires. In this approach, the interior and the exterior domain electrostatics are described by Poisson's equation (or Poisson's equation coupled with Schrodinger's equation when quantum-mechanical effects are dominant) and the boundary integral formulation of the potential equation, respectively. We employ a meshless finite cloud method and a boundary cloud method to solve the coupled equations self-consistently. The proposed approach significantly reduces the computational cost and provides a higher accuracy of the solution.

We present efficient computational methods for scattered point and meshless analysis of electrostatic microelectromechanical systems (MEMS). Electrostatic MEM devices are governed by coupled mechanical and electrostatic energy domains. A self-consistent analysis of electrostatic MEMS is implemented by combining a finite cloud method-based interior mechanical analysis with a boundary cloud method (BCM)-based exterior electrostatic analysis. Lagrangian descriptions are used for both mechanical and electrostatic analyses. Meshless finite cloud and BCMs, combined with fast algorithms and Lagrangian descriptions, are flexible, efficient, and attractive alternatives compared to conventional finite element/boundary element methods for self-consistent electromechanical analysis. Numerical results are presented for MEM switches, a micromirror device, a lateral comb drive microactuator, and an electrostatic comb drive device. Simulation results are compared with experimental and previously reported data for many of the examples discussed in this paper and a good agreement is observed.

We present efficient computational methods for scattered point and meshless analysis of electrostatic microelectromechanical systems (MEMS). Electrostatic MEMS are governed by coupled mechanical and electrostatic energy domains. A self-consistent analysis of electrostatic MEMS is implemented by combining a finite cloud method based interior mechanical analysis with a boundary cloud method based exterior electrostatic analysis. Lagrangian descriptions are used for both mechanical and electrostatic analyses. Meshless finite cloud and boundary cloud methods combined with fast algorithms and Lagrangian descriptions are flexible, efficient and attractive alternatives compared to conventional finite element/boundary element methods for self-consistent electromechanical analysis. Numerical results are presented for an electrostatic comb drive device.

The performance of micro-electro-mechanical systemsdepends on the interaction between electrical, mechanical,and fluidic forces. Simulating this coupled problem is made moredifficult by the fact that most MEMS devices are innately three-dimensionaland geometrically complicated. It is possible to simulateefficiently these devices using domain-specific solvers, providedthe coupling betweendomains can be handled effectively. Inthis paper we will survey recent developments in coupled-domainsimulation, and give computational comparisons between relaxation,multi-level Newton, and Newton-Iterative methods for 3-Delectromechanical analysis.

In order to optimize interconnect to avoid signal integrity problems, very fast and accurate 3-D capacitance extraction is essential.Fast algorithms, such as the multipole or precorrected Fast Fourier Transform (FFT) accelerated methods in programs like FASTCAP, must be combined with techniques to exploit the emerging cluster-of-workstation based parallel computers like the IBM SP2.In this paper, we examine parallelizing the precorrected FFT algorithm for 3-D capacitance extraction and present several algorithms for balancing workload and reducing communication time.Results from a prototype implementation on an eight processor IBM SP2 are presented for several test examples, and the largest of these examples achieves nearly linear parallel speed-up.

Stable and robust finite element methods for the convective hydrodynamic model of semiconductor devices are developed and implemented on distributed memory parallel computers. Specifically, a stable and accurate space-time and Galerkin/least-squares finite element formulation is developed for the hydrodynamic transport equations for the conservation laws. In addition, Galerkin finite element methods are employed for the Poisson and lattice thermal diffusion equations. The inclusion of the lattice thermal diffusion equation in the numerical solution of the convective hydrodynamic model is presented for the first time. Numerical results for a bipolar transistor are included to illustrate the effectiveness of the numerical methods. Numerical simulations of semiconductor devices using the convective hydrodynamic model require a significant amount of computations. A single-program-multiple-data (SPMD) programming model is proposed for the implementation of the hydrodynamic model on distributed memory parallel computers. Employing the SPMD programming model, a serial program developed on a workstation can be converted into a parallel program with minimal changes. The parallel program has been ported to a wide range of distributed memory parallel computers including the iPSC/860 hypercube, the Touchstone Delta machine, and the IBM SP-1. Parallel performance results are reported for a bipolar transistor, silicon MESFET and diodes. The results indicate that the parallel hydrodynamic device simulator exhibits excellent speedups and scalability on distributed memory parallel computers with minimum communication overhead.