Andrew Lumsdaine

Conjugate direction waveform methods for transient two-dimensional simulation of MOS devices

A conjugate-direction based acceleration to the waveform relaxation (WR) algorithm is derived. Experimental results demonstrated the effectiveness of the acceleration when solving the large, sparsely connected algebraic and differential system generated by standard spatial discretization of the 2D time-dependent semiconductor device equations. The waveform conjugate-direction methods were up to 15 times faster than ordinary WR.<<ETX>>

A band relaxation algorithm for reliable and parallelizable circuit simulation

A variable-band relaxation algorithm for solving large linear systems is developed as an alternative to Gauss-Jacobi relaxation. This algorithm seeks to improve the reliability of Gauss-Jacobi relaxation by extracting a variable-sized band from the matrix and solving that band directly. This leads to a relaxation algorithm with provably better convergence properties. The algorithm can be used effectively on a massively parallel computer because band matrices can be solved in log(n) time on n/2 processors. Test results are presented which compare the convergence properties of variable-band and Gauss-Jacobi relaxation.<<ETX>>

Parallel simulation algorithms for grid-based analog signal processors

Specialized algorithms for circuit-level simulation of grid-based analog signal processing arrays on a massively parallel processor are described and implementation results presented. The trapezoidal rule is used to discretize the differential equations that describe the analog array behavior, Newtons method is used to solve the nonlinear equations generated at each time-step, and a block conjugate-gradient squared algorithm is used to solve the linear equations generated by Newtons method. Excellent parallel performance of the algorithm is achieved through the use of a novel, but very natural, mapping of the circuit data onto the massively parallel architecture. The mapping takes advantage of the underlying computer architecture and the structure of the analog array problem. Experimental results demonstrate that a full-size Connection Machine can provide a 1400 times speedup over a SUN-4/280 workstation.<<ETX>>

Accelerating Dynamic Iteration Methods with Application to Semiconductor Device Simulation

In this paper, we apply a Galerkin method to solving the system of second-kind Volterra integral equations which characterize the classical dynamic iteration methods for the linear time-varying initial value problem. It is shown that the Galerkin approximations can be computed iteratively using conjugate-direction algorithms. The resulting iterative methods are combined with an operator Newton method and applied to solving the differential-algebraic system generated by spatial discretization of the time-dependent semiconductor device equations. Experimental results are included which demonstrate the conjugate-direction methods are significantly faster than classical dynamic iteration methods.

Massively parallel simulation algorithms for grid-based analog signal processors

This paper presents the algorithms for CMVSIM, a program for performing the transient simulation of grid based analog signal processors on a massively parallel computer. A grid-based equation formulation approach and a block-diagonal preconditioned CGS algorithm are described, and it is shown how they are used to efficiently perform transient simulation using the massively parallel Connection Machine. Experimental results using CMVSIM to simulate realistic image processing circuits are given to demonstrate that the algorithms presented are effective for a general class of grid-based signal processors. In particular, the results presented demonstrate that CMVSIM: running on a full-size Connection Machine can be as much as 650 times faster than what is, to the authors knowledge, the fastest serial transient simulation algorithm running on a SUN-4/490 workstation. >