The waveform ICGS technique for parallel transient simulation of semiconductor devices

In this paper, the parallelization aspects of the accelerated waveform relaxation algorithms for the transient simulation of semiconductor devices on parallel distributed memory computers are studied. These methods are competitive with standard pointwise methods on serial architectures, but are significantly faster on parallel computers. We make use of an improved parallel version of the conjugate gradient squared method (ICGS) combining elements of numerical stability and parallel algorithm design, for solving the resulting sequence of time-varying sparse linear differential-algebraic initial-value problems arising at each linearization step with waveform Newton. We reorganize the algorithm such that all the inner products, matrix-vector multiplications and vector updates of a single iteration step are independent and communication time required for inner product can be overlapped efficiently with computation time of vector updates. Therefore, the bottleneck of the performance, namely the cost of global communication on parallel distributed memory computers can be significantly reduced. The resulting ICGS algorithm maintains the favorable properties of the original algorithm while not increasing the computational costs.