The waveform Biconjugate gradient method for parallel transient simulation of semiconductor devices

In this paper, we mainly study the parallelization aspects of the accelerated waveform relaxation algorithms for the transient simulation of semiconductor devices on parallel distributed memory computers since these method are competitive with standard pointwise methods on serial machines, but are significantly faster on parallel computers. Here we are using an efficient parallel version of the Biconjugate gradient method (BiCG) proposed in [6] combining elements of numerical stability and parallel algorithm design, for solving the resulting sequence of time-varying sparse linear differential-algebraic initial-value problems (IVP) arising at each linearization step with waveform Newton. The algorithm is derived such that all inner products and matrix-vector multiplications of a single iteration step are independent. Therefore, the cost of global communication can be significantly reduced. Experimental results carried out On Parsytec massively parallel systems with regards to the comparison with other accelerated approaches such as convolution SOR and waveform GMRES techniques on waveform relaxation algorithm. and pointwise methods are described as well.