The parallel waveform IQMR algorithm for transient simulation of semiconductor devices

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 methods are competitive with standard pointwise methods on serial machines, but are significantly faster on parallel computers. We propose an improved version of the quasi-minimal residual (IQMR) method by using the Lanczos process as a major component 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. For the Lanczos process stability is obtained by a coupled two-term procedure that generates Lanczos vectors scaled to unit length. The algorithm is derived such that all inner products and matrix-vector multiplications of a single iteration step are independent and communication time required for inner product can be overlapped efficiently with computation time. Therefore, the cost of global communication can be significantly reduced. Experimental results carried out on a Parsytec GC regarding a comparison with other accelerated approaches such as convolution SOR and waveform GMRES techniques on the waveform relaxation algorithm and pointwise methods are also described.