Waveform iterative methods for parallel solution of initial value problems

The traditional approach for computing the solution to large systems of ordinary differential or differential-algebraic equations typically includes discretization in time with an implicit integration formula. The primary opportunity for parallelization is therefore limited to the linear system solution that is performed at each timestep. Waveform techniques, on the other hand, decompose the problem at the equation level and solve for different components of the system independently, using previous iterates from other processors as inputs. This approach is particularly well-suited for message-passing computing environments, especially those with high communication latency because synchronization and communication take place infrequently and communication consists of large packets of information. We present an MPI-based implementation of a waveform relaxation-based semiconductor device simulation program and provide experimental results using this program to solve the time dependent semiconductor drift-diffusion equations on a cluster of workstations