Performance Evaluation of Linear Solvers Employed for Semiconductor Device Simulation

We present the motivation and results of a benchmarking project for linear solvers employed for semiconductor device and circuit simulation. Based on examples coming from current research projects, the performance of a specific set of linear solvers is evaluated. In rare circumstances the results show that it is important to choose the appropriate type of solver for different kind of simulations. 1 Motivation and Introduction A significant part of the computation time of a numerical semiconductor device simulation is spent on solving equation systems. Basically, such simulations require the solution of a nonlinear PDE system discretized on a grid. The nonlinear problem is solved by a damped Newton algorithm demanding the solution of a non-symmetric and sparse linear equation system at each step. Since the remarkably increased performance of todays average computers inspires to even more costly simulations (e.g. optimizations and mixed-mode device/circuit simulations), a further speed-up of the simulators is highly appreciated. In the course of this work we evaluated and compared the performance of several solvers. Rather than using a set of single matrices, this work is based on complete simulations with consistent settings, as typically encountered during daily work. An in-house assembly and solver system has been developed, which is currently employed by the multi-dimensional device and circuit simulator MINIMOS-NT [1]. The assembly module [2] provides an API to the simulator models, several conditioning measures, sorting and scaling, which have been found to be essential for many solver types. Two iterative solvers, namely BI-CGSTAB and GMRES(M) [3] in combination with an ILU-preconditioner, as well as a Gaussian solver, all implemented in C++, are available. Specific properties for quality management are the main reasons for providing these solvers. With regard to the growing demand for computational power, the on-going development of highly-optimized mathematical code must not be neglected. For that reason, the solver module has been equipped with an interface to external solvers. At the moment, two external modules can be employed: First, the Parallel Sparse Direct Linear Solver