5. The Solver Module

The assembly and solution of sparse linear equation systems is a fundamental task in numerical simulators which discretize nonlinear partial differential equations on a mesh. As already discussed in Section 2.3.1, the Newton method [136] is commonly used as a linearization technique, which requires the solution of one linear equation system per iteration step.

As solving linear equation systems is a common and well-known computational task, an overview of third party solutions is given in Section 5.1. However, there are four main reasons for providing, maintaining, and extending an in-house solver module:

1. Whereas the calculation of the model contributions represents the physical modeling and thus the main purpose of employing TCAD tools in general, the largest share of the run-time of the numerical simulators is spent in the linear modules, that is for assembling and solving linear equation systems. In order to quantify this statement, a respective evaluation was performed, which is discussed in Section 5.5.2. A subsequent evaluation was performed to analyze the performance of various solver systems for different kinds of simulation tasks. So the in-house solver module does not provide only one linear solver, but an interface to various in-house and external solver systems.

2. The solvability of a linear equation system depends on specific properties of the system itself, for example the condition of the system matrix. Although several measures have already been taken to improve these properties (see Chapter 4), some kinds of solver techniques may still fail during the calculation of the solution. For that reason, again a choice of several different solver systems can increase the probability for finding a useful solution for the complete simulation task. However, insufficient convergence for example may also point to inappropriate simulation setups such as inadequate meshes or inaccurate physical modeling. Hence, the behavior of the solver modules and respective feed-back information can be used to assess and improve the complete simulation. It is therefore advantageous to benefit from a direct access to the solver module.

3. External modules are often bound to license agreements, which frequently contain restrictions especially for commercial application. As the institute provides its codes to industrial partners and binary release versions to the general public, third party license requirements would restrict such distributions. So an in-house solver module enables the institute to independently release complete versions which are directly applicable also from a legal point of view.

4. The quality assessment approach of MINIMOS-NT (see Section C.4) requires a deterministic behavior of the solver system both in the short and long run. By using the in-house solvers, which are intended to remain basically unmodified, this behavior can be assumed to be guaranteed.