In the world of elementary particles we are confronted with quantum field theories with a high level of complexity, the so-called gauge theories. All physical quantities in the realm of elementary particles ought to be computed from the underlying gauge theory. This is not possible by purely analytical techniques. An alternative way is to work on a discrete space- time lattice. The paper presents an introduction into the issues and compares two algorithms for Landau gauge fixing in lattice quantum chromodynamics on the connection machines CM2 and CM5.
The Cornell method and the Los Alamos method are introduced. Remarks to the implementation of the iteration process (convergence criteria, accelerating procedures) emphasize the difficulties occurring in this process. A detailed comparison of the result of the two algorithms, including problems of parallelization (Hardware configuration, performance, communication time etc.), finishes the paper.