THE PRINCIPLE OF INDIRECT ELIMINATION

The principle of indirect elimination states that an algorithm for solving discretized differential equations can be used to identify its own bad-converging modes. When the number of bad-converging modes of the algorithm is not too large, the modes thus identified can be used to strongly improve the convergence. The method presented here is applicable to any linear algorithm like relaxation or multigrid. An example from theoretical physics, the Dirac equation in the presence of almost-zero-modes arising from instantons, is studied. Using the principle, bad-converging modes are removed efficiently. It is sketched how the method can be used for a Conjugate Gradient algorithm. Applied locally, the principle is one of the main ingredients of the Iteratively Smoothing Unigrid algorithm.