ON THE MULTIGRID TECHNIQUE FOR SOLVING 3-DIMENSIONAL BOUNDARY-VALUE ENGINEERING PROBLEMS

The paper proposes an iterative technique with a similar multi-grid operator for solving complex spatial boundary value problems. The description of the method and efficient vectorial algorithms based on a simple data structure applicable to solving three-dimensional engineering problems are presented. The discussion of the method's convergence includes theoretical grounds and practical aspects. We give a general proof of convergence and consider the model cases to estimate the rate of convergence. We also address the histories of convergence derived from the numerical tests and consider two examples of practical problems.