The multigrid method in solid mechanics: Part II—Practical applications

Abstract The performance of the multigrid algorithm is investigated by solving some large, practical, three dimensional solid mechanics problems. The convergence of the method is sensitive to factors such as the amount of bending present and the degree of mesh non‐uniformity, as was also observed in Part I for two dimensional problems. However, in contrast to Part I, no proportionality is observed between the total number of operations to convergence and the problem size. Despite such behaviour, the multigrid algorithm proves to be an effective matrix equation solver for solid mechanics poblems. It is orders of magnitude faster than a direct factorization method, and yields converged solutions several times faster than the Jacobi preconditioned conjugate gradient method.