## The multigrid method in solid mechanics. I: Algorithm description and behaviour.(English)Zbl 0724.73269

Summary: A multigrid algorithm is described that can be used to obtain the finite element solution of linear elastic solid mechanics problems. The method is applied to some two-dimensional problems to evaluate its strenths and weaknesses. Extensive studies are made to determine the convergence behaviour of the method. In general, this depends on many factors: the number of degrees-of-freedom in the discretization, characteristics of the algorithm, Poisson’s ratio when it is closed to $$0\cdot 5$$, the amount of bending deformation in the problem under consideration, and the degree of nonuniformity in the mesh. Only certain values of the multigrid parameters allow a converged solution to be obtained with a computational effort proportional to the number of degrees-of-freedom. These values include the optimum ones, i.e. those that lead to convergence with the least computational effort. The constant of proportionality is only independent of the number of degrees-of-freedom and still depends on the other factors listed above.

### MSC:

 74S30 Other numerical methods in solid mechanics (MSC2010) 74S05 Finite element methods applied to problems in solid mechanics 65F10 Iterative numerical methods for linear systems

Zbl 0724.73270
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### References:

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