A non-nested Galerkin multi-grid method for solving linear and nonlinear solid mechanics problems Original Research Article

A non-nested Galerkin multi-grid method is proposed in this paper for the iterative solution of general linear and nonlinear problems arising in solid mechanics. As the Galerkin strategy has been fully adopted in the standard multi-grid method for the generation of coarse mesh equations and only the geometrical information for coarse meshes is utilised, the resulting approach is relatively easy to incorporate into existing solution procedures, and is particularly suitable for implementation in materially non-linear cases. Furthermore, the capability of using non-nested unstructured meshes provides great flexibility to handle any problem with complex geometry. Key issues involved in the theoretical and practical aspects for the construction of transfer operators and efficient implementation of Galerkin coarse grid approximation are extensively addressed, and application to geometrically nonlinear problems is also discussed. Finally, a selected set of numerical examples, which cover major classes of problems in solid mechanics including linear elastic, materially nonlinear (elasto-plastic) in small strain, geometrically nonlinear elastic and geometrically nonlinear elasto-plastic problems, and also include both symmetric and unsymmetric cases, are presented to provide an assessment of the performance of the proposed approach.