Multigrid Preconditioner for Unstructured Nonlinear 3D FE Models

Abstract

Multigrid and multigrid-preconditioned conjugate-gradient solution techniques applicable for unstructured 3D finite-element models that may involve sharp discontinuities in material properties, multiple element types, and contact nonlinearities are developed. Their development is driven by the desire to efficiently solve models of rigid pavement systems that require explicit modeling of spatially varying and discontinuous material properties, bending elements meshed with solid elements, and separation between the slab and subgrade. General definitions for restriction and interpolation operators applicable to models composed of multiple, displacement-based isoparametric finite-element types are proposed. Related operations are used to generate coarse mesh element properties at integration points, allowing coarse-level coefficient matrices to be computed by a simple assembly of element stiffness matrices. The proposed strategy is shown to be effective on problems involving spatially varying material properties, even in the presence of large variations within coarse mesh elements. Techniques for solving problems with nodal contact nonlinearities using the proposed multigrid methods are also described. The performance of the multigrid methods is assessed for model problems incorporating irregular meshes and spatially varying material properties, and for a model of two rigid pavement slabs subjected to thermal and axle loading that incorporates nodal contact conditions and both solid and bending elements.