A new and efficient approach to generate dedicated three-dimensional (3D) finite element meshes for further multiscale analysis of polycrystalline microstructure behavior under loading conditions is the subject of the present research. An explicit image of microstructure is created on the basis of a digital material representation approach. The Monte Carlo (MC) method is used in order to obtain 3D representation of the investigated morphology. Then, information obtained from the MC method is transferred to the initial, coarse, finite element mesh. This mesh in the subsequent steps of the developed approach is modified based on the information provided from the adaptive finite element solver. The two phase ferritic martensitic microstructure is selected as a case study. A description of the proposed finite element mesh generation algorithm as well as an example of application of the obtained mesh to the multiscale model of plastic deformation under tension are presented in the paper.

The main aim of the work is development and comparison of algorithms for mesh creation that can be further used to investigate material behavior under loading conditions, on the basis of digital material representation. Particular attention is put on development of conforming meshes for two-phase materials. Two approaches are investigated within the present work. The first is based on mesh refinement along particular microstructure features. The second incorporates the cellular automata phase transformation model into the finite element adaptation technique. Description of the two approaches and an example of application of the obtained meshes to analyze multiscale material behavior under plastic deformation condition are presented.

The article presents the design and optimization of GPU kernels for numerical integration, as it is applied in the standard form in finite element codes. The optimization process employs auto-tuning, with the main emphasis on the placement of variables in shared memory or registers. OpenCL and first order FEM approximation are selected for code design, but the techniques are also applicable to CUDA programming model and other types of finite element discretizations (including discontinuous Galerkin and isogeometric). The auto-tuning optimization is performed for four example graphics processors and the obtained results are discussed.