Parallel iterative partitioned coupling procedure for multi-scale piezoelectric finite element analysis

This paper presents parallel multi-scale piezoelectric finite element (FE) analyses of piezoelectric ceramics by using the scanning electron microscope (SEM) and the electron backscatter diffraction (EBSD) measured crystal morphology model based on the crystallographic homogenization method. Since coefficient matrix of FE equation for the electromechanical coupling problem is not positive definite and strongly ill-condition, a parallel iterative partitioned coupling procedure based on the block Gauss-Seidel (BGS) method with the conjugate gradient (CG) solver is applied to the multi-scale analysis. 3-dimensional micro polycrystal morphology of a barium titanate ceramic is measured by using the SEM-EBSD apparatus and introduced to the parallel multi-scale analysis. We investigate on micro FE modeling with crystal orientation distribution and convergences of both the BGS method and the CG solver.