Adaptive Projection‐Based Interpolation as a Pre‐Processing Tool in the Finite Element Workflow for Elasticity Simulations of the Dual Phase Microstructures

Abstract

An improvement to the workflow used in modeling boundary‐value problems in complex materials, which allows for reducing computational time by the factor of 5 while maintaining comparable quality of the solution is proposed in this paper. After formulating the main goals of the paper, a review of the state‐of‐the‐art techniques used for generating a digital material representation is presented. This is followed by a description of the procedure for solving boundary‐value problems and finding a representation of a given microstructure in a desired functional base. Finally, we showcase how to combine these techniques to obtain mentioned significant calculation speedup. Developed approach is validated during investigation of a selected case study, which is modeling of a linear elastic deformation of a dual phase ferritic–martensitic steel under thermal loading conditions.

Modeling of the Absorption of the Electromagnetic Wave Energy in the Human Head Induced by Cell Phone

“…These values correspond to different material data. Next, we utilize a projection based interpolation technique [3] [4] to generate a continuous approximation of the material data, compare Figure 2. We utilize three dimensional h adaptation algorithm [5] with hexahedral finite elements, with the error estimator based on the L2 norm difference between the local element approximation and the MRI scan data.…”

Application of projection-based interpolation algorithm for non-stationary problem

“…In this paper, we present an alternative projection-based interpolation solver that reduces the computational cost to O(N ) in the case of sequential execution and even further to O( N c ) when we use c cores. The projection-based interpolation technique has been successfully used for generating continuous approximations of two-or threedimensional bitmaps, with applications to material science [10,11,12,15] or modeling of the human head [8]. In this paper, we focus on utilizing the Projection-Based Interpolation (PBI) algorithm for solving a sequence of projection problems arising from the Euler scheme used for time discretization of non-stationary problems.…”