Assessing the accuracy of different remapping methods in adaptive mesh refinement

Abstract

Additive manufacturing of metals has attracted much attention over the last years, promoting the development of several computational models for numerical simulation of the laser powder bed fusion (LPBF) process. Nevertheless, the finite element analysis of the LPBF process requires a large computational time. Thus, adaptive mesh refinement strategies are commonly adopted to reduce computational cost, which require some remapping procedure to transfer the state variables from the old mesh to the new one. The present study analyses two different remapping algorithms, namely the Inverse Isoparametric Mapping (IIM) and the Dual Kriging (DK) method. The IIM method uses the shape functions of the finite elements, while the DK method provides an explicit parametric interpolation. The case study adopted covers both coarsening and refinement procedures, using a mathematical function to define the mapped state variable. The accuracy of the remapping methods was lower in the refinement in comparison with the coarsening procedure. The error in the approximation is lower using the DK method in comparison with the IIM method. However, the IIM method does not suffer from error propagation in successive stages of either refinement/derefinement or coarsening/decoarsening.