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In the present work we introduce a complete set of algorithms to efficientlyperform adaptive refinement and coarsening by exploiting truncated hierarchicalB-splines (THB-splines) defined on suitably graded isogeometric meshes, thatare called admissible mesh configurations. We apply the proposed algorithms totwo-dimensional linear heat transfer problems with localized moving heatsource, as simplified models for additive manufacturing applications. We firstverify the accuracy of the admissible adaptive scheme with respect to anoverkilled solution, for then comparing our results with similar schemes whichconsider different refinement and coarsening algorithms, with or without takinginto account grading parameters. This study shows that the THB-splineadmissible solution delivers an optimal discretization for what concerns notonly the accuracy of the approximation, but also the (reduced) number ofdegrees of freedom per time step. In the last example we investigate thecapability of the algorithms to approximate the thermal history of the problemfor a more complicated source path. The comparison with uniform andnon-admissible hierarchical meshes demonstrates that also in this case ouradaptive scheme returns the desired accuracy while strongly improving thecomputational efficiency.

Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes