High-order methods for thermal behavior of plate structures with internal heat sources

The paper proposes solving transient heat transfer in plates using high-order isogeometric analysis and high-order time integration schemes. The problem is often faced in fire-structure interaction where the heat transfer is coupled with the stress analysis. A major advantage for the proposed approach comes from high order continuity between elements. Thus, the need for rotational degrees of freedom is eliminated when analyzing the stresses in plates and the same mesh can also be used to recover the heat transfer patterns. To achieve the full potential of such high-order finite elements in space, we also use high-order time integration schemes so that the numerical solution can be significantly more accurate than the standard approaches. Furthermore, the isogeometric analysis is also used to represent the exact geometry thanks to the basis functions generated from Non-Uniform Rational B-Splines. Several test examples for the transient diffusion problem are presented. Compared to standard methods and for a prescribed accuracy the proposed approach requires significantly fewer degrees of freedom and a corresponding improvement in the computational efficiency.