Imposition of essential boundary condition in heat conduction problem based on Isogeometric analysis

One of the major concerns with Isogeometric analysis is finding an efficient approach to impose essential boundary conditions (EBCs). Non-interpolating nature of NURBS leads to the non-satisfaction of Kronecker delta property therefore, imposing EBCs is not a straightforward task. The purpose of this paper is using a two-step method to impose EBCs for improving the accuracy of solution field in transient heat flow within two-dimensional region. In the proposed approach, The EBCs are defined on Dirichlet boundary as determined temperatures and independent of time. In the first step, EBCs are built into the variational formulation weakly, choosing weight function appropriately. In the second step, with fixed condition, the system of equations is adjusted appropriately. For investigation of the proposed approach, two numerical examples have been performed. The results demonstrate significant improvement in accuracy and rate of convergence in comparison with direct imposition of essential boundary condition and finite element method

Keywords:

isogeometric , essential boundary conditions , transient heat flow