Isogeometric analysis for electrostatic problem with inhomogeneous boundary conditions

Preliminary isogeometric analysis(IGA) is not suitable for electrostatic problem with inhomogeneous boundary conditions,due to the non-interpolatory feature of non-uniform rational B-splines(NURBS) employed in IGA.In this paper,virtual work equation with Lagrange multiplier is established for inhomogeneous boundary conditions and weakened to augmented algebraic equations containing control variables involved with NURBS elements and discretized Lagrange multipliers corresponding to inhomogeneous boundary.The modified method is suitable for electrostatic problem with inhomogeneous boundary conditions even though the degree of freedom is little increased.The numerical results,compared with analytical solution and conventional finite element method,show that the proposed method is effective to inhomogeneous boundary and yields much better results,consumes less amount of DOFs,and obtains quicker convergence than traditional method.