A Reduced Lagrange Multiplier Method for Dirichlet Boundary Conditions in Isogeometric Analysis (TCEIA) - Lupinepublishers

A Reduced Lagrange Multiplier Method for Dirichlet Boundary Conditions in Isogeometric Analysis by Shuohui Yin in TCEIA - Lupinepublishers

Although the well-known standard Lagrange multiplier method (LMM) can even produce higher accuracy and easier implementation than other conventional schemes (e.g., the modified variational principle, the Nitsche’s method), however it inherently owns many difficulties in solving the system of discretized equations, mainly caused by new unknown Lagrange multipliers. The LMM naturally increases the problem size and leads to a poorly conditioned matrix equation. The singularity is also often encountered because of inappropriate selection of interpolation space for the Lagrange multiplier. In this paper, we propose an improved method, called reduced Lagrange multiplier method, which can overcome such drawbacks raised by the LMM in treating the Dirichlet-type boundary conditions in terms of Isogeometric Analysis.

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