A meshfree-based local Galerkin method with condensation of degree of freedom

• Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form.
• The local discrete equation is established by using moving kriging interpolation based on cells with arbitrary shape.
• Computational efficiency of present method is improved for nearly 22 times compared with the method proposed by Lei Gu in the numerical example.
• Numerical example also shows that the present method has good accuracy and convergence.

Condensation technique of degree of freedom is firstly proposed to improve the computational efficiency of meshfree method with Galerkin weak form. In present method, scattered nodes without connectivity are divided into several subsets by cells with arbitrary shape. The local discrete equations are established over each cell by using moving kriging interpolation, in which the nodes that located in the cell are used for approximation. Then, the condensation technique can be introduced into the local discrete equations by transferring equations of inner nodes to equations of boundary nodes based on cell. In the scheme of present method, the calculation of each cell is carried out by meshfree method with Galerkin weak form, and local search is implemented in interpolation. Numerical examples show that the present method has high computational efficiency and convergence, and good accuracy is also obtained.