An improved truly meshless method based on a new shape function and nodal integration

An improved truly meshless method is presented for three-dimensional (3D) electromagnetic problems. In the proposed method, the computational time for the construction of the introduced shape function is lower than the other meshless methods considerably. An efficient and stable nodal integration technique based on the Taylor series extension is also used in the proposed meshless method. Weak-form formulations adopted for creating discretized system equations of electrostatic and electromagnetic 3D problems are also presented. In the proposed fast truly meshless method, unlike in traditional meshless schemes where background mesh is utilized to compute integrals, nodal integration is used to avoid meshing. The numerical solutions for electrostatic and electromagnetic problems show that the presented method is a robust meshfree method and possesses better computational properties compared with traditional meshless methods. Copyright © 2012 John Wiley & Sons, Ltd.