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

Abstract

SUMMARYAn 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.

Unconditionally stable improved meshless methods for electromagnetic time-domain modeling

“…Recently, a new method to resolve one of the biggest difficulties in meshless methods, i.e. shape function construction, has been engendered in Razmjoo et al (2010aRazmjoo et al ( , b, 2011bRazmjoo et al ( , 2012. Based on the data fitting algorithm and PUM, a complete approach for constructing shape functions has been introduced and its performance in electromagnetic and electrostatic problems has been investigated.…”

Meshfree-enriched electromagnetic finite element formulation using nodal integration

“…A stabilized conforming nodal integration was later proposed to fulfill the linear exactness. Recently, an efficient nodal integration scheme based on Taylor series expansion was developed in conjunction with the modified meshfree shape functions for electromagnetic analysis. A smoothed particle electromagnetics method based on the nodal integration scheme was also developed for the simulation of 3D transient electromagnetic problems.…”

Criterion for selecting the shape functions in electromagnetic meshless methods

“…However, one of the major problems that is high computational cost, still exists in meshless method. Recently, some direct meshless methods have been proposed to solve the time consumption issue [3][4][5][6][7]. The direct and conventional (indirect) meshless methods are different just in construction of the shape functions, whereas the direct meshless method proposes the shape functions, directly [3][4][5][6][7].…”

“…Recently, some direct meshless methods have been proposed to solve the time consumption issue [3][4][5][6][7]. The direct and conventional (indirect) meshless methods are different just in construction of the shape functions, whereas the direct meshless method proposes the shape functions, directly [3][4][5][6][7]. This novel method caused a great reduction in time consumption, because of cancelling the first matrix inversion calculation step and improved the accuracy by proposing an analytical shape function, which its derivatives exist, analytically [7].…”