The RBF Meshless Method And It's Application In The Numerical Analysis On MEMS Electromagnetic Problems

Meshless method developed recently is a new type of numerical methods. It was introduced for solving many PDEs. Meshless methods give up depending on unit. There are many kinds of meshless methods now, such as EFG, LSC, RBF. These methods are divided into two classes: those based on collocations and those based on weak forms. The first class is truly meshless method and does not require a mesh structure or a numerical integration procedure. EFG belongs to those based on weak forms, PCM belongs to those based on collocations.Collocation-based Meshfree Method has been developed based on weighted residual approach. No background mesh for integration, this method is a truly meshless technique without mesh discretization. This type of methods uses a set of nodes distributed in solving domain instead of traditional elements. The interior nodes satisfy the balance equation; the boundary points satisfy the boundary conditions. In order to avoid the ill-posed equation, we must use the special stabilization scheme. Numerical results indicate that this method is effective.Radial Basis Function(RBF) is a kind of special function. In this paper, we introduce Radial Basis Function into meshless method and study the RBF meshless method in detail. We propose the Hermit interpolation scheme to solve the PDEs which have Neumman boundary conditions.The multiquadric radial basis function method (MQ RBF or, simply, MQ) is ranked the best based on its high accuracy, ease of implementation, good visual aspect, and low execution time and storage requirements in this class of RBF meshless methods. Numerical results indicate that this method is more effective than FEM.In this paper, the principle of improved MQ is discussed, and 3D electromagnetic problems are solved. It is achieved by adding a set of nodes (which can lie inside or outside of the solving domain) adjacent to the boundary and, correspondingly, add and additional set of collocation equations obtained via collocation of the PDE on the boundary [5]. Numerical results show a considerable improvement in accuracy over the traditional MQ method and more effective and accurate than FEM.