A Primary Computational Unifying Platform Based On The Meshless Method

Electromagnetic wave is the foundation of modern communication system,therefore,the analysis and solution about various electromagnetic field problem is requisite.With many years of studies,different numerical methods have been proposed and developed in time-and frequency-domain.The preprocessing step alongside with these methods is meshing solution domain,which is time-consuming especially for the complex structures.If this process can be avoided,the simulation would become simple.The meshless method can achieve this goal since it is based on the scattered nodes.Therefore,with the basis of meshless method,this paper applies it in electromagnetic simulations and some novel methods are proposed.First,paper presents the mathematical principles of the meshless method through formula derivation.After introducing the meshless method to Maxwell's equations some basic theories can be obtained,such as iterative formulation and dispersion characteristics.Moreover,the meshless method is extended to analyze the electromagnetic problems in plasma medium.In addition,many existing numerical methods have been proposed based on different principles.To unify these methods and the meshless method,they are all derived by node-based weighted-residues method.Next,in the solution of Maxwell's equations with RPIM method,two curl equations are solved through the iteration of electric and magnetic fields.The precondition of this process is Voronoi tessellation.To avoid this complex process,utilize the meshless method to solve wave equation and field solution then can be obtained only with one type of node.Moreover,due to the conformal capacity of meshless method and simplicity of FDTD method,these two methods are considered to hybridize and analyze special structures.In addition,a new absorbing boundary conditions(ABCs)is introduced into wave equation for accurate open simulation.In the derivation,we can find results same as other ABCs.At last,with some manipulations in the time domain,a novel unconditionally stable meshless is proposed and this method can exceed the limit of time step.The effectiveness of this method is validated with numerical experiments and proved theoretically.Last,based on wave equation and eigen analysis,a novel analytical time-domain method for electromagnetic modeling is proposed.The proposed method is only discretized in space,temporal domain keeps continuous.Therefore,this method can obtain field solution at any time instantly.Furthermore,there is no error due to the discretization in time.