A refinement algorithm for electromagnetic field computations using a combination of finite element and meshless methods is introduced. Bridging scales are used to separate the finite element and meshless shape functions to make the refinement hierarchical and to uphold the mathematical properties such as consistency and linear independence for all the bases. To facilitate the application of the proposed algorithm, details about the node addition, requirements for the node distribution, and relationships between the finite element and meshless shape functions, as well as the determination of the stop criterion are also fully addressed. Primary numerical results are reported to demonstrate and validate the applicability and advantages of the proposed algorithm over traditional ones.
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