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The development of hierarchical bases of the additive kind for corner singularities in triangular cells

Singular basis functions are known to improve the accuracy and convergence of numerical solutions when field singularities are present. Existing singular bases may be classified as substitutive or additive. Additive functions can be shown to provide a robust representation, that can adapt to situations when the field singularity is not produced by a particular excitation. In this presentation, a hierarchical additive type of basis is proposed for corner singularities in two-dimensional electromagnetic field problems. An investigation of the resulting matrix condition numbers is also reported.