volume | PIER Journals

Abstract

This paper presents a convex meshfree framework for solving the scalar Helmholtz equation in the waveguide analysis of electromagnetic problems. The generalized meshfree approximation (GMF) method using inverse tangent basis functions and cubic spline weight functions is employed to construct the first-order convex approximation which exhibits a weak Kronecker-delta property at the waveguide boundary and allows a direct enforcement of homogenous Dirichlet boundary conditions for the transverse magnetic (TM) mode analyses. Three arbitrary waveguide examples are analyzed to demonstrate the accuracy of the presented formulation, and comparison is made by the analytical, finite element and meshfree solutions.

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Dr. Li-Fang Wang