HIGHER-ORDER ISOPARAMETRIC RECTANGULAR ELEMENT BASED FINITE ELEMENT METHOD FOR EIGENVALUE PROBLEMS IN ELECTROMAGNETICS
Keywords:
finite element method, fem, isoparametric formulation, Jacobian transformation, minimum isoparametric elements, quadrilateral element, Galerkin method, eigenvalue problem, electromagnetics.Abstract
In this paper, I have presented a different approach to the finite element method for solving the eigenvalue problem in electromagnetics using the isoparametric rectangular element for the arbitrarily shaped domain. The concept behind this approach is to map the whole geometrical domain into the minimum quadrilaterals (curve edges, if any). Then, every four vertices of a quadrilateral are transformed into a master rectangular element in a natural coordinate system using the Lagrangian interpolation basis function and Jacobin matrix. This is not a new concept, but an observed fact is that we can simply achieve a high degree of accuracy using very less isoparametric elements of a high order. After this, the method of residual and Galerkin method is used to solve the weak form of the Helmholtz equation on a circular waveguide using a single second-order quadrilateral element and ridged circular waveguide.
