Application of Web-splines for Coaxial Waveguides Gökhan Apaydin 1, 2 , Niyazi Ari 1 , and Selim Seker 2 1 University of Technology Technoparkstrasse 1, Zürich, 8005, Switzerland gapaydin@hsz-t.ch , nari@hsz-t.ch 2 Department of Electrical and Electronic Engineering Bogazici University, Istanbul, 34340, Turkey seker@boun.edu.tr Abstract: This paper illustrates the weighted extended b-splines as basis functions for finite element method in electromagnetics. This method does not need mesh generation, and is applied to coaxial waveguide applications. The results are compared with the exact solutions in literature. The maximum relative error is used for comparison. This method can be used in more electromagnetic applications for future studies. Keywords: Finite Element Method, Waveguides, Web-splines 1. Introduction Waveguides are used to transfer power and communication signals from one place to another. Coaxial waveguide, which is used to connect radio frequency components, is one of them. The field configurations should satisfy the wave equation and given boundary condition. The finite element method (FEM) is one of the numerical solution methods for partial differential equations. Some engineering applications use partial differential equations which are difficult to solve. This method is powerful to find solutions for irregular domains or inhomogeneous media. The wave equations can be solved by using FEM. The idea is to use piecewise continuous functions and meshes for approximation. Mesh generation causes time consumption; so many researches have been done [1-4]. The basis splines (b-splines), which are used in data fitting, numerical approximation, computer aided design etc., were developed by Carl de Boor, de Casteljau, Bezier [5-6]. The b-splines can be considered as basis functions for FEM. But boundary conditions cause instability. Then Hollig developed extended b-splines and weighted extended b-splines (web-splines) as basis functions for different boundary conditions [7-11]. Therefore accurate results have been obtained using fewer nodes. This paper presents web-splines and their implementations for electromagnetic problems such as two dimensional electromagnetic wave equations for coaxial waveguides. The cutoff wave numbers of modes for the coaxial waveguides are studied. The numerical approximations are compared with the analytical results. 2. Web-splines Web-spline method is a new type of meshless finite elements without using mesh generation. The standard uniform b-spline n b of degree n for one dimension is defined by the recursion [5, 11] as 23rd Annual Review of Progress in Applied Computational Electromagnetics March 19-23, 2007 - Verona, Italy ©2007 ACES 1147