<p>Waveguides are used to transmit electromagnetic signals.Their geometry is typically long and slender their particularshape can be used in the design of computational methods. Onlyspecial modes are transmitted and eigenvalue and eigenvectoranalysis becomes important.</p><p>We develop a .nite-element code for solving theelectromagnetic .eld problem in closed waveguides .lled withvarious materials. By discretizing the cross-section of thewaveguide into a number of triangles, an eigenvalue problem isderived. A general program based on Arnoldi’s method andARPACK has been written using node and edge elements toapproximate the .eld. A serious problem in the FEM was theoccurrence of spurious solution, that was due to impropermodeling of the null space of the curl operator. Therefore edgeelements has been chosen to remove non physical spurioussolutions that arises.</p><p>Numerical examples are given for homogeneous andinhomogeneous waveguides, in the homogeneous case the resultsare compared to analytical solutions and the right order ofconvergence is achieved. For the more complicated inhomogeneouswaveguides with and without striplines, comparison has beendone with results found in literature together with gridconvergence studies.</p><p>The code has been implemented to be used in an industrialenvironment, together with full 3-D time and frequency domainsolvers. The2-D simulations has been used as input for full3-D time domain simulations, and the results have been comparedto what an analytical input would give.</p>

Waveguides are used to transmit electromagnetic signals.Their geometry is typically long and slender their particularshape can be used in the design of computational methods. Onlyspecial modes are transmitted and eigenvalue and eigenvectoranalysis becomes important. We develop a .nite-element code for solving theelectromagnetic .eld problem in closed waveguides .lled withvarious materials. By discretizing the cross-section of thewaveguide into a number of triangles, an eigenvalue problem isderived. A general program based on Arnoldi’s method andARPACK has been written using node and edge elements toapproximate the .eld. A serious problem in the FEM was theoccurrence of spurious solution, that was due to impropermodeling of the null space of the curl operator. Therefore edgeelements has been chosen to remove non physical spurioussolutions that arises. Numerical examples are given for homogeneous andinhomogeneous waveguides, in the homogeneous case the resultsare compared to analytical solutions and the right order ofconvergence is achieved. For the more complicated inhomogeneouswaveguides with and without striplines, comparison has beendone with results found in literature together with gridconvergence studies. The code has been implemented to be used in an industrialenvironment, together with full 3-D time and frequency domainsolvers. The2-D simulations has been used as input for full3-D time domain simulations, and the results have been comparedto what an analytical input would give. / NR 20140805