%0 Report %1 adam1997eigenvalue %A Adam, Stefan %A Arbenz, Peter %A Geus, Roman %C Zürich %D 1997 %K 65f15-numerical-eigenvalues-eigenvectors 65n30-pdes-bvps-finite-elements 78m10-optics-electromagnetism-finite-element-method %N 275 %R 10.3929/ethz-a-006652182 %T Eigenvalue solvers for electromagnetic fields in cavities %U https://www.research-collection.ethz.ch/handle/20.500.11850/69323 %X We investigate algorithms for computing steady state electromagnetic waves in cavities. The Maxwell equations for the strength of the electric field are solved by (1) a penalty method using common linear and quadratic node-based finite elements, and (2) a mixed method with linear and quadratic finite edge elements for the eld values and corresponding node-based finite elements for the Lagrange multiplier. These are two approaches that avoid so-called spurious modes which are introduced if the divergence-free condition for the electric eld is not treated properly. The resulting large sparse matrix eigenvalue problems have been solved by various algorithms (1) subspace iteration, (2) block Lanczos algorithm, (3) implicitly restarted Lanczos algorithm and (4) Jacobi-Davidson algorithm. For all finite element approximations we compare the amount of work it takes each solver to compute a few of the smallest positive eigenvalues and corresponding eigenmodes to a given accuracy.

@techreport{adam1997eigenvalue, abstract = {We investigate algorithms for computing steady state electromagnetic waves in cavities. The Maxwell equations for the strength of the electric field are solved by (1) a penalty method using common linear and quadratic node-based finite elements, and (2) a mixed method with linear and quadratic finite edge elements for the eld values and corresponding node-based finite elements for the Lagrange multiplier. These are two approaches that avoid so-called spurious modes which are introduced if the divergence-free condition for the electric eld is not treated properly. The resulting large sparse matrix eigenvalue problems have been solved by various algorithms (1) subspace iteration, (2) block Lanczos algorithm, (3) implicitly restarted Lanczos algorithm and (4) Jacobi-Davidson algorithm. For all finite element approximations we compare the amount of work it takes each solver to compute a few of the smallest positive eigenvalues and corresponding eigenmodes to a given accuracy.}, added-at = {2022-02-22T01:14:48.000+0100}, address = {Zürich}, author = {Adam, Stefan and Arbenz, Peter and Geus, Roman}, biburl = {https://www.bibsonomy.org/bibtex/250a98059580278b1de6adae6de57abc8/gdmcbain}, doi = {10.3929/ethz-a-006652182}, institution = {ETH Zürich, Departement Informatik}, interhash = {5315e31953c03ce5d9d21e4929309052}, intrahash = {50a98059580278b1de6adae6de57abc8}, keywords = {65f15-numerical-eigenvalues-eigenvectors 65n30-pdes-bvps-finite-elements 78m10-optics-electromagnetism-finite-element-method}, language = {en}, month = oct, number = 275, timestamp = {2022-02-22T01:29:57.000+0100}, title = {Eigenvalue solvers for electromagnetic fields in cavities}, type = {Technische Berichte}, url = {https://www.research-collection.ethz.ch/handle/20.500.11850/69323}, year = 1997 }