hp-Adaptation for the FEM Analysis of Waveguides

[摘要] Thenite element method (FEM) is a powerful tool for the computational analysis of a wide rangeof electromagnetic problems. As the complexity of the problems is increased so are the demandsin terms of the computational resources required to obtain a su ciently accurate solution. In anattempt to obtain a desired accuracy at a lower computational cost adaptive and higher ordermethods are often employed. These methods generally entail re ning the solution only in the areaswhere greater complexity is required, thus decreasing the total computational demand.The adaptivenite element method is implemented and used to analyse the transverse electriccutoeigenmodes of 2D waveguiding structures. The higher order hierarchical vector basis functionsthat form part of this implementation are automatically generated to very high orders, with theresults presented in excellent agreement to analytical ones where applicable. Accuracy to the order ofnumeric precision is attained. Using these adaptive methods, it is also possible to achieve improvedcost e ciency of the error metrics considered with respect to storage requirements and computationalcost.

[发布机构] Stellenbosch University