Comparison of hp-adaptive methods in finite element electromagnetic wave propagation

Purpose - This paper aims to show that simple geometry-based lip-algorithms using an explicit a posteriori error estimator are efficient in wave propagation computation of complex structures containing geometric singularities. Design/methodology/approach - Four different hp-algorithms are compared with common h- and p-adaptation in electrostatic and time-harmonic problems regarding efficiency in number of degrees of freedom and runtime. An explicit a posterio error estimator in energy norm is used for adaptive algorithms. Findings - Residual-based error estimation is sufficient to control the adaptation process. A geometry-based hp-algorithm produces the smallest number of degrees of freedom and results in shortest runtime. Predicted error algorithms may choose inappropriate kind of refinement method depending on p-enrichment threshold value. Achieving exponential error convergence is sensitive to the element-wise decision on h-refinement or p-enrichment. Research limitations/implications - Initial mesh size must be sufficiently small to confine influence of phase lag error. Practical implications - Information on implementation of hp-algorithm, and use of explicit error estimator in electromagnetic wave propagation is provided. Originality/value - The paper is a resource for developing efficient finite element software for high-frequency electromagnetic field computation providing guaranteed error bound.