Comparison ofhp‐adaptive methods in finite element electromagnetic wave propagation

Abstract

For AuthorsIf you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation.*Related content and download information correct at time of download. Purpose -This paper aims to show that simple geometry-based hp-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 posteriori 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.

Adaptive FEM with Domain Decomposition Method for Partitioned-Based Fluid–Structure Interaction

“…Hence, in our implementation, although the error estimator is evaluated separately, a common formulation for both the fluid and structure domains is used. The residual-based error indicator η is the weighted sum of element and edge contributions [35],…”

Subdivision Directional Fields

“…This paradigm is extensively employed in the FEM literature when using either refined elements (h-refinement) or higherorder basis functions (p-refinement) [Babuška and Suri 1994]. This has also been applied to vector fields in planes and in volumes [Schober and Kasper 2007]. A major difference in which our subdivision method departs from both of these approaches is that the geometry of the target limit surface is different from that of the control coarse mesh.…”

Finite Element Method for Fluid Structure Interaction with hp-Adaptivity

“…The approach for adaptivity taken in this work follows the one presented in [7]. It is well known that h-adaptivity is better suited in a class of problem where the smoothness of solution is compromised.…”

“…A posteriori error indicator is used based on a residual estimator of each element. Thirdly, a simple algorithm to decide between the hand p-adaptivity is constructed using prescribed key points at certain locations in the domain of the problem following the approach in [7]. Finally, since the domain is to be discretized with triangular elements, a red-green-blue refinement technique is used for mesh adaptivity.…”

“…For structure domain the residual comes from the Lagrangian STVK formulation of (3). The second term measures discontinuity of the computed flux inside Ω while the third term is for the boundary Γ.The global error indicator η is as usual the sum of η K over all the elementsThe approach for adaptivity taken in this work follows the one presented in [7]. It is well known that h-adaptivity is better suited in a class of problem where the smoothness of solution is compromised.…”