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1 – 2 of 2Marc Schober and Manfred Kasper
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…
Abstract
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.
Details
Keywords
IN this number we make some commemoration of the twenty‐five years so happily achieved by the King‐Emperor. As our contributors show, the cardinal event of the whole of the Reign…
Abstract
IN this number we make some commemoration of the twenty‐five years so happily achieved by the King‐Emperor. As our contributors show, the cardinal event of the whole of the Reign, so far as libraries were concerned, was the passing of the Public Libraries Act of 1919. The generations change rapidly, and there are few to‐day who remember acutely the penury and struggle which were involved in the fact that all public library expenditure had to be kept within “the limit of the penny rate.” It is possibly true that the average community has taken no very intelligent advantage of the breaking of its financial fetters; in no town in the British Empire can it be said that there is anything approaching generosity, let alone extravagance, towards libraries. Even in the greatest cities, where they have built fine buildings and opened them with much ceremony, the rate allocation for their maintenance is not nearly of the scale that finds acceptance, or did find acceptance, in the United States. That is because we are young people in an old country. The tradition dies hard that education is a luxury and that libraries, which in the eyes of many are only remotely related to education, are an even greater luxury. We heard it said recently that many local authorities regarded the libraries as a sort of joke, and delighted to cut down their expenditure upon them. This lugubrious way of opening our remarks upon the Jubilee is only by way of pointing out that to‐day, at any rate, we have the power to go ahead if we convince our authorities that it is desirable to do so.