The hp-adaptive FEM based on continuous Sobolev embeddings: isotropic refinements

The aim of this paper is to present a new class of smoothness testing strategies in the context of hp-adaptive refinements based on continuous Sobolev embeddings. In addition to deriving a modified form of the 1d smoothness indicators introduced in [26], they will be extended and applied to a higher dimensional framework. A few numerical experiments in the context of the hp-adaptive FEM for a linear elliptic PDE will be performed.

Valle d’Aosta section of the Sesia Zone: multi-stage HP metamorphism and assembly of a rifted continental margin

The spectrum characteristic of the EMC ranges from eclogites (containing omphacite and/or jadeite, garnet, phengite, glaucophane, zoisite, chloritoid, rutile) to phengite schists, calcschists, and marbles, as well as a variety of orthogneisses. Despite the intense polyphase deformation and HP-metamorphic recrystallization, it is possible in some locations to recognize pre-Alpine characteristics in some of the protoliths. For instance, two types of felsic orthogneiss can be distinguished in the Aosta Valley, one derived from Permian granitoids (with local preservation of intrusive contacts, magmatic inclusions, leucocratic veins and other magmatic structures; Stop 3), the other derived from pre-Variscan leuco-monzogranite, such as the building stone mined at the “Argentera” quarry near Settimo Vittone / Montestrutto (Stop 2; so-called “Verde Argento” contains jadeite, phengite, K-feldspar, quartz). Polycyclic and more rarely monocyclic metasediments contain evidence of a complex Alpine PTDt-evolution, locally including relics of their prograde history from blueschist, one or more stages at eclogite facies. Recent petrochronological studies have dated this HP-evolution of the Sesia Zone in some detail. In the area visited, clear evidence of HP-cycling has been identified in one km-size tectonic slice (Stop 1), but not in adjacent parts of the EMC, indicating “yo-yo tectonics”. Partial retrogression and attendant ductile to brittle deformation of the HP-rocks is evident in one of the outcrops (Stop 4). Apart from the four localities in the Sesia Zone, a final outcrop introduces HP-rocks of the adjacent Piemonte oceanic unit, specifically calc-schists and ophiolite members of the “Zermatt-Saas” zone. The hilltop outcrop (Stop 5) displays foliated antigorite schist with peridotite relics (clinopyroxene, spinel) containing lenses derived from doleritic dykes. These fine-grained metarodingites and the folded veins containing Mg-chlorite and titanoclinohumite within serpentinite once again indicate equilibration under low-temperature eclogite facies conditions. However, these units reached that HP stage more than 20 Ma after the youngest eclogite facies imprint recognized in the Sesia Zone. Despite nearly half a century of intense study in the Sesia Zone, the complex assembly of its HP-terranes and their relation to more external parts of the Western Alps remains incompletely understood. This field guide merely introduces a few of the classic outcrops and discusses some of the critical evidence they contain, but it could not incorporate details on each stage of the evolution recognized so far.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

3D hp-adaptive finite element simulations of a magic-T electromagnetic waveguide structure

This paper employs a 3D hp self-adaptive grid-refinement finite element strategy for the solution of a particular electromagnetic waveguide structure known as Magic-T. This structure is utilized as a power divider/combiner in communication systems as well as in other applications. It often incorporates dielectrics, metallic screws, round corners, and so on, which may facilitate its construction or improve its design, but significantly difficult its modeling when employing semi-analytical techniques. The hp-adaptive finite element method enables accurate modeling of a Magic-T structure even in the presence of these undesired materials/geometries. Numerical results demonstrate the suitability of the hp-adaptive method for modeling a Magic-T rectangular waveguide structure, delivering errors below 0.5% with a limited number of unknowns. Solutions of waveguide problems delivered by the self-adaptive hp-FEM are comparable to those obtained with semi-analytical techniques such as the Mode Matching method, for problems where the latest methods can be applied. At the same time, the hp-adaptive FEM enables accurate modeling of more complex waveguide structures.

A three-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities

We propose the use of a highly-accurate three-dimensional (3D) fully automatic hp-adaptive finite element method (FEM) for the characterization of rectangular waveguide discontinuities. These discontinuities are either the unavoidable result of mechanical/electrical transitions or deliberately introduced in order to perform certain electrical functions in modern communication systems. The proposed numerical method combines the geometrical flexibility of finite elements with an accuracy that is often superior to that provided by semi-analytical methods. It supports anisotropic refinements on irregular meshes with hanging nodes, and isoparametric elements. It makes use of hexahedral elements compatible with high-order H(curl)H(curl) discretizations. The 3D hp-adaptive FEM is applied for the first time to solve a wide range of 3D waveguide discontinuity problems of microwave communication systems in which exponential convergence of the error is observed.

Goal-oriented self-adaptive hp-strategies for finite element analysis of electromagnetic scattering and radiation problems

In this paper, a fully automatic goal-oriented hp-adaptive finite element strategy for open region electromagnetic problems (radiation and scattering) is presented. The methodology leads to exponential rates of convergence in terms of an upper bound of an user-prescribed quantity of interest. Thus, the adaptivity may be guided to provide an optimal error, not globally for the field in the whole finite element domain, but for specific parameters of engineering interest. For instance, the error on the numerical computation of the S-parameters of an antenna array, the field radiated by an antenna, or the Radar Cross Section on given directions, can be minimized. The efficiency of the approach is illustrated with several numerical simulations with two dimensional problem domains. Results include the comparison with the previously developed energy-norm based hp-adaptivity.

A comparison between PML, infinite elements and an iterative BEM as mesh truncation methods for HP self-adaptive procedures in electromagnetics

Finite element hp-adaptivity is a technology that allows for very accurate numerical solutions. When applied to open region problems such as radar cross section prediction or antenna analysis, a mesh truncation method needs to be used. This paper compares the following mesh truncation methods in the context of hp-adaptive methods: Infinite Elements, Perfectly Matched Layers and an iterative boundary element based methodology. These methods have been selected because they are exact at the continuous level (a desirable feature required by the extreme accuracy delivered by the hp-adaptive strategy) and they are easy to integrate with the logic of hp-adaptivity. The comparison is mainly based on the number of degrees of freedom needed for each method to achieve a given level of accuracy. Computational times are also included. Two-dimensional examples are used, but the conclusions directly extrapolated to the three dimensional case.

Medidas experimentales de la complejidad computacional de un código autoadaptativo HP para problemas abiertos acelerado mediante ACA

The aim of the novel experimental measures presented in this paper is to show the improvement achieved in the computation time for a 2D self-adaptive hp finite element method (FEM) software accelerated through the Adaptive Cross Approximation (ACA) method. This algebraic method (ACA) was presented in an previous paper in the hp context for the analysis of open region problems, where the robust behaviour, good accuracy and high compression levels of ACA were demonstrated. The truncation of the infinite domain is settled through an iterative computation of the Integral Equation (IE) over a ficticious boundary, which, regardless its accuracy and efficiency, turns out to be the bottelneck of the code. It will be shown that in this context ACA reduces drastically the computational effort of the problem.

Validación de HP UV-LED para la detección en continuo de contaminantes en aguas continentales mediante fluorescencia

La preservación del medio ambiente, el avance en las técnicas para que el impacto de la actividad humana sobre la fauna y flora sea lo menor posible, hacen que se deban monitorizar los diversos indicadores de calidad. El presente estudio viene motivado debido a que actualmente existen sistemas de medida y control en continuo de la calidad de las aguas, al margen de los estudios de laboratorio por toma de muestras, a través de los cuales se obtienen indicadores de calidad. El desarrollo tecnológico en analizadores en continuo para la medida de fósforo, amonio, DBO y otros, hacen que cada vez se consiga un control más exhaustivo de la calidad en tiempo real. Sin embargo, la detección temprana de contaminantes que no deben encontrarse presentes en el agua, hacen que el desarrollo de sensores de detección de estos contaminantes sea de gran utilidad. A este respecto, las técnicas mediante fluorescencia presentan enormes ventajas, ya que no existe contacto directo con la muestra, reduciéndose el desgaste y alargando el tiempo entre mantenimientos, como se ha comprobado en numerosos desarrollos con tecnología láser. Para la producir fluorescencia, tradicionalmente se vienen utilizando en el laboratorio principalmente lámparas de gas y monocromadores. Los nuevos LED de alta potencia en el espectro ultravioleta son una alternativa muy interesante que además puede ser aplicada en los mencionados sistemas de medición en continuo. En este trabajo se realiza un estudio de viabilidad de estos dispositivos como fuentes de excitación para la producción de fluorescencia tomando como contaminantes los hidrocarburos. El funcionamiento en estaciones en continuo hace que se tenga que realizar además ensayos de vida acelerados, así como estudios de modos de trabajo. Al respecto de la fluorescencia producida, se estudia la influencia de factores que pueden afectar a las medidas, tales como la temperatura. El estudio del espectro y su análisis para la identificación del contaminante es otro de los puntos desarrollados en este trabajo. Por último, y dado que la monitorización se realiza en modo continuo, es necesario un sistema de comunicaciones compacto y fiable: en este apartado se analizan los metamateriales como solución tecnológica, ya que se adapta perfectamente a la filosofía de estas estaciones de medición. ABSTRACT Currently the monitoring of quality indicators is a need to preserve the environment and minimize the impact of human activity on the fauna and flora. Currently there are measuring systems and continuous monitoring of water quality, regardless of sampling laboratory studies, through which quality indicators are obtained. Technological development in continuous analyzers for the measurement of phosphorus, ammonia, BOD and others increasingly make a more comprehensive real-time quality control is achieved. However, early detection of contaminants that should not be present in the water, make the development of sensors for detecting these contaminants is very useful. In this regard, fluorescence techniques have huge advantages, since there is no direct contact with the sample, reducing wear and extending the time between maintenance, as has been demonstrated in numerous developments in laser technology. To produce fluoresce, traditionally are being used mainly gas lamps and monochromators at the laboratory. The new high-power LEDs in the ultraviolet spectrum are a very interesting alternative that can also be applied in the above continuous measurement systems. In this paper a viability study of these devices as excitation sources to produce fluorescence using hydrocarbon as contaminants is performed. The stations in continuous operation makes it necessary to also perform accelerated life tests and studies operating modes. In regard to the fluorescence produced, the influence of factors that may affect the measurements, such as temperature is studied. The study of the spectrum and analysis to identify the contaminant is another of the points developed in this work. Finally, since the monitoring is carried out in continuous mode, a compact and reliable communication is necessary: in this section metamaterials as a technological solution is analyzed since it fits perfectly with the philosophy of these measuring stations.