A simple adaptive mesh generator for 2-D finite element calculations (optical waveguide theory)

Fernández, FA; Yong, Yuan; Ettinger, RD

doi:10.1109/20.250774

Cited by 18 publications

(3 citation statements)

References 12 publications

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“…[18][19][20] AMR determines the appropriate distribution of the degree of refinement throughout a pre-defined mesh. Conditioned appropriately, AMR refines an initial mesh using a minimal number of iterations.…”

Section: Adaptive Mesh Refinementmentioning

confidence: 99%

Adaptive Risk Refinement Methodology for Gas Turbine Engine Rotor Disks

Moody¹,

Millwater²,

Enright³

2008

49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference &Amp;lt;br> 16th AIAA/ASME/AHS Ada

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Probabilistic fracture mechanics is a well-established method for predicting the probability-of-fracture (POF) of gas turbine engine rotor disks subject to low-cycle fatigue.An adaptive risk refinement methodology (ARRM) was developed to automate zone discretization and refinement that are typically associated with this approach. ARRM generates initial meshes using an adaptive nodal selection feature designed to optimize accuracy and efficiency. Adaptive mesh refinement (AMR) is performed until a converged risk solution is obtained. ARRM employs several techniques including skeletonization, constrained Delaunay triangulation (CDT), superparametric interpolation, and adaptive mesh refinement. A numerical example is provided to illustrate the effectiveness of the methodology. Nomenclature Δσ= stress range d s = shifting distance F = fracture of an initial anomaly located in a zone K = number of zones l e = projection path length m = iteration number P[A i ] = probability of having an anomaly in a zone P [B i |A i ] = conditional probability-of-fracture given an anomaly in a zone P[F i ] = probability-of-fracture of an initial anomaly located in a zone P disk = probability-of-fracture in a disk POF = probability-of-fracture

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Section: Adaptive Mesh Refinementmentioning

confidence: 99%

Adaptive Risk Refinement Methodology for Gas Turbine Engine Rotor Disks

Moody¹,

Millwater²,

Enright³

2008

49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference &Amp;lt;br> 16th AIAA/ASME/AHS Ada

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“…An approximate JPDF is constructed using probability of fracture values associated with anomalies placed at discrete points along the perimeter of the component and at selected locations within the interior of the component. The discrete points are connected to form a mesh of elements using a Delaunay triangulation algorithm 9,10 . Anomaly occurrence rates are assigned to elements based on the relative values of the element volumes.…”

mentioning

confidence: 99%

Efficient Integration of Sampling-Based Spatial Conditional Failure Joint Probability Densities

Enright

Millwater²,

Moody

2007

48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…Neighbouring elements need to be subdivided to retain mesh conformity, when not using hanging nodes. Earlier approaches (Ratnajeevan and Hoole, 1990;Fernandez et al, 1993;Golias et al, 1994;Díaz-Morcillo et al, 2000;Tsuji and Koshiba, 2000) concentrate on h-adaptivity by introducing error estimates and criteria whether to refine a mesh cell or not. h-refinement is needed in case of singularities or phase lag at high wave numbers (Ihlenburg and Babuška, 1997;Babuška and Strouboulis, 2001;Monk, 2003;Ainsworth, 2004) and results in polynomial convergence.…”

Section: Introductionmentioning

confidence: 99%

Comparison ofhp‐adaptive methods in finite element electromagnetic wave propagation

Schober

Kasper

2007

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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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.

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A simple adaptive mesh generator for 2-D finite element calculations (optical waveguide theory)

Cited by 18 publications

References 12 publications

Adaptive Risk Refinement Methodology for Gas Turbine Engine Rotor Disks

Adaptive Risk Refinement Methodology for Gas Turbine Engine Rotor Disks

Efficient Integration of Sampling-Based Spatial Conditional Failure Joint Probability Densities

Comparison ofhp‐adaptive methods in finite element electromagnetic wave propagation

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