Adaptive refinement in 2‐D finite element applications

Golias, N.A.; Tsiboukis, T.D.

doi:10.1002/jnm.1660040204

Cited by 18 publications

(9 citation statements)

References 11 publications

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“…A slightly different and computationally more expensive error indicator initially proposed by Golias and Tsiboukis [15], [29] is the error indicator…”

Section: Adaptive Refinement Strategiesmentioning

confidence: 99%

Adaptive multiresolution antenna modeling using hierarchical mixed-order tangential vector finite elements

Andersen

Volakis²

2001

IEEE Trans. Antennas Propagat.

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Hierarchical mixed-order tangential vector finite elements (TVFEs) for tetrahedra are attractive for accurate and efficient finite element or hybrid finite element/boundary integral (FE/BI) simulation of complicated electromagnetic problems. They provide versatility in the geometrical modeling of physical structures, guarantee solutions free of spurious modes, and allow a local increase of resolution by combination of mixed-order TVFEs of different orders within a computational domain. Regions with higher order mixed-order TVFEs can be selected a priori or be found adaptively via methods for a posteriori error estimation or indication. This paper demonstrates the merits of various explicit residual methods for a posteriori error indication via adaptive refinement of FE/BI solutions of electromagnetic radiation problems using hierarchical mixed-order TVFEs for tetrahedra.Index Terms-Antennas, finite-element methods (FEMs), numerical methods, tangential vector finite element.

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“…A slightly different and computationally more expensive error indicator initially proposed by Golias and Tsiboukis [15], [29] is the error indicator…”

Section: Adaptive Refinement Strategiesmentioning

confidence: 99%

Adaptive multiresolution antenna modeling using hierarchical mixed-order tangential vector finite elements

Andersen

Volakis²

2001

IEEE Trans. Antennas Propagat.

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“…The procedure is repeated until the required number of elements nel or number of nodes nno is reached. At last, a final optimization takes place by moving each node that does not lie on a boundary or interface of the mesh, toward the centroid of the polygon, formed by its neighboring nodes [16]. Also, a last Delaunay triangulation takes place.…”

Section: Table I For Each Input Vector the Node Number Of The Bmu Located At The Previous Search That Took Place For The Same Input Vectomentioning

confidence: 99%

A finite-element mesh generator based on growing neural networks

Triantafyllidis

Labridis

2002

IEEE Trans. Neural Netw.

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A mesh generator for the production of high-quality finite-element meshes is being proposed. The mesh generator uses an artificial neural network, which grows during the training process in order to adapt itself to a prespecified probability distribution. The initial mesh is a constrained Delaunay triangulation of the domain to be triangulated. Two new algorithms to accelerate the location of the best matching unit are introduced. The mesh generator has been found able to produce meshes of high quality in a number of classic cases examined and is highly suited for problems where the mesh density vector can be calculated in advance.

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“…The mesh is smoothed following a Laplacian smoothing scheme for a set of nodes in the manner described in Reference [4]: nodes are moved to the centre of gravity of the connected nodes if none of the connected triangles are twisted. This procedure is repeated several times.…”

Section: Smoothingmentioning

confidence: 99%

Boundary‐sensitive mesh generation using an offsetting technique

Krause

Strecker²,

Fichtner

2000

Int. J. Numer. Meth. Engng.

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In the simulation of semiconductor processes and devices it may be necessary to generate surface parallel meshes. One important example occurs in MOS transistors where the electrons ow along the silicon surface underneath a gate. It is desired beneÿcial in terms of accuracy to have rather long mesh edges parallel and rather small edges orthogonal to those currents. For most of the devices quadtree techniques have been used with big success (GarretÃ on G. A hybrid approach to 2D and 3D mesh generation for semiconductor device simulation. PhD Thesis, Integrated Systems Laboratory, ETH Zurich, 1999. GarretÃ on G, Villablanca L, Strecker N, Fichtner W. Uniÿed grid generation and adaptation for device simulation. Proceedings of SISDEP'95, Erlangen, Germany, 6-8 September 1995; 6:468-471.) If the interface is not axis aligned, however, a quadtree-based approach does not generate meshes of this quality, resulting in a larger numerical error or in convergence problems during equation solution.We present here a modiÿed advancing front grid generator that inserts surface parallel mesh lines; the interior of the region is ÿlled with layers of nearly rectangular quadrilaterals, and not triangles as in conventional advancing front generators (see George PL, Sveno E. The advancing front mesh generation method revisited. Here we follow references of Johnston BP, Sullivan JM. Fully automatic two dimensional mesh generation using normal o setting. International Journal for Numerical Methods in Engineering 1992; 33:425-442; Blacker TD, Stephenson MB. Paving: a new approach to automated quadrilateral mesh generation. International Journal for Numerical Methods in Engineering 1991; 32:811; Rees M. Combining quadrilateral and triangular meshing using the advancing front approach. we use a di erent point location scheme, in the sense that the opposite edge of the quadrilateral is kept parallel if possible. At each layer the marching distance is increased by a coarsening factor; reÿnement is therefore controlled by the initial marching distance and the coarsening factor. A maximum edge length is guaranteed.The generation of o setting layers stops when the front intersects itself. The remaining polygon is triangulated. As a ÿnal step the mesh is converted to a Delaunay conforming mesh by swapping edges and inserting points.The implementation in two dimensions has been tested successfully using realistic examples from device simulations.

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Adaptive refinement in 2‐D finite element applications

Cited by 18 publications

References 11 publications

Adaptive multiresolution antenna modeling using hierarchical mixed-order tangential vector finite elements

Adaptive multiresolution antenna modeling using hierarchical mixed-order tangential vector finite elements

A finite-element mesh generator based on growing neural networks

Boundary‐sensitive mesh generation using an offsetting technique

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