Hierarchical Bases for Nonhierarchic 3-D Triangular Meshes

Andriulli, Francesco P.; Vipiana, F.; Vecchi, G.

doi:10.1109/tap.2008.926756

Cited by 92 publications

(69 citation statements)

References 17 publications

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“…• ; 1 8 9 < ====== (see [5] for alternative techniques). Once these current distributions have been constructed, one can compute the associated model coefficients with:…”

Section: Figure 1 Simplicial Complex Dual Of a Triangulationmentioning

confidence: 99%

Indirect effects of lightning on aircraft engine

Aguilera¹,

Lair²,

Issac³

et al. 2015

International Conference on Lightning [Amp ] Static Electricity (ICOLSE 2015)

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“…• ; 1 8 9 < ====== (see [5] for alternative techniques). Once these current distributions have been constructed, one can compute the associated model coefficients with:…”

Section: Figure 1 Simplicial Complex Dual Of a Triangulationmentioning

confidence: 99%

Indirect effects of lightning on aircraft engine

Aguilera¹,

Lair²,

Issac³

et al. 2015

International Conference on Lightning [Amp ] Static Electricity (ICOLSE 2015)

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“…The numerical computations are indeed done by expanding the chosen current distributions in conventional finite element spaces. This method can also be compared to hierarchical techniques in integral equation modelling ( [3]) and indeed we use techniques, previously applied in that context, to find partitionings of the interaction configuration (see [4]). However, our purpose is not to define a universal model and, therefore, we formulate our model on a single level in such a hierarchy which provides us with the pertinent degrees of freedom to obtain a good correspondence with only very specific physical phenomena.…”

Section: Introductionmentioning

confidence: 99%

Macro-modelling of lightning strokes on aircraft

Michielsen¹,

Issac²,

Aguilera³

et al. 2014

2014 XXXIth URSI General Assembly and Scientific Symposium (URSI GASS)

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Lightning phenomena are relatively slow electromagnetic processes and can be modelled in quasi-static approximation even on rather large structures like aeroplanes. Modelling the interaction of lightning currents with electronic equipment in an aircraft is a great challenge because of the geometrical complexity. Using universal methods like finite difference or finite element techniques on a complete mesh of the entire configuration is not an option in a design stage where many iterations are required. In this paper, we describe a macro-modelling technique which accounts for the geometrical detail while taking benefit from the quasi-static nature of the phenomena. We show that with these techniques rapid time domain (or frequency domain) simulations on complete lightning configurations can be done giving results very close to the results of exhaustive universal modelling and measurement.

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“…The generation scheme is inherently based on a decomposition of the solution space into a solenoidal sub-space and a non-solenoidal remainder; this intrinsically avoids the low-frequency breakdown [3][4][5][6][7][8][9]. As shown in [2], the resulting hierarchic set of basis functions acts as a very effective preconditioner for dense meshes.…”

Section: Introductionmentioning

confidence: 99%

Two-tier non-simplex grid hierarchic basis for general 3D meshes

Vipiana

Andriulli

Vecchi

2009

Waves in Random and Complex Media

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This paper deals with hierarchical bases for the preconditioning of the Electric Field Integral Equation on arbitrary 3D meshes with triangular cells. The basis functions are constructed on subsequent groupings of the initial triangular cells, which give rise to a nested family of meshes with non-simplex cells. The previously published hierarchic set of basis functions acts as a preconditioner for dense meshes, but it may lose effectiveness when the domain of the most extended basis functions is comparable with the wavelength, thus limiting the application range of the method. The present work undertakes to overcome this limitation by introducing two tiers of basis functions, related to the hierarchic cell groupings. By suitably modifying the grouping algorithm a coarser level is obtained, on which non-hierarchic basis functions are defined. Hierarchy in the basis function defined on detail meshes is preserved instead. Numerical results show the effectiveness for structures with electrical sizes beyond the resonance region.

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Hierarchical Bases for Nonhierarchic 3-D Triangular Meshes

Cited by 92 publications

References 17 publications

Indirect effects of lightning on aircraft engine

Indirect effects of lightning on aircraft engine

Macro-modelling of lightning strokes on aircraft

Two-tier non-simplex grid hierarchic basis for general 3D meshes

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