scholarly journals Hybrid Function Representation for Heterogeneous Objects

2021 ◽  
pp. 101098
Author(s):  
A. Tereshin ◽  
A. Pasko ◽  
O. Fryazinov ◽  
V. Adzhiev
Keyword(s):  
Function Representation ◽  
Heterogeneous Objects ◽  
Hybrid Function

Surface and Volume Discretization of Functionally Based Heterogeneous Objects

2003 ◽  
Vol 3 (4) ◽  
pp. 285-294 ◽  
Author(s):  
Elena Kartasheva ◽  
Valery Adzhiev ◽  
Alexander Pasko ◽  
Oleg Fryazinov ◽  
Vladimir Gasilov
Keyword(s):  
Mesh Generation ◽  
Tetrahedral Mesh ◽  
Initial Surface ◽  
Element Analysis ◽  
Function Representation ◽  
And Topology ◽  
Heterogeneous Objects ◽  
Discretization Algorithm ◽  
Tetrahedral Mesh Generation ◽  
Initial Object

The presented approach to discretization of functionally defined heterogeneous objects is oriented towards applications associated with numerical simulation procedures, for example, finite element analysis (FEA). Such applications impose specific constraints upon the resulting surface and volume meshes in terms of their topology and metric characteristics, exactness of the geometry approximation, and conformity with initial attributes. The function representation of the initial object is converted into the resulting cellular representation described by a simplicial complex. We consider in detail all phases of the discretization algorithm from initial surface polygonization to final tetrahedral mesh generation and its adaptation to special FEA needs. The initial object attributes are used at all steps both for controlling geometry and topology of the resulting object and for calculating new attributes for the resulting cellular representation.

scholarly journals On the Marchenko equation for multicomponent single-sided reflection data

2014 ◽  
Vol 199 (3) ◽  
pp. 1367-1371 ◽  
Author(s):  
Kees Wapenaar ◽  
Evert Slob
Keyword(s):  
Green’S Function ◽  
Recent Work ◽  
Green's Function ◽  
Scattered Field ◽  
Iterative Solution ◽  
Virtual Source ◽  
Function Representation ◽  
Reflection Data ◽  
Marchenko Equation ◽  
Multicomponent Data

Abstract Recent work on the Marchenko equation has shown that the scalar 3-D Green's function for a virtual source in the subsurface can be retrieved from the single-sided reflection response at the surface and an estimate of the direct arrival. Here, we discuss the first steps towards extending this result to multicomponent data. After introducing a unified multicomponent 3-D Green's function representation, we analyse its 1-D version for elastodynamic waves in more detail. It follows that the main additional requirement is that the multicomponent direct arrival, needed to initiate the iterative solution of the Marchenko equation, includes the forward-scattered field. Under this and other conditions, the multicomponent Green's function can be retrieved from single-sided reflection data, and this is demonstrated with a 1-D numerical example.

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