Function representation with circle inversion map systems

2017 ◽  
Author(s):  
Bryson Boreland ◽  
Herb Kunze
Keyword(s):  
Function 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.

scholarly journals CAD/CAM System for Additive Manufacturing with a Robust and Efficient Topology Optimization Algorithm Based on the Function Representation

2021 ◽  
Vol 11 (16) ◽  
pp. 7409
Author(s):  
Dmitry Popov ◽  
Yulia Kuzminova ◽  
Evgenii Maltsev ◽  
Stanislav Evlashin ◽  
Alexander Safonov ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
3D Modeling ◽  
Mechanical Tests ◽  
Simulation Data ◽  
Function Representation ◽  
Modeling Simulation ◽  
Cad Cam ◽  
Design Ideas ◽  
Good Agreement

Additive manufacturing erases the distance between design ideas and finished parts. However, designers must use several software tools to use these advantages. Moreover, these tools operate with different representations of geometry. This paper describes the architecture of a new CAD/CAM system that uses only the function representation of the geometry (FRep). It provides all widely used design operations and allows an engineer to employ robust and efficient topology optimization algorithms. The developed CAD/CAM system consists of 3D modeling, simulation, topology optimization, and direct manufacturing modules. We successfully printed designed parts and performed mechanical tests of printed parts. The results of tests show good agreement with simulation data. The system makes it possible to create structures with the desired properties in a fast and flexible way. The proposed approach significantly helps in designing additive manufacturing process and saves time for its users.

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