The formally second-order BDF ADI difference/compact difference scheme for the nonlocal evolution problem in three-dimensional space

2021 ◽  
Author(s):  
Leijie Qiao ◽  
Da Xu ◽  
Wenlin Qiu
Keyword(s):  
Difference Scheme ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Second Order ◽  
Evolution Problem ◽  
Compact Difference Scheme ◽  
Compact Difference ◽  
Three Dimensional Space

scholarly journals Constructive Geometric Models with Imaginary Objects

2020 ◽  
pp. short27-1-short27-9
Author(s):  
Denis Voloshinov ◽  
Alexandra Solovjeva
Keyword(s):  
Projective Geometry ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Higher Order ◽  
Second Order ◽  
The Other ◽  
Significant Obstacle ◽  
The Relationship ◽  
Planar Drawing ◽  
Three Dimensional Space

The article is devoted to the consideration of a number of theoretical questions of projective geometry related to specifying and displaying imaginary objects, especially, conics. The lack of development of appropriate constructive schemes is a significant obstacle to the study of quadratic images in three-dimensional space and spaces of higher order. The relationship between the two circles, established by the inversion operation with respect to the other two circles, in particular, one of which is imaginary, allows obtain a simple and effective method for indirect setting of imaginary circles in a planar drawing. The application of the collinear transformation to circles with an imaginary radius also makes it possible to obtain unified algorithms for specifying and controlling imaginary conics along with usual real second-order curves. As a result, it allows eliminate exceptional situations that arise while solving problems with quadratic images in spaces of second and higher order.

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