0

Some papers (eg1., p. 2980) on isogeometric analysis talk about some geometric being exact or some geometry being expressed exactly.

The paper also says that

However, as NURBS patches (of higher order) are capable of representing most geometries exactly, ...

What does it mean?

mavavilj
  • 7,270
  • Without seeing the paper, which I'm not going to pay for, I'd guess that $(0,0),(1,0),(1/2,\sqrt{3}/2)$ is an equilateral triangle expressed exactly, while $(0.0,0.0),(1.0,0.0),(0.5,0.866025)$ is an equilateral triangle expressed approximately. – Mark McClure Apr 15 '17 at 14:50
  • @MarkMcClue Or with the quote that I added in mind, could it mean "using continuous functions", rather than step/piecewise functions? – mavavilj Apr 15 '17 at 14:54
  • Or then if one considers NURBS curves being used like in interpolation, then it could mean exact in Taylor series sense. That the error approaches or becomes $0$. – mavavilj Apr 15 '17 at 14:55
  • From the abstract "An old dilemma in structural shape optimization is the needed tight link between design model or geometric description and analysis model. The intention of this paper is to show that isogeometric analysis offers a potential and promising way out of this dilemma. " – Chickenmancer Apr 15 '17 at 15:56
  • Seems like @Mark McClure has the right idea – Chickenmancer Apr 15 '17 at 15:57

1 Answers1

1

This is one frequently encountered selling point of isogeometric analysis. For example, in finite element methods the boundary of a circular computational domain must be discretized using piecewise polynomials whereas in isogeometric analysis such geometry can be represented also in the discrete problem. This discrepancy between the original computational domain and the discretized domain is sometimes referred to as consistency error. If there is no such inconsistency then the geometry is said to be exact.

Thus, it means that the discrete solution truly represents a function defined in the original intended domain and not in a domain which is 'approximately the same'. It depends on the context what we mean by 'approximately the same' but you get the general idea.

knl
  • 1,295
  • 9
  • 15