Q2. What are the properties that make T-splines useful for finite element analysis?
They allow us to build spaces that are complete up to a desired polynomial degree, as smooth as an equivalent NURBS basis, and capable of being locally refined in a manner similar to PB-splines but while keeping the original geometry and parameterization unchanged.
Q3. What are the latest trends in engineering analysis and highperformance computing?
Recent trends taking place in engineering analysis and highperformance computing are also demanding greater precision and tighter integration of the overall modeling–analysis process.
Q4. What is the simplest way to define a T-mesh?
The authors begin by defining an index space version of a T-mesh as a rectangular tiling of a region in R2 such that each edge of every rectangle has positive integer value.
Q5. What is the construction of a rational B-spline curve in Rds?
The construction of a rational B-spline curve in Rds begins by choosing a set of control points Pwi for a B-spline curve in Rdsþ1 with knot vector N ¼ n1; . . . ; nnþpþ1 .
Q6. What is the reason why one should believe that the time is right to transform the technology of these?
Given the incredible inertia existing in the design and analysis industries, one may reasonably ask why one should believe that the time is right to transform the technology of these industries.
Q7. What is the last example of the hemispherical shell with stiffener?
The last example the authors consider is the hemispherical shell with stiffener presented in Rank et al. [39] who solved the problem using a finite element method and p-refinement strategy.
Q8. What is the effect of refinement on the T-meshes?
The authors see that the resulting T-meshes are refined near the interior and boundary layers and the effects of refinement are quite localized.
Q9. What is the refinement algorithm for Tmeshes?
In passing the authors note that the refinement algorithm described in [42] depends on the order of the elements identified for refinement and, in certain cases, the refinement can propagate throughout a Tmesh.
Q10. What is the current state of the art in isogeometric analysis?
The current state-of-the-art in isogeometric analysis is as follows: A number of single and multiple patch NURBS-based parametric models have been developed and analyzed [4,7,18,19,27,30,52].
Q11. Why is automatic adaptive mesh refinement not widely adopted in industry?
Automatic adaptive mesh refinement has not been as widely adopted in industry as one might assume fromthe extensive academic literature because mesh refinement requires access to the exact geometry, and thus it also requires seamless and automatic communication with CAD, which simply does not exist.
Q12. What is the basic problem of a three-dimensional representation of the solid?
The basic problem is to develop a three-dimensional (trivariate) representation of the solid in such a way that the surface representation is exactly preserved.
Q13. What is the procedure for inserting knots into a surface?
If instead of a curve the authors wish to insert knots into one of the knot vectors, N‘, of a surface or solid, the authors utilize the same procedure.