# ICES REPORT 1205 January 2012 An Isogeometric Design-through-analysis Methodology based on Adaptive Hierarchical Refinement of NURBS , Immersed Boundary Methods , and T-spline CAD Surfaces

@inproceedings{SchillingerICESR1, title={ICES REPORT 1205 January 2012 An Isogeometric Design-through-analysis Methodology based on Adaptive Hierarchical Refinement of NURBS , Immersed Boundary Methods , and T-spline CAD Surfaces}, author={Dominik Schillinger and Luca Ded{\`e} and Michael A. Scott and John A. Evans and Michael J. Borden and Ernst Rank and Thomas J. R. Hughes} }

We explore hierarchical refinement of NURBS as a basis for adaptive isogeometric and immersed boundary analysis. We use the principle of B-spline subdivision to derive a local refinement procedure, which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions. We test hierarchical refinement of NURBS for some elementary fluid and structural analysis problems in two and three dimensions and attain… CONTINUE READING

#### From This Paper

##### Figures, tables, and topics from this paper.

#### Citations

##### Publications citing this paper.

Showing 1-10 of 67 extracted citations

## Adaptive Spline-based Finite Element Method with Application to Phase-field Models of Biomembranes by Wen Jiang

View 9 Excerpts

Highly Influenced

## Mathematical Methods for Curves and Surfaces

View 5 Excerpts

Highly Influenced

## Algorithms for the implementation of adaptive isogeometric methods using hierarchical splines 1608

View 4 Excerpts

Highly Influenced

## Analysis in Computer Aided Design : Nonlinear Isogeometric B-Rep Analysis of Shell Structures

View 11 Excerpts

Highly Influenced

## Isogeometric analysis: an overview and computer implementation aspects

View 15 Excerpts

Highly Influenced

#### References

##### Publications referenced by this paper.

Showing 1-10 of 108 references

## Foundations of Multidimensional and Metric Data Structures

View 4 Excerpts

Highly Influenced

## An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry

View 4 Excerpts

Highly Influenced

## Realization of an integrated structural design process: analysis-suitable geometric modelling and isogeometric analysis

View 8 Excerpts

Highly Influenced

## Isogeometric Analysis: Toward Integration of CAD and FEA

View 9 Excerpts

Highly Influenced

## The Finite Cell Method for Three-Dimensional Problems of Solid Mechanics

View 7 Excerpts

Highly Influenced

## Finite Cell Method: h- and p- extension for embedded domain methods in solid mechanics

View 6 Excerpts

Highly Influenced

## Finite Element Methods with B-Splines

View 8 Excerpts

Highly Influenced

## Natural Hierarchical Refinement for Finite Element Methods

View 11 Excerpts

Highly Influenced

## Surface Fitting with Hierarchical Splines

View 13 Excerpts

Highly Influenced

## Hierarchical B-spline refinement

View 14 Excerpts

Highly Influenced