A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0

Vázquez, Rafael

doi:10.1016/j.camwa.2016.05.010

Cited by 148 publications

(99 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We solve the model problem (1) with a suitable f that makes it necessary to refine towards a corner, noticing however that the condition number does not depend on f . Since we lack a true implementation of T-splines, we have run the tests using the Octave/Matlab software GeoPDEs [17,38] for some particular T-meshes, defining a tensor-product space for each level, and then collecting the active functions of different levels. Our implementation is clearly inefficient for Tsplines, hence we do not present computational times.…”

Section: Numerical Resultsmentioning

confidence: 99%

BPX preconditioners for isogeometric analysis using analysis-suitable T-splines

Cho

Vázquez

2018

IMA Journal of Numerical Analysis

View full text Add to dashboard Cite

We propose and analyze optimal additive multilevel solvers for isogeometric discretizations of scalar elliptic problems for locally refined T-meshes. Applying the refinement strategy in [33] we can guarantee that the obtained T-meshes have a multilevel structure, and that the associated T-splines are analysis-suitable, for which we can define a dual basis and a stable projector. Taking advantage of the multilevel structure, we develop two BPX preconditioners: the first on the basis of local smoothing only for the functions affected by a newly added edge by bisection, and the second smoothing for all the functions affected after adding all the edges of the same level. We prove that both methods have optimal complexity, and present several numerical experiments to confirm our theoretical results, and also to compare the practical performance of the proposed preconditioners.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

BPX preconditioners for isogeometric analysis using analysis-suitable T-splines

Cho

Vázquez

2018

IMA Journal of Numerical Analysis

View full text Add to dashboard Cite

show abstract

“…This procedure can be understood as follows: Let for the given physical details of the geometry its parametric values such as the order of the NURBS basis functions, knot vectors, and control points are defined in each parametric directions such that the geometry retains its original shape. Based on these input values, a subroutine 'nrbmak' [34] is incorporated in place of the FEA geometry constructing subroutines to get the discretized form of the NURBS geometry. The format of this subroutine is where V n; g; f ð Þ represents the NURBS described solid.…”

Section: Construction Of Nurbs Discretized Geometriesmentioning

confidence: 99%

“…Then, subsequently, the 'nrbsctrlplot' and 'nrbsctrlplot' subroutines [34] are incorporated in the code structure for the visualization of required geometry S n; g ð Þ by executing the following commands nrbsctrlplot S n; g ð Þ ð Þ nrbsctrlplot S n; g ð Þ ð Þ…”

Section: Construction Of Nurbs Discretized Geometriesmentioning

confidence: 99%

“…Then, at these n and g coordinates of an element f X e ; the NURBS basis functions and their first order derivatives are calculated with the help of the following subroutines [34]: Fig. 5 Plot of NURBS discretized geometry a with n cp ¼ 12 number of control points, and b for nel ¼ 2 number of elements.…”

Section: Evaluation Of Nurbs Basis Functions and Their Mapping In Igamentioning

confidence: 99%

See 1 more Smart Citation

IGA: A Simplified Introduction and Implementation Details for Finite Element Users

Agrawal

Gautam

2018

J. Inst. Eng. India Ser. C

View full text Add to dashboard Cite

Isogeometric analysis (IGA) is a recently introduced technique that employs the Computer Aided Design (CAD) concept of Non-uniform Rational B-splines (NURBS) tool to bridge the substantial bottleneck between the CAD and finite element analysis (FEA) fields. The simplified transition of exact CAD models into the analysis alleviates the issues originating from geometrical discontinuities and thus, significantly reduces the design-toanalysis time in comparison to traditional FEA technique. Since its origination, the research in the field of IGA is accelerating and has been applied to various problems. However, the employment of CAD tools in the area of FEA invokes the need of adapting the existing implementation procedure for the framework of IGA. Also, the usage of IGA requires the in-depth knowledge of both the CAD and FEA fields. This can be overwhelming for a beginner in IGA. Hence, in this paper, a simplified introduction and implementation details for the incorporation of NURBS based IGA technique within the existing FEA code is presented. It is shown that with little modifications, the available standard code structure of FEA can be adapted for IGA. For the clear and concise explanation of these modifications, step-by-step implementation of a benchmark plate with a circular hole under the action of in-plane tension is included.

show abstract

“…The reference implementation described in this paper is built on the GeoPDEs package for Isogeometric Analysis in Matlab and Octave [8,9]. This package provides a framework for implementing and testing new isogeometric methods for PDEs.…”

mentioning

confidence: 99%

The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis

2020

View full text Add to dashboard Cite

A reference implementation of a new method in isogeometric analysis (IGA) is presented. It delivers lowcost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed by element-scale quadrature. To generate surrogate matrices, quadrature must only be performed on a fraction of the elements in the computational domain. In this way, quadrature determines only a subset of the entries in the final matrix. The remaining matrix entries are computed by a simple B-spline interpolation procedure. We present the modifications and extensions required for a reference implementation in the open-source IGA software library GeoPDEs. The exposition is fashioned to help facilitate similar modifications in other contemporary software libraries.Method name: Surrogate matrix method for isogeometric analysis

show abstract

A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0

Cited by 148 publications

References 24 publications

BPX preconditioners for isogeometric analysis using analysis-suitable T-splines

BPX preconditioners for isogeometric analysis using analysis-suitable T-splines

IGA: A Simplified Introduction and Implementation Details for Finite Element Users

The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis

Contact Info

Product

Resources

About