A fast elasto-plastic formulation with hierarchical matrices and the boundary element method

Zechner, Jürgen; Beer, Gernot

doi:10.1007/s00466-012-0756-0

Cited by 9 publications

(13 citation statements)

References 33 publications

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“…Its applicability covers many different problems. In the context of the presented formulation, the extension to the elasto-static [53] and elasto-plastic BEM [49] is of particular interest.…”

Section: Hierarchical Matricesmentioning

confidence: 99%

Fast isogeometric boundary element method based on independent field approximation

Marussig

Zechner

Beer

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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132

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An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology is demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.

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Section: Hierarchical Matricesmentioning

confidence: 99%

Fast isogeometric boundary element method based on independent field approximation

Marussig

Zechner

Beer

et al. 2015

Computer Methods in Applied Mechanics and Engineering

Self Cite

132

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show abstract

“…is taken like the formulation presented in [43]. If integral free jump terms are present, they are already integrated in the system matrices K. If the surface Γ is smooth and the kernel function U is regular, entries of the system matrix only consist of pointwise evaluations…”

Section: Discretization With the Nyström Methodsmentioning

confidence: 99%

“…The results for the three dimensional convergence study sketched in Figure 16 required the application of a fast method which introduces additional numerical approximation. In the presented case, hierarchical matrices (H-matrices) are taken, where the approximation quality of the boundary integral operators is controllable by a recursive criterion [50,43] and set to at least one magnitude lower than the achieved overall accuracy. V p = 1 p = 2 p = 3 p = 4 Figure 15: Convergence rates for the discrete double and single layer potential on the torus for the exterior Laplace problem.…”

Section: Torusmentioning

confidence: 99%

The isogeometric Nyström method

Zechner

Marussig

Beer

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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In this paper the isogeometric Nyström method is presented. It's outstanding features are: it allows the analysis of domains described by many different geometrical mapping methods in computer aided geometric design and it requires only pointwise function evaluations just like isogeometric collocation methods. The analysis of the computational domain is carried out by means of boundary integral equations, therefor only the boundary representation is required. The method is thoroughly integrated into the isogeometric framework. For example, the regularization of the arising singular integrals performed with local correction as well as the interpolation of the pointwise existing results are carried out by means of Bézier elements.The presented isogeometric Nyström method is applied to practical problems solved by the Laplace and the Lamé-Navier equation. Numerical tests show higher order convergence in two and three dimensions. It is concluded that the presented approach provides a simple and flexible alternative to currently used methods for solving boundary integral equations, but has some limitations.

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“…In [20,21] the cell method is extended to cover the simulation of elastic inclusions with different material properties and in [22] applied to a fast BEM formulation.…”

Section: Previous Workmentioning

confidence: 99%

Advanced Boundary Element analysis of geotechnical problems with geological inclusions

Beer

Duenser

2016

Computers and Geotechnics

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A fast elasto-plastic formulation with hierarchical matrices and the boundary element method

Cited by 9 publications

References 33 publications

Fast isogeometric boundary element method based on independent field approximation

Fast isogeometric boundary element method based on independent field approximation

The isogeometric Nyström method

Advanced Boundary Element analysis of geotechnical problems with geological inclusions

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