Fast isogeometric boundary element method based on independent field approximation

Marussig, Benjamin; Zechner, Jürgen; Beer, Gernot; Fries, Thomas‐Peter

doi:10.1016/j.cma.2014.09.035

Cited by 132 publications

(83 citation statements)

References 60 publications

(100 reference statements)

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“…Especially, if non-conforming partitions of trimmed surfaces are considered. The application of discontinuous collocation is an elegant remedy to this issue [6,7]. Using such schemes, collocation points along the boundary of γ are slightly shifted inside, thereby abolishing the link to adjacent surfaces.…”

Section: Isogeometric Boundary Element Methodsmentioning

confidence: 99%

“…In particular, each basis function B i of the unknown field is related to a certain x c i . It has been demonstrated by several authors [7,12,13] that the Greville abscissaeξ…”

Section: Isogeometric Boundary Element Methodsmentioning

confidence: 99%

“…The resulting benefits are that the evaluation of Cauchy data becomes more efficient and the refinement procedure is simplified. Moreover, it has been demonstrated that the approximation quality is hardly effected by such a combination [7,13].…”

Section: Subparametric Patchesmentioning

confidence: 99%

“…The following sections provide an overview of the proposed methodology. They actually recap and unify the main features presented in [6][7][8]. Hence, the interested reader is particularly referred to the first one of these references for an in-depth discussion.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Integration of Design and Analysis Through Boundary Integral Equations

Marussig

Zechner

Beer

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The direct integration of Computer Aided Geometric Design (CAGD) models into a numerical simulation improves the accuracy of the geometrical representation of the problem as well as the efficiency of the overall analysis process.In this work, the complementary features of isogeometric analysis and boundary integral equations are combined to obtain a coalescence of design and analysis which is based on a boundary-only discretization. Following the isogeometric concept, the functions used by CAGD are employed for the simulation. An independent field approximation is applied to obtain a more flexible and efficient formulation. In addition, a procedure is presented which allows a stable analysis of trimmed geometries and a straightforward positioning of collocation points.Several numerical examples demonstrate the characteristics and benefits of the proposed approach. In particular, the independent field approximation improves the computational efficiency and reduces the storage requirements without any loss of accuracy. The proposed methodology permits a seamless integration of the most common design models into an analysis of linear elasticity problems. 6526Benjamin Marussig, Jürgen Zechner, Gernot Beer, and Thomas-Peter Fries INTRODUCTIONIsogeometric analysis aims to close the existing gap between the design process and analysis such that a simulation can be performed without generating a mesh. Consequently, the accuracy and efficiency of the overall simulation process is improved, since meshing is timeconsuming [1, 2] and introduces additional (geometrical) approximation errors. In addition, the basis functions used by design models, i.e. NURBS, provide further benefits such as high continuity [3,4].However, during the last years, it has become clear that a true integration of design and analysis is far from trivial due to several reasons: first of all, most engineering design models are based on a boundary representation (B-Rep) rather than a volume description. Secondly, three dimensional B-Rep models are usually defined by a non-conforming partition of NURBS surfaces, i.e. their mathematical parametrizations have no explicit relation to each other. Thirdly, each boundary surface is based on a tensor product structure which is a very efficient representation but has limitations due to its four sided nature. As a result, almost all NURBS based design models use trimming procedures to increase the flexibility of tensor product surfaces. This means that only a certain area of a surface is visualized while the underlying mathematical parametrization remains unchanged.In this work, a coherent framework is presented which allows a seamless integration of trimmed NURBS models into an analysis. In general, the governing equations of the problem are expressed by means of boundary integral equations which are discretized by a numerical approximation method. Here, the boundary element method (BEM) is used since it is the most versatile approach. However, it should be pointed out that other schemes like the Nyst...

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Section: Isogeometric Boundary Element Methodsmentioning

confidence: 99%

“…In particular, each basis function B i of the unknown field is related to a certain x c i . It has been demonstrated by several authors [7,12,13] that the Greville abscissaeξ…”

Section: Isogeometric Boundary Element Methodsmentioning

confidence: 99%

Section: Subparametric Patchesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Integration of Design and Analysis Through Boundary Integral Equations

Marussig

Zechner

Beer

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recourse is always made to some type of mathematical model, usually a set of partial differential equations (PDEs). The resulting problem is solved numerically using a wide variety of discretisation methods including finite element methods [22][23][24][25][26], finite differences, meshfree methods [27], isogeometric approaches [28,29], geometry independent field approximation [30,31], scaled-boundary finite elements [32][33][34][35][36], boundary element approaches [37], enriched boundary elements [38] or combinations thereof [39][40][41].…”

Section: Case Study 2: Digital Twins In Engineering and Personalisedmentioning

confidence: 99%

What makes Data Science different? A discussion involving Statistics2.0 and Computational Sciences

Ley

Bordas

2018

Int J Data Sci Anal

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Data Science is today one of the main buzzwords, be it in business, industrial or academic settings. Machine learning, experimental design, data-driven modelling are all, undoubtedly, rising disciplines if one goes by the soaring number of research papers and patents appearing each year. The prospect of becoming a "Data Scientist" appeals to many. A discussion panel organised as part of the European Data Science Conference (European Association for Data Science (EuADS)) https:// euads.org/edsc/ asked the question: "What makes Data Science different?" In this paper, we give our own, personal and multi-faceted view on this question, from a Statistics and an Engineering perspective. In particular, we compare Data Science to Statistics and discuss the connection between Data Science and Computational Sciences.

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An interpolation‐based fast multipole method for higher‐order boundary elements on parametric surfaces

Dölz

Harbrecht

Peters

2016

Numerical Meth Engineering

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SUMMARYIn this article, a black-box higher order fast multipole method for solving boundary integral equations on parametric surfaces in three spatial dimensions is proposed. Such piecewise smooth surfaces are the topic of recent studies in isogeometric analysis. Due to the exact surface representation, the rate of convergence of higher order methods is not limited by approximation errors of the surface. An element-wise clustering strategy yields a balanced cluster tree and an efficient numerical integration scheme for the underlying Galerkin method. By performing the interpolation for the fast multipole method directly on the reference domain, the cost complexity in the polynomial degree is reduced by one order. This gain is independent of the application of either H-or H 2 -matrices. In fact, several simplifications in the construction of H 2 -matrices are pointed out, which are a by-product of the surface representation. Extensive numerical examples are provided in order to quantify and qualify the proposed method.

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Fast isogeometric boundary element method based on independent field approximation

Cited by 132 publications

References 60 publications

Integration of Design and Analysis Through Boundary Integral Equations

Integration of Design and Analysis Through Boundary Integral Equations

What makes Data Science different? A discussion involving Statistics2.0 and Computational Sciences

An interpolation‐based fast multipole method for higher‐order boundary elements on parametric surfaces

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