Abstract This work outlines the use of a black-box fast multipole method to accelerate the far-field computations in an isogeometric boundary element method. The present approach makes use of T-splines to discretise both the geometry and analysis fields allowing a direct integration of CAD and analysis technologies. A black-box fast multipole method of O ( N ) complexity is adopted that minimises refactoring of existing boundary element codes and facilitates the use of different kernels. This paper outlines an algorithm for implementing the open-source black-box fast multipole method BBFMM3D 1 within an existing isogeometric boundary element solver, but the approach is general in nature and can be applied to any boundary element surface discretisation. The O ( N ) behaviour of the approach is validated and compared against a standard direct solver. Finally, the ability to model large models of arbitrary geometric complexity directly from CAD models is demonstrated for potential problems.
Last. Michael A. Scott(BYU: Brigham Young University)H-Index: 27
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In this paper we present a new method termed Truncated Hierarchical Catmull–Clark Subdivision (THCCS), which generalizes truncated hierarchical B-splines to control grids of arbitrary topology. THCCS basis functions satisfy partition of unity, are linearly independent, and are locally refinable. THCCS also preserves geometry during adaptive hh-refinement and thus inherits the surface continuity of Catmull–Clark subdivision, namely C2C2-continuous everywhere except at the local region surrounding...
One of the major goals of isogeometric analysis is direct design-to-analysis, i.e., using computer-aided design (CAD) files for analysis without the need for mesh generation. One of the primary obstacles to achieving this goal is CAD models are based on surfaces, and not volumes. The boundary element method (BEM) circumvents this difficulty by directly working with the surfaces. The standard basis functions in CAD are trimmed nonuniform rational B-spline (NURBS). NURBS patches are the tensor pro...
We describe an accelerated direct solver for the integral equations which model low-frequency acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given on triangles, a setting which generalizes the typical one of triangulated surfaces, and the integral equations are discretized via a high-order Nystrom method. This allows for rapid convergence in cases in which high-order surface information is available. The high-order discretization tec...
A boundary element method (BEM), based on non-uniform rational B-splines (NURBS), is used to find solutions to three-dimensional wave scattering problems governed by the Helmholtz equation. The method is extended in a partition-of-unity sense, multiplying the NURBS functions by families of plane waves; this method is called the eXtended Isogeometric Boundary Element Method (XIBEM). In this paper, the collocation XIBEM formulation is described and numerical results are given. The numerical result...
Abstract 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 bound...
In this paper we couple collocated Boundary Element Methods (BEM) with unstructured analysis-suitable T-spline surfaces for solving a linear Boundary Integral Equation (BIE) arising in the context of a ship-hydrodynamic problem, namely the so-called Neumann–Kelvin problem, following the formulation by Brard (1972) and Baar and Price (1988). The local-refinement capabilities of the adopted T-spline bases, which are used for representing both the geometry of the hull and approximating the solution...
Last. Michael A. Scott(BYU: Brigham Young University)H-Index: 27
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We establish several fundamental properties of analysis-suitable T-splines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended T-mesh of an analysis-suitable T-spline, is contained in the corresponding analysis-suitable T-spline space. This is accomplished through the theory of perturbed analysis-suitable T-spline spaces and a simple topological dimension formula. Second, we establis...
An isogeometric boundary element method based on T-splines is used to simulate acoustic phenomena. We restrict our developments to low-frequency problems to establish the fundamental properties of the proposed approach. Using T-splines, the computer aided design (CAD) and boundary element analysis are integrated without recourse to geometry clean-up or mesh generation. A regularized Burton–Miller formulation is used resulting in integrals which are at most weakly singular. We employ a collocatio...
Abstract The recently proposed locally refined B-splines, denoted LR B-splines, by Dokken et al. (2013) [6] may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided design and finite element analysis. In this paper, we propose local refinement strategies for adaptive isogeometric analysis using LR B-splines and investigate its performance by doing numerical tests on well known benchmark cases. The theory behind LR B-spline is not presented ...
#1Luca Heltai(SISSA: International School for Advanced Studies)H-Index: 21
#2Marino Arroyo(UPC: Polytechnic University of Catalonia)H-Index: 40
Last. Antonio DeSimone(SISSA: International School for Advanced Studies)H-Index: 43
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Isogeometric analysis (IGA) is emerging as a technology bridging computer aided geometric design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that describe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major ope...
#2Weiyin Ma(CityU: City University of Hong Kong)H-Index: 22
Abstract null null UE-splines are generalizations of uniform polynomial splines, trigonometric splines, hyperbolic splines and exponential splines defined as parametric splines in non-rational form. At the same time, they can exactly represent a wide class of basic analytic shapes commonly used in engineering applications. Further, UE-splines with uniform knot intervals can be conveniently generated by subdivision methods. In this paper, we use them to model many kinds of basic analytic shapes a...
#1H.S. Yang(BIT: Beijing Institute of Technology)H-Index: 3
#1Huashi Yang(BIT: Beijing Institute of Technology)
Last. Rui Dai(BIT: Beijing Institute of Technology)H-Index: 1
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Abstract In this paper, the collocation-based isogeometric boundary element method (IGABEM) is combined with the isogeometric Reissner–Mindlin shell elements to conduct the mixed dimensional solid–shell coupling analysis. On the basis of taking advantages of the geometric smoothness and exactness of isogeometric analysis (IGA), this method can reduce the computational scale of the solid part and eliminate the procedure of constructing analysis-suitable volumetric discretizations. In addition, th...
We introduce \texttt{PBBFMM3D}, a parallel black-box method for computing kernel matrix-vector multiplication, where the underlying kernel is a non-oscillatory function in three dimensions. While a naive method requires \O(N^2)computation, \texttt{PBBFMM3D} reduces the cost to \O(N)work. In particular, our algorithm requires only the ability to evaluate the kernel function, and is thus a black-box method. To further accelerate the computation on shared-memory machines, a parallel algorithm...
#2Chunying Dong(BIT: Beijing Institute of Technology)H-Index: 19
Abstract In recent years, more and more attention has been paid to isogeometric methods, in which shape functions are used to accurately describe CAD models and approximate unknown fields. The isogeometric boundary element method (IGABEM) realizes the integration on the exact boundary of the region, which means there is no geometric discretization error. In this paper, a more general interface integral formula for elastic energy increment of heterogeneous materials is extended from previous work...
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the computed domain. This topic has been addressed in previous papers but the approach presented here is a considerable improvement in terms of efficiency and accuracy. One innovation is that initial stresses instead of body forces are used. This then allows a one ste...
Abstract Isogeometric boundary element method is a computer simulation algorithm that can directly utilize the data of a geometric model represented by its surface. Catmull-Clark subdivision surfaces are a widely used technique in 3D computer graphics to construct complicated geometries. In the present work, we combine Catmull-Clark subdivision surfaces with isogeometric boundary element method to simulate acoustic propagation in semi-infinite domains. The present method can produce fast and hig...
#1Leilei Chen(Xinyang Normal University)H-Index: 11
#2Chuang Lu(USTC: University of Science and Technology of China)H-Index: 1
Last. Changjun Zheng(Hefei University of Technology)H-Index: 15
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A novel boundary element method based on subdivision surfaces is applied to simulate wave scattering problems governed by the Helmholtz equation. The Loop subdivision scheme widely used in the CAD ...
Last. Timon Rabczuk(Bauhaus University, Weimar)H-Index: 101
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Abstract This study focuses on the efficient computational model for predicting the structural vibration induced underwater acoustic radiation in shallow marine environment. In the proposed model, the finite element method (FEM) is used to calculate the vibration response of the shell structures and the singular boundary method (SBM) with near-field and far-field Green’s functions is used to simulate the underwater acoustic radiation excited by shell structural vibration in shallow water marine ...
Abstract Among the various types of structural optimization, topology has been occupying a prominent place over the last decades. It is considered the most versatile because it allows structural geometry to be determined taking into account only loading and fixing constraints. This technique is extremely useful in the design phase, which requires increasingly complex computational modeling. Modern geometric modeling techniques are increasingly focused on the use of NURBS basis functions. Consequ...
Abstract This paper presents an acoustic topology optimization approach using isogeometric boundary element methods based on subdivision surfaces to optimize the distribution of sound adsorption materials adhering to structural surfaces. The geometries are constructed from triangular control meshes through Loop subdivision scheme, and the associated Box-spline functions that generate limit smooth subdivision surfaces are employed to discretize the acoustic boundary integral equations. The effect...