A spectral multipole method for efficient solution of large‐scale boundary element models in elastostatics

Peirce, Anthony; Napier, J.A.L.

doi:10.1002/nme.1620382307

Cited by 94 publications

(49 citation statements)

References 9 publications

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“…Besides, the state-of-the-art in BE methods also includes the new fast multipole BE algorithms, in principle based on the use of Taylor-expanded fundamental kernels for evaluating, in group form, the influence of far-field contributions at the near-field collocation points. As a result, not all entries of the BE matrices (but only those associated with the interaction of the near-field variables with themselves) have to be explicitly calculated, thereby substantially reducing storage memory and number of operations [4][5][6]. Actually, nowadays, the BEM is competitive in many significant engineering applications [7,8], posing as an attractive alternative to the more general FEM, on its turn still largely applied by engineers and scientists to solve problems on many different areas.…”

Section: Introductionmentioning

confidence: 99%

Application of a generic domain‐decomposition strategy to solve shell‐like problems through 3D BE models

Araújo

Silva

Telles

2006

Commun. Numer. Meth. Engng.

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SUMMARYEfficient integration algorithms and solvers specially devised for boundary-element procedures have been established over the last two decades. A good deal of quadrature techniques for singular and quasisingular boundary-element integrals have been developed and reliable Krylov solvers have proven to be advantageous when compared to direct ones, also in case of non-Hermitian matrices. The former has implied in CPU-time reduction during the assembling of the system of equations and the latter in its faster solution. Here, a triangular polar co-ordinate transformation and the Telles co-ordinate transformation are employed separately and combined to develop the matrix-assembly routines (integration routines). In addition, the Jacobi-preconditioned Biconjugate Gradient solver (J-BiCG) is used along with a generic substructuring boundary element algorithm. Thus, solution CPU time and computer memory can be considerably reduced. Discontinuous boundary elements are also included to simplify the coupling of the BE models (substructures). Numerical experiments involving 3D thin-walled domains (shell-like structural elements) are carried out to show the performance of the computer code with respect to accuracy and efficiency of the system solution. Precision, CPU-time and potential applications of the BE code developed are commented upon.

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Section: Introductionmentioning

confidence: 99%

Application of a generic domain‐decomposition strategy to solve shell‐like problems through 3D BE models

Araújo

Silva

Telles

2006

Commun. Numer. Meth. Engng.

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“…The main goal was to reduce the CPU time in FMM accelerated BEM to O(N). Thereafter this new technique was applied for solving elasticity [3] and fluids [4] problems in large-scale. Some years after, [5] announced the FMM as one of the top algorithms in scientific computing that were developed in the 20th century.…”

Section: Introductionmentioning

confidence: 99%

Optimization Using Topological Derivative and Boundary Element Method With Fast Multipole

Braga¹,

Anflor²,

Albuquerque³

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. The objective of this work is to compare topologies resulting from direct BEM (Boundary Element Method) with a BEM accelerated by Fast Multipole Method (FMM). A formulation of fast multipole boundary element (FMBEM) is introduced in order to turn the optimization process more attractive in the point of view of the computational cost. The formulation of the fast multipole is briefly summarized. A topological-shape sensitivity approach is used to select the points showing the lowest sensitivities, where material is removed by opening a cavity. As the iterative process evolves, the original domain has holes progressively removed, until a given stop criteria is achieved. A benchmark is investigated by

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“…The method was developed for, and has been successfully applied to rock mechanics area such as mining engineering [17,18], fracture analysis [19,20], and wellbore stabilities [12]. We have applied DDM here using both constant and higher-order elements.…”

Section: Introductionmentioning

confidence: 99%

Testing and Review of Various Displacement Discontinuity Elements for LEFM Crack Problems

Jo¹,

Hurt²

2013

Effective and Sustainable Hydraulic Fracturing

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The numerical modeling of hydraulic fractures in unconventional reservoirs presents significant challenges for field applications. There remains a need for accurate models that field personnel can use, yet remains consistent to the underlying physics of the problem [1]. For numerical simulations, several authors have considered a number of issues: the coupling between fracture mechanics and fluid dynamics in the fracture [2], fracture interaction [3][4][5], proppant transport [6], and others [7][8][9]. However, the available literature within the oil and gas industry often ignores the importance of the crack tip in modeling applications developed for engineering design. The importance of accurate modeling of the stress induced near the crack tip is likely critical in complex geological reservoirs where multiple propagating crack tips are interacting with natural fractures. This study investigates the influence of various boundary element numerical techniques on the accuracy of the calculated stress intensity factor near the crack tip and on the fracture profile, in general. The work described here is a part of a long-term project in the development of more accurate and efficient numerical simulations for field engineering applications.For this investigation, the authors used the displacement discontinuity method (DDM). The numerical technique is applied using constant and higher-order elements. Further, the authors also applied special crack tip elements, derived elsewhere [10], to capture the square root displacement variation at the crack tip, expected from Linear Elastic Fracture Mechanics (LEFM). The authors expect that special crack tip elements will provide the necessary flexibility to choose other tip profiles. The crack tip elements may prove instrumental for efficient modeling of the different near-tip displacement profiles exhibited by Viscosity-Dominated or Toughness-Dominated regimes in hydraulic fracture propagation. As others have shown [1,4,7], the accuracy of tip asymptote is critical in characterizing the stresses in the near-tip region of a propagating fracture.The authors examined the numerically derived stress intensity factor for several crack geometries with and without higher-order elements and with and without special tip elements, to analytical solutions. As expected, they found that the cases with higher-order elements and special tip elements provide more accurate results than the cases with constant displacement discontinuity and/or no tip elements. However, the numerical technique developed still proved efficient.These results show that numerical simulators can incorporate proper crack-tip treatments effectively. In addition, higher-order elements increase computational efficiency by reducing the number of elements instead of simply increasing the discretization of constant displacement elements. The accurate modeling of stress intensity factors is necessary to better simulate curved fractures, kinked cracks and interaction between fractures.

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A spectral multipole method for efficient solution of large‐scale boundary element models in elastostatics

Cited by 94 publications

References 9 publications

Application of a generic domain‐decomposition strategy to solve shell‐like problems through 3D BE models

Application of a generic domain‐decomposition strategy to solve shell‐like problems through 3D BE models

Optimization Using Topological Derivative and Boundary Element Method With Fast Multipole

Testing and Review of Various Displacement Discontinuity Elements for LEFM Crack Problems

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