280 research outputs found

    Optimally refined isogeometric analysis

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    Performance of direct solvers strongly depends upon the employed discretization method. In particular, it is possible to improve the performance of solving Isogeometric Analysis (IGA) discretizations by introducing multiple C-continuity hyperplanes that act as separators during LU factorization [8]. In here, we further explore this venue by introducing separators of arbitrary continuity. Moreover, we develop an efficient method to obtain optimal discretizations in the sense that they minimize the time employed by the direct solver of linear equations. The search space consists of all possible discretizations obtained by enriching a given IGA mesh. Thus, the best approximation error is always reduced with respect to its IGA counterpart, while the solution time is decreased by up to a factor of 60.David Pardo has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 644602, the Projects of the Spanish Ministry of Economy and Competitiveness with reference MTM2016-76329-R (AEI/FEDER, EU), and MTM2016-81697-ERC, the BCAM "Severo Ochoa" accreditation of excellence SEV-2013-0323, and the Basque Government through the BERC 2014-2017 program, and the Consolidated Research Group Grant IT649-13 on "Mathematical Modeling, Simulation, and Industrial Applications (M2SI)

    Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes

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    In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are called admissible mesh configurations. We apply the proposed algorithms to two-dimensional linear heat transfer problems with localized moving heat source, as simplified models for additive manufacturing applications. We first verify the accuracy of the admissible adaptive scheme with respect to an overkilled solution, for then comparing our results with similar schemes which consider different refinement and coarsening algorithms, with or without taking into account grading parameters. This study shows that the THB-spline admissible solution delivers an optimal discretization for what concerns not only the accuracy of the approximation, but also the (reduced) number of degrees of freedom per time step. In the last example we investigate the capability of the algorithms to approximate the thermal history of the problem for a more complicated source path. The comparison with uniform and non-admissible hierarchical meshes demonstrates that also in this case our adaptive scheme returns the desired accuracy while strongly improving the computational efficiency.Comment: 20 pages, 12 figure

    A priori error for unilateral contact problems with Lagrange multiplier and IsoGeometric Analysis

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    In this paper, we consider unilateral contact problem without friction between a rigid body and deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem using an active-set strategy and for a primal space of NURBS of degree pp and p−2p-2 for a dual space of B-Spline. A inf-sup stability is proved to ensure a good property of the method. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two- and three-dimensional and in small and large deformation demonstrate the accuracy of the proposed method

    IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains

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    This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC algorithm is very natural since they are tensor-based PDE solvers, which are precisely what is required by the MISC machinery. Moreover, the combination-technique formulation of MISC allows the straight-forward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.Comment: version 3, version after revisio
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