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THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis
Local refinement with hierarchical B-spline structures is an active topic of research in the context of geometric modeling and isogeometric analysis. By exploiting a multilevel control structure, weExpand
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Geometry + Simulation Modules: Implementing Isogeometric Analysis
TLDR
We propose G+SMO (Geometry+Simulation Modules), an open-source, C++ library for IGA, based on abstract classes for discretization basis, geometry map, assembler, solver and so on. Expand
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Deflation and certified isolation of singular zeros of polynomial systems
TLDR
We develop a new symbolic-numeric algorithm for the certification of singular isolated points, using their associated local ring structure and certified numerical computations. Expand
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Adaptively refined multi-patch B-splines with enhanced smoothness
TLDR
A spline space suitable for Isogeometric Analysis (IgA) on multi-patch domains is presented. Expand
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Multipatch Discontinuous Galerkin Isogeometric Analysis
Isogeometric Analysis (IgA) uses the same class of basis functions for both representing the geometry of the computational domain and approximating the solution of the boundary value problem underExpand
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Low rank tensor methods in Galerkin-based isogeometric analysis
Abstract The global (patch-wise) geometry map, which describes the computational domain, is a new feature in isogeometric analysis. This map has a global tensor structure, inherited from theExpand
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On numerical integration in isogeometric subdivision methods for PDEs on surfaces
Abstract Subdivision surfaces offer great flexibility in capturing irregular topologies combined with higher order smoothness. For instance, Loop and Catmull–Clark subdivision schemes provide C 2Expand
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Integration by interpolation and look-up for Galerkin-based isogeometric analysis
Even though isogeometric analysis has a clear advantage regarding the number of degrees of freedom needed to achieve a certain level of accuracy, the time needed for matrix assembly (by means ofExpand
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Matrix Generation in Isogeometric Analysis by Low Rank Tensor Approximation
TLDR
We show how to represent the matrices that occur in IGA as sums of a small number of Kronecker products of auxiliary matrices defined by univariate integrals. Expand
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Partial tensor decomposition for decoupling isogeometric Galerkin discretizations
Abstract System matrix assembly for isogeometric (i.e., spline-based) discretizations of partial differential equations is more challenging than for classical finite elements, due to the increasedExpand
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