The value of continuity: Refined isogeometric analysis and fast direct solvers
MetadataShow full item record
© 2016 Elsevier B.V.We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce . C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method "refined Isogeometric Analysis (rIGA)". To illustrate the impact of the continuity reduction, we analyze the number of Floating Point Operations (FLOPs), computational times, and memory required to solve the linear system obtained by discretizing the Laplace problem with structured meshes and uniform polynomial orders. Theoretical estimates demonstrate that an optimal continuity reduction may decrease the total computational time by a factor between . p2 and . p3, with . p being the polynomial order of the discretization. Numerical results indicate that our proposed refined isogeometric analysis delivers a speed-up factor proportional to . p2. In a . 2D mesh with four million elements and . p=5, the linear system resulting from rIGA is solved 22 times faster than the one from highly continuous IGA. In a . 3D mesh with one million elements and . p=3, the linear system is solved 15 times faster for the refined than the maximum continuity isogeometric analysis.
Showing items related by title, author, creator and subject.
Mora Paz, J.; Mantilla Gonzalez, J.; Calo, Victor (2017)A numerical method is formulated based on Finite Elements, Iso- geometric Analysis and a Multiscale technique. Isogeometric Analysis, which uses B-Splines and NURBS as basis functions, is applied to evaluate its performance. ...
Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemesPuzyrev, Vladimir; Deng, Quanling; Calo, Victor (2017)This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner ...
Calo, Victor; Deng, Quanling; Puzyrev, Vladimir (2017)© 2017 The Authors. Published by Elsevier B.V. We use blended quadrature rules to reduce the phase error of isogeometric analysis discretizations. To explain the observed behavior and quantify the approximation errors, ...