The value of continuity: Refined isogeometric analysis and fast direct solvers
Here, 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 C0separators 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 p ^{2} and p ^{3}, with pp being the polynomial order of the discretization. Numerical results indicate that our proposed refined isogeometric analysis delivers a speedup factor proportional to p ^{2}. 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 ismore »
 Authors:

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 Basque Center for Applied Mathematics (BCAM), Bilbao (Spain)
 Basque Center for Applied Mathematics (BCAM), Bilbao (Spain); Univ. of the Basque Country UPV.EHU, Leioa (Spain); Ikerbasque (Basque Foundation for Sciences), Bilbao (Spain)
 King Abdullah Univ. of Science and Technology (KAUST), Thuwal (Saudi Arabia); Consejo Nacional de Investigaciones Cientificas y Tecnicas, Santa Fe (Argentina); Univ. Nacional del Litoral, Santa Fe (Argentina)
 AGH Univ. of Science and Technology, Krakow (Poland)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Curtin Univ., Bentley, WA (Australia); Commonwealth Scientific and Industrial Research Organisation (CSIRO), Kensington, WA (Australia)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Computer Methods in Applied Mechanics and Engineering
 Additional Journal Information:
 Journal Name: Computer Methods in Applied Mechanics and Engineering; Journal ID: ISSN 00457825
 Publisher:
 Elsevier
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; isogeometric analysis (IGA); finite element analysis (FEA); refined isogeometric analysis (rIGA); direct solvers; multifrontal solvers; krefinement
 OSTI Identifier:
 1327763
 Alternate Identifier(s):
 OSTI ID: 1429198
Garcia, Daniel, Pardo, David, Dalcin, Lisandro, Paszynski, Maciej, Collier, Nathan, and Calo, Victor M. The value of continuity: Refined isogeometric analysis and fast direct solvers. United States: N. p.,
Web. doi:10.1016/j.cma.2016.08.017.
Garcia, Daniel, Pardo, David, Dalcin, Lisandro, Paszynski, Maciej, Collier, Nathan, & Calo, Victor M. The value of continuity: Refined isogeometric analysis and fast direct solvers. United States. doi:10.1016/j.cma.2016.08.017.
Garcia, Daniel, Pardo, David, Dalcin, Lisandro, Paszynski, Maciej, Collier, Nathan, and Calo, Victor M. 2016.
"The value of continuity: Refined isogeometric analysis and fast direct solvers". United States.
doi:10.1016/j.cma.2016.08.017. https://www.osti.gov/servlets/purl/1327763.
@article{osti_1327763,
title = {The value of continuity: Refined isogeometric analysis and fast direct solvers},
author = {Garcia, Daniel and Pardo, David and Dalcin, Lisandro and Paszynski, Maciej and Collier, Nathan and Calo, Victor M.},
abstractNote = {Here, 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 C0separators 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 pp being the polynomial order of the discretization. Numerical results indicate that our proposed refined isogeometric analysis delivers a speedup 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.},
doi = {10.1016/j.cma.2016.08.017},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {8}
}