PetIGA: A framework for high-performance isogeometric analysis

Dalcin, Lisandro; Collier, Nathaniel; Vignal, Philippe; Cortes, Adriano M. A.; Calo, Victor M.

doi:10.1016/j.cma.2016.05.011

Title: PetIGA: A framework for high-performance isogeometric analysis

Journal Article · Wed May 25 00:00:00 EDT 2016 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2016.05.011· OSTI ID:1327764

^[1]; Collier, Nathaniel ^[2]; Vignal, Philippe ^[3]; Cortes, Adriano M. A. ^[3]; Calo, Victor M. ^[3]

King Abdullah Univ. of Science and Technology (KAUST), Thuwal (Saudi Arabia); Centro de Investigacion de Metodos Computacionales (CIMEC), Santa Fe (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Santa Fe (Argentina)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
King Abdullah Univ. of Science and Technology (KAUST), Thuwal (Saudi Arabia)

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility of PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. Lastly, we show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1327764

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 308, Issue C; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 95 works

Citation information provided by
Web of Science

References (52)

Isogeometric analysis of the advective Cahn–Hilliard equation: Spinodal decomposition under shear flow Liu, Ju; Dedè, Luca; Evans, John A. Journal of Computational Physics, Vol. 242 https://doi.org/10.1016/j.jcp.2013.02.008	journal	June 2013
Igatools: An Isogeometric Analysis Library Pauletti, M. Sebastian; Martinelli, Massimiliano; Cavallini, Nicola SIAM Journal on Scientific Computing, Vol. 37, Issue 4 https://doi.org/10.1137/140955252	journal	January 2015
Efficient quadrature for NURBS-based isogeometric analysis Hughes, T. J. R.; Reali, A.; Sangalli, G. Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 5-8 https://doi.org/10.1016/j.cma.2008.12.004	journal	January 2010
The role of continuity in residual-based variational multiscale modeling of turbulence Akkerman, I.; Bazilevs, Y.; Calo, V. M. Computational Mechanics, Vol. 41, Issue 3 https://doi.org/10.1007/s00466-007-0193-7	journal	June 2007
A NURBS-based immersed methodology for fluid–structure interaction Casquero, Hugo; Bona-Casas, Carles; Gomez, Hector Computer Methods in Applied Mechanics and Engineering, Vol. 284 https://doi.org/10.1016/j.cma.2014.10.055	journal	February 2015
Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows Bazilevs, Y.; Calo, V. M.; Cottrell, J. A. Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 1-4 https://doi.org/10.1016/j.cma.2007.07.016	journal	December 2007
Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers Woźniak, M.; Kuźnik, K.; Paszyński, M. Computers & Mathematics with Applications, Vol. 67, Issue 10 https://doi.org/10.1016/j.camwa.2014.03.017	journal	June 2014
Energy exchange analysis in droplet dynamics via the Navier–Stokes–Cahn–Hilliard model Espath, L. F. R.; Sarmiento, A. F.; Vignal, P. Journal of Fluid Mechanics, Vol. 797 https://doi.org/10.1017/jfm.2016.277	journal	May 2016
Isogeometric analysis of the Cahn–Hilliard phase-field model Gómez, Héctor; Calo, Victor M.; Bazilevs, Yuri Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 49-50 https://doi.org/10.1016/j.cma.2008.05.003	journal	September 2008
Jacobian-free Newton–Krylov methods: a survey of approaches and applications Knoll, D. A.; Keyes, D. E. Journal of Computational Physics, Vol. 193, Issue 2 https://doi.org/10.1016/j.jcp.2003.08.010	journal	January 2004
Isogeometric analysis of free-surface flow Akkerman, I.; Bazilevs, Y.; Kees, C. E. Journal of Computational Physics, Vol. 230, Issue 11 https://doi.org/10.1016/j.jcp.2010.11.044	journal	May 2011
On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers: ON THE COMPUTATIONAL EFFICIENCY OF ISOGEOMETRIC METHODS Collier, N.; Dalcin, L.; Calo, V. M. International Journal for Numerical Methods in Engineering, Vol. 100, Issue 8 https://doi.org/10.1002/nme.4769	journal	September 2014
NITSOL: A Newton Iterative Solver for Nonlinear Systems Pernice, Michael; Walker, Homer F. SIAM Journal on Scientific Computing, Vol. 19, Issue 1 https://doi.org/10.1137/S1064827596303843	journal	January 1998
Isogeometric Collocation Methods Auricchio, F.; Da Veiga, L. BeirÃO; Hughes, T. J. R. Mathematical Models and Methods in Applied Sciences, Vol. 20, Issue 11 https://doi.org/10.1142/S0218202510004878	journal	November 2010
Isogeometric divergence-conforming B-splines for the unsteady Navier–Stokes equations Evans, John A.; Hughes, Thomas J. R. Journal of Computational Physics, Vol. 241 https://doi.org/10.1016/j.jcp.2013.01.006	journal	May 2013
Geometry + Simulation Modules: Implementing Isogeometric Analysis: Geometry + Simulation Modules Jüttler, Bert; Langer, Ulrich; Mantzaflaris, Angelos PAMM, Vol. 14, Issue 1 https://doi.org/10.1002/pamm.201410461	journal	December 2014
Explicit Gaussian quadrature rules for $C^{1}$ cubic splines with symmetrically stretched knot sequences Ait-Haddou, Rachid; Bartoň, Michael; Calo, Victor Manuel Journal of Computational and Applied Mathematics, Vol. 290 https://doi.org/10.1016/j.cam.2015.06.008	journal	December 2015
An energy-stable convex splitting for the phase-field crystal equation Vignal, P.; Dalcin, L.; Brown, D. L. Computers & Structures, Vol. 158 https://doi.org/10.1016/j.compstruc.2015.05.029	journal	October 2015
libMesh : a C++ library for parallel adaptive mesh refinement/coarsening simulations Kirk, Benjamin S.; Peterson, John W.; Stogner, Roy H. Engineering with Computers, Vol. 22, Issue 3-4 https://doi.org/10.1007/s00366-006-0049-3	journal	November 2006
Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration Vignal, Philippe; Sarmiento, Adel; Côrtes, Adriano M. A. Procedia Computer Science, Vol. 51 https://doi.org/10.1016/j.procs.2015.05.228	journal	January 2015
Isogeometric analysis of the isothermal Navier–Stokes–Korteweg equations Gomez, Hector; Hughes, Thomas J. R.; Nogueira, Xesús Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 25-28 https://doi.org/10.1016/j.cma.2010.02.010	journal	May 2010
Isogeometric Analysis of Hyperelastic Materials Using PetIGA Bernal, L. M.; Calo, V. M.; Collier, N. Procedia Computer Science, Vol. 18 https://doi.org/10.1016/j.procs.2013.05.328	journal	January 2013
n-Widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method Evans, John A.; Bazilevs, Yuri; Babuška, Ivo Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 21-26 https://doi.org/10.1016/j.cma.2009.01.021	journal	May 2009
deal.II---A general-purpose object-oriented finite element library Bangerth, W.; Hartmann, R.; Kanschat, G. ACM Transactions on Mathematical Software, Vol. 33, Issue 4 https://doi.org/10.1145/1268776.1268779	journal	August 2007
A continuation multilevel Monte Carlo algorithm Collier, Nathan; Haji-Ali, Abdul-Lateef; Nobile, Fabio BIT Numerical Mathematics, Vol. 55, Issue 2 https://doi.org/10.1007/s10543-014-0511-3	journal	September 2014
Those Who Will Not Learn From History... Wilson, Greg Computing in Science & Engineering, Vol. 10, Issue 3 https://doi.org/10.1109/MCSE.2008.86	journal	May 2008
Isogeometric Discrete Differential Forms in Three Dimensions Buffa, A.; Rivas, J.; Sangalli, G. SIAM Journal on Numerical Analysis, Vol. 49, Issue 2 https://doi.org/10.1137/100786708	journal	January 2011
Some estimates for h–p–k-refinement in Isogeometric Analysis Beirão da Veiga, L.; Buffa, A.; Rivas, J. Numerische Mathematik, Vol. 118, Issue 2 https://doi.org/10.1007/s00211-010-0338-z	journal	October 2010
An overview of the Trilinos project Heroux, Michael A.; Phipps, Eric T.; Salinger, Andrew G. ACM Transactions on Mathematical Software, Vol. 31, Issue 3 https://doi.org/10.1145/1089014.1089021	journal	September 2005
Hybrid scheduling for the parallel solution of linear systems Amestoy, Patrick R.; Guermouche, Abdou; L’Excellent, Jean-Yves Parallel Computing, Vol. 32, Issue 2 https://doi.org/10.1016/j.parco.2005.07.004	journal	February 2006
The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements Collier, Nathan; Dalcin, Lisandro; Pardo, David SIAM Journal on Scientific Computing, Vol. 35, Issue 2 https://doi.org/10.1137/120881038	journal	January 2013
An isogeometric locking-free NURBS-based solid-shell element for geometrically nonlinear analysis: An isogeometric locking-free NURBS-based solid-shell element for geometrically nonlinear analysis Bouclier, Robin; Elguedj, Thomas; Combescure, Alain International Journal for Numerical Methods in Engineering, Vol. 101, Issue 10 https://doi.org/10.1002/nme.4834	journal	December 2014
On calculating with B-splines de Boor, Carl Journal of Approximation Theory, Vol. 6, Issue 1 https://doi.org/10.1016/0021-9045(72)90080-9	journal	July 1972
A parallel finite element program on a Beowulf cluster Sonzogni, V. E.; Yommi, A. M.; Nigro, N. M. Advances in Engineering Software, Vol. 33, Issue 7-10 https://doi.org/10.1016/S0965-9978(02)00059-5	journal	July 2002
What Color Is Your Jacobian? Graph Coloring for Computing Derivatives Gebremedhin, Assefaw Hadish; Manne, Fredrik; Pothen, Alex SIAM Review, Vol. 47, Issue 4 https://doi.org/10.1137/S0036144504444711	journal	January 2005
A large deformation, rotation-free, isogeometric shell Benson, D. J.; Bazilevs, Y.; Hsu, M. -C. Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 13-16 https://doi.org/10.1016/j.cma.2010.12.003	journal	March 2011
Gaussian quadrature for splines via homotopy continuation: Rules for $C^{2}$ cubic splines Bartoň, Michael; Calo, Victor Manuel Journal of Computational and Applied Mathematics, Vol. 296 https://doi.org/10.1016/j.cam.2015.09.036	journal	April 2016
Three-dimensional isogeometric solutions to general boundary value problems of Toupin’s gradient elasticity theory at finite strains Rudraraju, S.; Van der Ven, A.; Garikipati, K. Computer Methods in Applied Mechanics and Engineering, Vol. 278 https://doi.org/10.1016/j.cma.2014.06.015	journal	August 2014
The Liouville–Bratu–Gelfand Problem for Radial Operators Jacobsen, Jon; Schmitt, Klaus Journal of Differential Equations, Vol. 184, Issue 1 https://doi.org/10.1006/jdeq.2001.4151	journal	September 2002
A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method Jansen, Kenneth E.; Whiting, Christian H.; Hulbert, Gregory M. Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 3-4 https://doi.org/10.1016/S0045-7825(00)00203-6	journal	October 2000
The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers Collier, Nathan; Pardo, David; Dalcin, Lisandro Computer Methods in Applied Mechanics and Engineering, Vol. 213-216 https://doi.org/10.1016/j.cma.2011.11.002	journal	March 2012
Simulation of laminar and turbulent concentric pipe flows with the isogeometric variational multiscale method Ghaffari Motlagh, Yousef; Ahn, Hyung Taek; Hughes, Thomas J. R. Computers & Fluids, Vol. 71 https://doi.org/10.1016/j.compfluid.2012.09.006	journal	January 2013
Geometric Modeling with Splines Cohen, Elaine; Riesenfeld, Richard F.; Elber, Gershon A K Peters/CRC Press https://doi.org/10.1201/9781439864203	book	July 2001
IPython: A System for Interactive Scientific Computing Perez, Fernando; Granger, Brian E. Computing in Science & Engineering, Vol. 9, Issue 3 https://doi.org/10.1109/MCSE.2007.53	journal	January 2007
GeoPDEs: A research tool for Isogeometric Analysis of PDEs de Falco, C.; Reali, A.; Vázquez, R. Advances in Engineering Software, Vol. 42, Issue 12 https://doi.org/10.1016/j.advengsoft.2011.06.010	journal	December 2011
PCBDDC: A Class of Robust Dual-Primal Methods in PETSc Zampini, Stefano SIAM Journal on Scientific Computing, Vol. 38, Issue 5 https://doi.org/10.1137/15M1025785	journal	January 2016
Matplotlib: A 2D Graphics Environment Hunter, John D. Computing in Science & Engineering, Vol. 9, Issue 3 https://doi.org/10.1109/MCSE.2007.55	journal	January 2007
Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials Kiendl, Josef; Hsu, Ming-Chen; Wu, Michael C. H. Computer Methods in Applied Mechanics and Engineering, Vol. 291 https://doi.org/10.1016/j.cma.2015.03.010	journal	July 2015
An iso Geometric Analysis Approach for the Study of Structural Vibrations Reali∗, A. Journal of Earthquake Engineering, Vol. 10, Issue sup001 https://doi.org/10.1080/13632460609350626	journal	January 2006
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement Hughes, T. J. R.; Cottrell, J. A.; Bazilevs, Y. Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 39-41 https://doi.org/10.1016/j.cma.2004.10.008	journal	October 2005
Isogeometric BDDC Preconditioners with Deluxe Scaling da Veiga, L. Beira͂o; Pavarino, L. F.; Scacchi, S. SIAM Journal on Scientific Computing, Vol. 36, Issue 3 https://doi.org/10.1137/130917399	journal	January 2014
The Numerical Evaluation of B -Splines Cox, M. G. IMA Journal of Applied Mathematics, Vol. 10, Issue 2 https://doi.org/10.1093/imamat/10.2.134	journal	January 1972

Cited By (16)

Phase-Field Modeling of Individual and Collective Cell Migration Moure, Adrian; Gomez, Hector Archives of Computational Methods in Engineering https://doi.org/10.1007/s11831-019-09377-1	journal	December 2019
A mechanical model reveals that non-axisymmetric buckling lowers the energy barrier associated with membrane neck constriction Vasan, R.; Rudraraju, S.; Akamatsu, M. Soft Matter https://doi.org/10.1101/672485	journal	November 2019
Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems Clavijo, Santiago P.; Espath, Luis; Calo, Victor M. RWTH Aachen University https://doi.org/10.18154/rwth-2021-08421	text	January 2021
On the Thermodynamics of the Swift-Hohenberg Theory Espath, Lfr; Sarmiento, Af; Dalcin, L. arXiv https://doi.org/10.48550/arxiv.1610.00180	text	January 2016
NURBS-SEM: a hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces Pitton, Giuseppe; Heltai, Luca arXiv https://doi.org/10.48550/arxiv.1804.08271	text	January 2018
Multiscale finite element calculations in Python using SfePy Cimrman, Robert; Lukeš, Vladimír; Rohan, Eduard Advances in Computational Mathematics, Vol. 45, Issue 4 https://doi.org/10.1007/s10444-019-09666-0	journal	May 2019
Refined isogeometric analysis for generalized Hermitian eigenproblems Hashemian, Ali; Pardo, David; Calo, Victor M. Computer Methods in Applied Mechanics and Engineering, Vol. 381 https://doi.org/10.1016/j.cma.2021.113823	journal	August 2021
Spectral approximation properties of isogeometric analysis with variable continuity Puzyrev, Vladimir; Deng, Quanling; Calo, Victor arXiv https://doi.org/10.48550/arxiv.1709.09815	text	January 2017
Non-invasive implementation of nonlinear isogeometric analysis in an industrial FE software Tirvaudey, Marie; Bouclier, Robin; Passieux, Jean-Charles Engineering Computations, Vol. 37, Issue 1 https://doi.org/10.1108/ec-03-2019-0108	journal	July 2019
Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematics and revealed by a three dimensional computational framework Auddya, Debabrata; Zhang, Xiaoxuan; Gulati, Rahul arXiv https://doi.org/10.48550/arxiv.2101.11929	text	January 2021
A continuum theory for mineral solid solutions undergoing chemo-mechanical processes Clavijo, Santiago P.; Espath, Luis; Sarmiento, Adel Continuum Mechanics and Thermodynamics, Vol. 34, Issue 1 https://doi.org/10.1007/s00161-021-01041-z	journal	July 2021
Groundwater Flow Modeling in Karst Aquifers: Coupling 3D Matrix and 1D Conduit Flow via Control Volume Isogeometric Analysis—Experimental Verification with a 3D Physical Model Malenica, Luka; Gotovac, Hrvoje; Kamber, Grgo Water, Vol. 10, Issue 12 https://doi.org/10.3390/w10121787	journal	December 2018
Multiscale finite element calculations in Python using SfePy Cimrman, Robert; Lukeš, Vladimír; Rohan, Eduard arXiv https://doi.org/10.48550/arxiv.1810.00674	text	January 2018
IGA: A Simplified Introduction and Implementation Details for Finite Element Users Agrawal, Vishal; Gautam, Sachin S. Journal of The Institution of Engineers (India): Series C, Vol. 100, Issue 3 https://doi.org/10.1007/s40032-018-0462-6	journal	May 2018
Recent Advances of Isogeometric Analysis in Computational Electromagnetics Bontinck, Zeger; Corno, Jacopo; De Gersem, Herbert arXiv https://doi.org/10.48550/arxiv.1709.06004	preprint	January 2017
HexGen and Hex2Spline: Polycube-based Hexahedral Mesh Generation and Spline Modeling for Isogeometric Analysis Applications in LS-DYNA Yu, Yuxuan; Wei, Xiaodong; Li, Angran arXiv https://doi.org/10.48550/arxiv.2011.14213	preprint	January 2020

Similar Records

PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces

Journal Article · Fri Oct 07 00:00:00 EDT 2016 · Journal of Computational Science · OSTI ID:1327764

Sarmiento, Adel; Cortes, Adriano; Garcia, Daniel; +3 more

PETSc Users Manual (Rev. 3.3)

Technical Report · Sat May 11 00:00:00 EDT 2013 · OSTI ID:1327764

Balay, S.; Brown, J.; Buschelman, K.; +7 more

PETSc Users Manual (Rev. 3.4)

Technical Report · Sun Jun 29 00:00:00 EDT 2014 · OSTI ID:1327764

Balay, S.; Brown, J.; Buschelman, K.; +7 more

Related Subjects

97 MATHEMATICS AND COMPUTING
isogeometric analysis
high-performance computing
finite element method
open-source software

Title: PetIGA: A framework for high-performance isogeometric analysis

Citation Formats

References (52)

Cited By (16)

Similar Records

Related Subjects