TY - GEN
T1 - Preconditioned conjugate gradient solvers for the generalized finite element method
AU - Fillmore, Travis B.
AU - Gupta, Varun
AU - Duarte, Carlos Armando
N1 - Funding Information:
Acknowledgements T.B. Fillmore and C.A. Duarte gratefully acknowledge the research funding under contract number AF Sub OSU 60038238 provided by the Collaborative Center in Structural Sciences (C2S2) at the Ohio State University, supported by the U.S. Air Force Research Laboratory.
Funding Information:
T.B. Fillmore and C.A. Duarte gratefully acknowledge the research funding under contract number AF Sub OSU60038238 provided by the Collaborative Center in Structural Sciences (C2S2) at the Ohio State University, supported by the U.S. Air Force Research Laboratory.
Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019
Y1 - 2019
N2 - This paper focuses on preconditioners for the conjugate gradient method and their applications to the Generalized FEM with global-local enrichments (GFEMgl) and the Stable GFEMgl. The preconditioners take advantage of the hierarchical struture of the matrices in these methods and the fact that most of the matrix does not change when simulating for example, the evolution of interfaces and fractures. The performance of the conjugate gradient method with the proposed preconditioner is investigated. A 3-D fracture problem is adopted for the numerical experiments.
AB - This paper focuses on preconditioners for the conjugate gradient method and their applications to the Generalized FEM with global-local enrichments (GFEMgl) and the Stable GFEMgl. The preconditioners take advantage of the hierarchical struture of the matrices in these methods and the fact that most of the matrix does not change when simulating for example, the evolution of interfaces and fractures. The performance of the conjugate gradient method with the proposed preconditioner is investigated. A 3-D fracture problem is adopted for the numerical experiments.
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U2 - 10.1007/978-3-030-15119-5_1
DO - 10.1007/978-3-030-15119-5_1
M3 - Conference contribution
AN - SCOPUS:85068337657
SN - 9783030151188
T3 - Lecture Notes in Computational Science and Engineering
SP - 1
EP - 17
BT - Meshfree Methods for Partial Differential Equations IX, 2017
A2 - Griebel, Michael
A2 - Schweitzer, Marc Alexander
A2 - Griebel, Michael
A2 - Schweitzer, Marc Alexander
PB - Springer
T2 - 9th International Workshop on Meshfree Methods for Partial Differential Equations, IWMMPDE 2017
Y2 - 18 September 2017 through 20 September 2017
ER -