Uneingeschränkter Zugang

A Projection Strategy for Improving the Preconditioner in the LOBPCG

, ,  und   
24. Juni 2025

Zitieren
COVER HERUNTERLADEN

Balay, S., Abhyankar, S., Adams, M., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W. et al. (2022). PETSc users manual, https://petsc.org/release/docs/manual. Search in Google Scholar

Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F. and Zhang, H. (2001). PETSc, http://www.mcs.anl.gov/petsc. Search in Google Scholar

Bathe, K.-J. and Wilson, E.L. (1973). Solution methods for eigenvalue problems in structural mechanics, International Journal for Numerical Methods in Engineering 6(2): 213–226. Search in Google Scholar

Bennighof, J.K. and Lehoucq, R.B. (2004). An automated multilevel substructuring method for eigenspace computation in linear elastodynamics, SIAM Journal on Scientific Computing 25(6): 2084–2106, DOI: 10.1137/S1064827502400650. Search in Google Scholar

Collignon, T. and Gijzen, M.V. (2010). Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids, International Journal of Applied Mathematics and Computer Science 20(1): 109–121, DOI: 10.2478/v10006-010-0008-4. Search in Google Scholar

Duersch, J.A., Shao, M., Yang, C. and Gu, M. (2018). A robust and efficient implementation of LOBPCG, SIAM Journal on Scientific Computing 40(5): C655–C676, DOI: 10.1137/17M1129830. Search in Google Scholar

Erhel, J. and Frédéric, G. (1997). An Augmented Subspace Conjugate Gradient, PhD thesis, INRIA, Rennes. Search in Google Scholar

Fan, X., Chen, P., Wu, R. and Xiao, S. (2014). Parallel computing study for the large-scale generalized eigenvalue problems in modal analysis, Science China Physics, Mechanics and Astronomy 57(3): 477–489. Search in Google Scholar

Feng, Y. and Owen, D. (1996). Conjugate gradient methods for solving the smallest eigenpair of large symmetric eigenvalue problems, International Journal for Numerical Methods in Engineering 39(13): 2209–2229. Search in Google Scholar

Geng, M. and Sun, S. (2023). Projection improved SPAI preconditioner for FGMRES, Numerical Mathematics: Theory, Methods and Applications 16(4): 1035–1052. Search in Google Scholar

Guarracino, M., Perla, F. and Zanetti, P. (2006). A parallel block Lanczos algorithm and its implementation for the evaluation of some eigenvalues of large sparse symmetric matrices on multicomputers, International Journal of Applied Mathematics and Computer Science 16(2): 241–249. Search in Google Scholar

Hernandez, V., Roman, J.E. and Vidal, V. (2003). SLEPc: Scalable Library for Eigenvalue Problem Computations, Lecture Notes in Computer Science 2565: 377–391. Search in Google Scholar

Hernandez, V., Roman, J.E. and Vidal, V. (2005). SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems, ACM Transactions on Mathematical Software (TOMS) 31(3): 351–362. Search in Google Scholar

Hetmaniuk, U. and Lehoucq, R. (2006). Basis selection in LOBPCG, Journal of Computational Physics 218(1): 324–332. Search in Google Scholar

Il’in, V. (2019). Projection methods in Krylov subspaces, Journal of Mathematical Sciences 240(6): 772–782. Search in Google Scholar

Knyazev, A.V. (2001). Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SIAM Journal on Scientific Computing 23(2): 517–541. Search in Google Scholar

Knyazev, A.V., Argentati, M.E., Lashuk, I. and Ovtchinnikov, E.E. (2007). Block locally optimal preconditioned eigenvalue xolvers (BLOPEX) in Hypre and PETSc, SIAM Journal on Scientific Computing 29(5): 2224–2239. Search in Google Scholar

Kolodziej, S.P., Aznaveh, M., Bullock, M., David, J., Davis, T.A., Henderson, M., Hu, Y. and Sandstrom, R. (2019). The suitesparse matrix collection website interface, Journal of Open Source Software 4(35): 1244. Search in Google Scholar

Kressner, D., Ma, Y. and Shao, M. (2023). A mixed precision LOBPCG algorithm, Numerical Algorithms 94(4): 1653–1671, DOI: 10.1007/s11075-023-01550-9. Search in Google Scholar

Lanczos, C. (1950). An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, Journal of Research of the National Bureau of Standards 45(4): 255—282. Search in Google Scholar

Li, Y., Chen, P.Y., Du, T. and Matusik, W. (2023). Learning preconditioners for conjugate gradient PDE solvers, International Conference on Machine Learning, Honolulu, USA, pp. 19425–19439. Search in Google Scholar

Roman, J.E., Campos, C., Romero, E. and Tomás, A. (2016). SLEPc users manual, Departamento di Sistemas Informàticos y Computación, Universitat Politècnica de València, TR DSIC-II/24/02, Rev 3. Search in Google Scholar

Saad, Y. (2003). Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia, USA. Search in Google Scholar

Sleijpen, G.L. and Van der Vorst, H.A. (2000). A Jacobi–Davidson iteration method for linear eigenvalue problems, SIAM Review 42(2): 267–293. Search in Google Scholar

Stathopoulos, A. and McCombs, J.R. (2010). PRIMME: PReconditioned Iterative MultiMethod Eigensolver: Methods and software description, ACM Transactions on Mathematical Software 37(2): 21:1–21:30. Search in Google Scholar

Sulaiman, I.M., Kaelo, P., Khalid, R. and Nawawi, M.K.M. (2024). A descent generalized RMIL spectral gradient algorithm for optimization problems, International Journal of Applied Mathematics and Computer Science 34(2): 225–233, DOI: 10.61822/amcs-2024-0016. Search in Google Scholar

Wu, L., Romero, E. and Stathopoulos, A. (2017). Primme svds: A high-performance preconditioned SVD solver for accurate large-scale computations, SIAM Journal on Scientific Computing 39(5): S248–S271, DOI: 10.1137/16M1082214. Search in Google Scholar

Yin, J., Voss, H. and Chen, P. (2013). Improving eigenpairs of automated multilevel substructuring with subspace iterations, Computers & Structures 119(1): 115–124. Search in Google Scholar

Yuan, M., Chen, P., Xiong, S., Li, Y. and Wilson, E.L. (1989). TheWYD method in large eigenvalue problems, Engineering computations 6(1): 49–57. Search in Google Scholar

Yuan, Y., Sun, S., Chen, P. and Yuan, M. (2021). Adaptive relaxation strategy on basic iterative methods for solving linear systems with single and multiple right-hand sides, Advances in Applied Mathematics and Mechanics 13(2): 378–403. Search in Google Scholar

Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
4 Hefte pro Jahr
Fachgebiete der Zeitschrift:
Mathematik, Angewandte Mathematik