{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T04:12:18Z","timestamp":1744949538550,"version":"3.37.3"},"reference-count":56,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T00:00:00Z","timestamp":1681171200000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014188","name":"MSIT","doi-asserted-by":"publisher","award":["2019R1C1C1004159"],"award-info":[{"award-number":["2019R1C1C1004159"]}],"id":[{"id":"10.13039\/501100014188","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,4,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this manuscript, we propose a new effective method for eigenpair reanalysis of large-scale finite element (FE) models. Our method utilizes the matrix block-partitioning algorithm in the Rayleigh\u2013Ritz approach and expresses the Ritz basis matrix using thousands of block matrices of very small size. To avoid significant computational costs from the projection procedure, we derive a new formulation that uses tiny block computations instead of global matrix computations. Additionally, we present an algorithm that recognizes which blocks are changed in the modified FE model to achieve computational cost savings when computing new eigenpairs. Through selective updating for the recognized blocks, we can effectively construct the new Ritz basis matrix and the new reduced mass and stiffness matrices corresponding to the modified FE model. To demonstrate the performance of our proposed method, we solve several practical engineering problems and compare the results with those of the combined approximation method, the most well-known eigenpair reanalysis method, and ARPACK, an eigenvalue solver embedded in many numerical programs.<\/jats:p>","DOI":"10.1093\/jcde\/qwad030","type":"journal-article","created":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T01:59:05Z","timestamp":1681178345000},"page":"959-978","source":"Crossref","is-referenced-by-count":1,"title":["Block-partitioned Rayleigh\u2013Ritz method for efficient eigenpair reanalysis of large-scale finite element models"],"prefix":"10.1093","volume":"10","author":[{"given":"Yeon-Ho","family":"Jeong","sequence":"first","affiliation":[{"name":"Division of Naval Architecture and Ocean Systems Engineering, Korea Maritime and Ocean University , 727 Taejong-ro, Yeongdo-gu, Busan 49112, Republic of Korea"}]},{"given":"Seung-Hwan","family":"Boo","sequence":"additional","affiliation":[{"name":"Division of Naval Architecture and Ocean Systems Engineering, Korea Maritime and Ocean University , 727 Taejong-ro, Yeongdo-gu, Busan 49112, Republic of Korea"}]},{"given":"Solomon C","family":"Yim","sequence":"additional","affiliation":[{"name":"School of Civil and Construction Engineering, Oregon State University , Corvallis OR 97331, USA"}]}],"member":"286","published-online":{"date-parts":[[2023,4,10]]},"reference":[{"key":"2023051114184922700_bib1","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1093\/jcde\/qwaa044","article-title":"Density-based shape optimization for fail-safe design","volume":"7","author":"Ambrozkiewicz","year":"2020","journal-title":"Journal of Computational Design and Engineering"},{"volume-title":"Finite element procedures","year":"2006","author":"Bathe","key":"2023051114184922700_bib2"},{"key":"2023051114184922700_bib3","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0045-7825(80)90012-2","article-title":"An accelerated subspace iteration method","volume":"23","author":"Bathe","year":"1980","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2023051114184922700_bib4","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1016\/j.apnum.2007.01.003","article-title":"An estimator for the diagonal of a matrix","volume":"57","author":"Bekas","year":"2007","journal-title":"Applied Numerical Mathematics"},{"key":"2023051114184922700_bib5","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.cpc.2005.05.005","article-title":"Computing charge densities with partially reorthogonalized Lanczos","volume":"171","author":"Bekas","year":"2005","journal-title":"Computer Physics Communications"},{"key":"2023051114184922700_bib6","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1137\/S1064827502400650","article-title":"An automated multilevel substructuring method for eigenspace computation in linear elastodynamics","volume":"25","author":"Bennighof","year":"2004","journal-title":"SIAM Journal on Scientific Computing"},{"key":"2023051114184922700_bib7","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1002\/nme.1620240305","article-title":"An improved computational technique for perturbations of the generalized symmetric linear algebraic eigenvalue problem","volume":"24","author":"Bickford","year":"1987","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"2023051114184922700_bib8","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1145\/1583991.1584053","article-title":"Parallel sparse matrix-vector and matrix-transpose-vector multiplication using compressed sparse blocks","volume-title":"Proceedings of the Twenty-first Annual Symposium on Parallelism in Algorithms and Architectures","author":"Bulu\u00e7","year":"2009"},{"volume-title":"Sparse matrix computations","year":"2014","author":"Bunch","key":"2023051114184922700_bib9"},{"key":"2023051114184922700_bib10","first-page":"21","article-title":"An implicitly restarted Lanczos method for large symmetric eigenvalue problems","volume":"2","author":"Calvetti","year":"1994","journal-title":"Electronic Transactions on Numerical Analysis"},{"key":"2023051114184922700_bib11","doi-asserted-by":"crossref","first-page":"106844","DOI":"10.1016\/j.compstruc.2022.106844","article-title":"A structural reanalysis assisted harmony search for the optimal design of structures","volume":"270","author":"Cao","year":"2022","journal-title":"Computers & Structures"},{"key":"2023051114184922700_bib12","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1002\/cnm.1640100203","article-title":"Eigensolution reanalysis of modified structures using perturbations and Rayleigh quotients","volume":"10","author":"Chen","year":"1994","journal-title":"Communications in Numerical Methods in Engineering"},{"key":"2023051114184922700_bib13","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s001580050155","article-title":"Comparison of several eigenvalue reanalysis methods for modified structures","volume":"20","author":"Chen","year":"2000","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023051114184922700_bib14","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.2514\/3.4741","article-title":"Coupling of substructures for dynamic analyses","volume":"6","author":"Craig","year":"1968","journal-title":"AIAA Journal"},{"volume-title":"Fundamentals of structural dynamics","year":"2006","author":"Craig","key":"2023051114184922700_bib15"},{"key":"2023051114184922700_bib16","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.procs.2012.04.007","article-title":"The sliced COO format for sparse matrix-vector multiplication on CUDA-enabled GPUs","volume":"9","author":"Dang","year":"2012","journal-title":"Procedia Computer Science"},{"key":"2023051114184922700_bib17","first-page":"663","article-title":"Optimization of block sparse matrix-vector multiplication on shared-memory parallel architectures","volume-title":"Proceedings of the 2016 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)","author":"Eberhardt","year":"2016"},{"key":"2023051114184922700_bib18","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1016\/j.ijheatmasstransfer.2016.02.061","article-title":"Fast and efficient analysis of transient nonlinear heat conduction problems using combined approximations (CA) method","volume":"97","author":"Feng","year":"2016","journal-title":"International Journal of Heat and Mass Transfer"},{"key":"2023051114184922700_bib19","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1093\/jcde\/qwaa066","article-title":"Crack development assessment using modal analysis in peridynamic theory","volume":"8","author":"Freimanis","year":"2021","journal-title":"Journal of Computational Design and Engineering"},{"key":"2023051114184922700_bib20","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1137\/0710032","article-title":"Nested dissection of a regular finite element mesh","volume":"10","author":"George","year":"1973","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"2023051114184922700_bib21","first-page":"1818","article-title":"The digital twin paradigm for future NASA and US Air Force vehicles","volume-title":"Proceedings of the 53rd AIAA\/ASME\/ASCE\/AHS\/ASC Structures, Structural Dynamics and Materials Conference","author":"Glaessgen","year":"2012"},{"key":"2023051114184922700_bib22","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1137\/S0895479888151111","article-title":"A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems","volume":"15","author":"Grimes","year":"1994","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"article-title":"Abaqus analysis user\u2019s manual version 6.10","year":"2011","author":"Hibbitt","key":"2023051114184922700_bib23"},{"volume-title":"The finite element method: Linear static and dynamic finite element analysis","year":"2012","author":"Hughes","key":"2023051114184922700_bib24"},{"key":"2023051114184922700_bib25","doi-asserted-by":"crossref","first-page":"106649","DOI":"10.1016\/j.compstruc.2021.106649","article-title":"A load balancing algorithm for the parallel automated multilevel substructuring method","volume":"257","author":"Hyun","year":"2021","journal-title":"Computers & Structures"},{"key":"2023051114184922700_bib26","doi-asserted-by":"crossref","first-page":"C410","DOI":"10.1137\/19M1280004","article-title":"A domain decomposition Rayleigh\u2013Ritz algorithm for symmetric generalized eigenvalue problems","volume":"42","author":"Kalantzis","year":"2020","journal-title":"SIAM Journal on Scientific Computing"},{"key":"2023051114184922700_bib27","first-page":"38","volume-title":"A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices","author":"Karypis","year":"1998"},{"key":"2023051114184922700_bib28","doi-asserted-by":"crossref","first-page":"1969","DOI":"10.1002\/nme.1032","article-title":"Procedures for approximate eigenproblem reanalysis of structures","volume":"60","author":"Kirsch","year":"2004","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"2023051114184922700_bib29","doi-asserted-by":"crossref","first-page":"4420","DOI":"10.1016\/j.cma.2005.09.013","article-title":"Nonlinear dynamic reanalysis of structures by combined approximations","volume":"195","author":"Kirsch","year":"2006","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2023051114184922700_bib30","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1061\/(ASCE)0733-9445(2007)133:3(440)","article-title":"Efficient dynamic reanalysis of structures","volume":"133","author":"Kirsch","year":"2007","journal-title":"Journal of Structural Engineering"},{"key":"2023051114184922700_bib31","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1016\/j.camwa.2012.06.011","article-title":"Parallel implementations of the trace minimization scheme TraceMIN for the sparse symmetric eigenvalue problem","volume":"65","author":"Klinvex","year":"2013","journal-title":"Computers & Mathematics with Applications"},{"key":"2023051114184922700_bib32","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.apnum.2003.11.011","article-title":"Computing smallest singular triplets with implicitly restarted Lanczos bidiagonalization","volume":"49","author":"Kokiopoulou","year":"2004","journal-title":"Applied Numerical Mathematics"},{"key":"2023051114184922700_bib33","doi-asserted-by":"crossref","DOI":"10.6028\/jres.045.026","article-title":"An iteration method for the solution of the eigenvalue problem of linear differential and integral operators","author":"Lanczos","year":"1950"},{"key":"2023051114184922700_bib34","doi-asserted-by":"crossref","first-page":"106895","DOI":"10.1016\/j.compstruc.2022.106895","article-title":"A reanalysis-based multi-fidelity (RBMF) surrogate framework for efficient structural optimization","volume":"273","author":"Lee","year":"2022","journal-title":"Computers & Structures"},{"key":"2023051114184922700_bib35","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1137\/S0895479895281484","article-title":"Deflation techniques for an implicitly restarted Arnoldi iteration","volume":"17","author":"Lehoucq","year":"1996","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"2023051114184922700_bib36","article-title":"ARPACK users\u2019 guide: Solution of large eigenvalue problems with implicitly restarted Arnoldi methods","author":"Lehoucq","year":"1998","journal-title":"Society for Industrial and Applied Mathematics"},{"key":"2023051114184922700_bib37","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.2514\/3.25246","article-title":"Convergence of the classical Rayleigh\u2013Ritz method and the finite element method","volume":"28","author":"Meirovitch","year":"1990","journal-title":"AIAA Journal"},{"key":"2023051114184922700_bib38","first-page":"1","article-title":"Accelerating large topology optimization: State-of-the-art and challenges","author":"Mukherjee","year":"2021","journal-title":"Archives of Computational Methods in Engineering"},{"key":"2023051114184922700_bib39","doi-asserted-by":"crossref","first-page":"114096","DOI":"10.1016\/j.cma.2021.114096","article-title":"Parametric deep energy approach for elasticity accounting for strain gradient effects","volume":"386","author":"Nguyen-Thanh","year":"2021","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2023051114184922700_bib40","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1016\/j.proeng.2012.09.551","article-title":"Modal assurance criterion","volume":"48","author":"Pastor","year":"2012","journal-title":"Procedia Engineering"},{"volume-title":"An introduction to the finite element method","year":"2004","author":"Reddy","key":"2023051114184922700_bib41"},{"volume-title":"SPARSKIT: A basic tool kit for sparse matrix computations","year":"1990","author":"Saad","key":"2023051114184922700_bib42"},{"key":"2023051114184922700_bib43","doi-asserted-by":"crossref","first-page":"112790","DOI":"10.1016\/j.cma.2019.112790","article-title":"An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications","volume":"362","author":"Samaniego","year":"2020","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"2023051114184922700_bib44","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/S0167-739X(00)00076-5","article-title":"PARDISO: A high-performance serial and parallel sparse linear solver in semiconductor device simulation","volume":"18","author":"Schenk","year":"2001","journal-title":"Future Generation Computer Systems"},{"key":"2023051114184922700_bib45","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1093\/jcde\/qwaa041","article-title":"Nonlocal vibration of carbon\/boron-nitride nano-hetero-structure in thermal and magnetic fields by means of nonlinear finite element method","volume":"7","author":"Sedighi","year":"2020","journal-title":"Journal of Computational Design and Engineering"},{"volume-title":"Introduction to linear algebra","year":"2009","author":"Strang","key":"2023051114184922700_bib46"},{"article-title":"Matrix perturbation theory in structural dynamics","year":"1993","author":"Su-huan","key":"2023051114184922700_bib47"},{"key":"2023051114184922700_bib48","doi-asserted-by":"crossref","first-page":"104553","DOI":"10.1016\/j.euromechsol.2022.104553","article-title":"Combined approximation based numerical vibration correlation technique for axially loaded cylindrical shells","volume":"93","author":"Tian","year":"2022","journal-title":"European Journal of Mechanics-A\/Solids"},{"key":"2023051114184922700_bib49","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1093\/jcde\/qwab043","article-title":"Computational analysis of the nonlinear vibrational behavior of perforated plates with initial imperfection using NURBS-based isogeometric approach","volume":"8","author":"VeisiAra","year":"2021","journal-title":"Journal of Computational Design and Engineering"},{"key":"2023051114184922700_bib50","doi-asserted-by":"crossref","first-page":"2191","DOI":"10.1016\/j.ymssp.2011.01.018","article-title":"Comparison of FRF measurements and mode shapes determined using optically image based, laser, and accelerometer measurements","volume":"25","author":"Warren","year":"2011","journal-title":"Mechanical Systems and Signal Processing"},{"key":"2023051114184922700_bib51","first-page":"27","article-title":"Applications of Pade approximation to mechanics","volume":"18","author":"Wu","year":"1996","journal-title":"Mechanics & Practice"},{"key":"2023051114184922700_bib52","doi-asserted-by":"crossref","first-page":"2203","DOI":"10.1002\/nme.1546","article-title":"A method for modal reanalysis of topological modifications of structures","volume":"65","author":"Yang","year":"2006","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"2023051114184922700_bib53","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.compstruc.2014.12.006","article-title":"Vibration reanalysis based on block combined approximations with shifting","volume":"149","author":"Zheng","year":"2015","journal-title":"Computers & Structures"},{"key":"2023051114184922700_bib54","doi-asserted-by":"crossref","first-page":"104225","DOI":"10.1016\/j.euromechsol.2021.104225","article-title":"Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning","volume":"87","author":"Zhuang","year":"2021","journal-title":"European Journal of Mechanics-A\/Solids"},{"key":"2023051114184922700_bib55","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1007\/s00158-015-1368-z","article-title":"Sensitivity reanalysis of static displacement using Taylor series expansion and combined approximate method","volume":"53","author":"Zuo","year":"2016","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"2023051114184922700_bib56","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1007\/s00158-016-1586-z","article-title":"Sensitivity reanalysis of vibration problem using combined approximations method","volume":"55","author":"Zuo","year":"2017","journal-title":"Structural and Multidisciplinary Optimization"}],"container-title":["Journal of Computational Design and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jcde\/advance-article-pdf\/doi\/10.1093\/jcde\/qwad030\/49809380\/qwad030.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/10\/3\/959\/50277746\/qwad030.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/10\/3\/959\/50277746\/qwad030.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T14:21:29Z","timestamp":1683814889000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/10\/3\/959\/7112094"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,10]]},"references-count":56,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,4,29]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwad030","relation":{},"ISSN":["2288-5048"],"issn-type":[{"type":"electronic","value":"2288-5048"}],"subject":[],"published-other":{"date-parts":[[2023,6]]},"published":{"date-parts":[[2023,4,10]]}}}