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dc.contributor.authorHashemian, A. 
dc.contributor.authorPardo, D. 
dc.contributor.authorCalo, V.M.
dc.description.abstractWe use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku = λMu). rIGA conserves the desirable properties of maximum-continuity isogeometric analysis (IGA) while it reduces the solution cost by adding zero-continuity basis functions, which decrease the matrix connectivity. As a result, rIGA enriches the approximation space and reduces the interconnection between degrees of freedom. We compare computational costs of rIGA versus those of IGA when employing a Lanczos eigensolver with a shift-and-invert spectral transformation. When all eigenpairs within a given interval [λ_s,λ_e] are of interest, we select several shifts σ_k ∈ [λ_s,λ_e] using a spectrum slicing technique. For each shift σ_k, the factorization cost of the spectral transformation matrix K − σ_k M controls the total computational cost of the eigensolution. Several multiplications of the operator matrix (K − σ_k M)^−1 M by vectors follow this factorization. Let p be the polynomial degree of the basis functions and assume that IGA has maximum continuity of p−1. When using rIGA, we introduce C^0 separators at certain element interfaces to minimize the factorization cost. For this setup, our theoretical estimates predict computational savings to compute a fixed number of eigenpairs of up to O(p^2) in the asymptotic regime, that is, large problem sizes. Yet, our numerical tests show that for moderate-size eigenproblems, the total observed computational cost reduction is O(p). In addition, rIGA improves the accuracy of every eigenpair of the first N_0 eigenvalues and eigenfunctions, where N_0 is the total number of modes of the original maximum-continuity IGA discretization.en_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectRefined isogeometric analysisen_US
dc.subjectGeneralized Hermitian eigenproblemen_US
dc.subjectLanczos eigensolveren_US
dc.subjectSpectral transformationen_US
dc.subjectShift-and-invert approachen_US
dc.titleRefined isogeometric analysis for generalized Hermitian eigenproblemsen_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108111RB-I00en_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021en_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEKen_US
dc.journal.titleComputer Methods in Applied Mechanics and Engineeringen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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