Refined isogeometric analysis of quadratic eigenvalue problems

Certain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve eigenproblems. rIGA discretization, while conserving desirable properties maximum-continuity (IGA), reduces interconnection between degrees freedom by adding low-continuity basis functions. This connectivity reduction in rIGA’s algebraic system results faster matrix LU factorizations when using multifrontal direct solvers. compare computational costs versus those IGA employing Krylov eigensolvers eigenproblems arising 2D vector-valued multifield problems. For large problem sizes, eigencomputation cost is governed factorization, followed several matrix–vector and vector–vector multiplications, which correspond projections. minimize introducing C0 C1 separators at specific element interfaces for our generalizations curl-conforming Nédélec divergence-conforming Raviart–Thomas finite elements. Let p be polynomial degree functions; factorization up O((p?1)2) times compared asymptotic regime. Thus, theoretically improves total sufficiently sizes. Yet, practical cases moderate-size eigenproblems, improvement rate deteriorates as number computed eigenvalues increases because multiple operations. Our numerical tests show accelerates eigensystems O(p?1) moderately sized we seek compute a reasonable eigenvalues.