Performance Comparison of Two PETSc-based Eigensolvers for Quadratic PDE Problems
沈廉智, Lien-Chih Shen · 2012
In this thesis, we systematically investigate the numerical performance of two eigenpackages for solving quadratic eigenvalue problems (QEPs), namely Scalable Library for Eigenvalue Problem Computations (SLEPc) and Parallel Jacobi-Davidson Package (PJDPack) are both in common built-on-top of Portable, Extensible, Toolkits for Scientific computation (PETSc) [3]. The major differeces between these two eigenpackages is that SLEPc adopts the linearization approach and provides several linear eigensolvers to solve the resulting companion GEPs. On the other hand, the PJD algorithm is the only kernel solver of PJDPack that targets directly the QEP. To draw the concrete conclusions, we generate a large number of test cases using a Matlab-based toolbox, a collection of nonlinear eigenvalue problem (NLEVP) with a diversity of matrix properties and conduct intense numerical experiments to evaluate the performance in terms of robustness, accuracy and efficiency.