Accurate Determination of Thousands of Eigenvalues for Large-Scale Eigenvalue Problems

Systematic Determination of Eigenfields in Time and in Frequency Domain

“…Therefore, an LU factorization followed by the forward-backward substitution is performed using the SuperLU direct solver package with reordering the rows and columns of the given matrix such that sparse factors can be obtained. Once the LU decomposition itself is computed, this procedure is repeatedly applied to solve the multiple system of equations with different right-hand-side vectors [13]. Finally, the runtime options from the PETSc library include control over the choice of solvers without any additional coding cost.…”

“…Among the basic implementations of the (B-)Lanczos algorithm and its extension using spectral transformation [13], a novel combination with a filtering method for the standard and the generalized eigenvalue problem is proposed within this paper as a valuable tool to enable the computation of interior eigenpairs as well as to speed up the convergence. Moreover, the implementation facilitates a distributed-memory architecture with a message passing interface (MPI) parallelization strategy such that a higher mesh resolution can be considered and the computational costs will be still kept on an acceptable level.…”