3D nested eigenanalysis on finite element grids

The computation of several of the leftmost eigenpairs of generalized symmetric eigenproblems in 3-D finite element (FE) discretizations is addressed using the nested iteration deflation accelerated conjugate gradient (NI-DACG) method previously studied and improved by the authors in a 2-D framework. Numerical results from the flow (diffusion type) equation integrated over tetrahedral FE shows speed-ups relative to DACG ranging between 2 up to more than 10 depending on the aspect ratio of the elements used. NI-DACG also compares favourably with the performance of IRAM, i.e. the implicit restarted Arnoldi method, implemented in the eigenvalue package ARPACK.