FEAST Solver Package

Current status:
  • Solving Ax=ex or Ax=eBx, A is real symmetric or complex Hermitian, B is symmetric or Hermitian positive definite.
  • Two libraries: SMP version (one node), and MPI version (multi-nodes).
  • Real/Complex and Single/Double precisions,
  • All FEAST interfaces compatible with Fortran (77, 90) and C. All the FEAST interfaces require (any) BLAS and LAPACK packages.
  • Source code and pre-compiled libraries provided for common architectures (x64).
  • Reverse communication interfaces (RCI): Maximum flexibility for application-specific.
  • Predefined driver interfaces for dense, banded, and sparse formats: Less flexibility but easy to use ("plug and play")
  • Large number of examples provided and documentation included,
  • FEAST utility drivers for sparse systems included: users can provide directly their sparse systems for quick testing, timing, etc. .
Current development:
  • FEAST for non-symmetric eigenvalue problem (including non-Hermitian and complex symmetric).
  • NLFEAST, new scheme for solving the non-linear eigenvector problems (e.g. for electronic structure calculations).

FEAST Algorithm

Some of the important capabilities of the FEAST algorithm described in [1] can be outlined as follows:
  • Fast convergence - FEAST converges in ~2-3 iterations with very high accuracy
  • Naturally captures all multiplicities
  • No-(explicit) orthogonalization procedure
  • Reusable subspace - can benefit from suitable initial guess for solving series of eigenvalue problems that are close one another
  • Ideally suited for large sparse systems- allows the use of iterative methods.
  • the scalability of the FEAST algorithm is first and foremost dependent on the scalability of the inner linear system solver;
  • Three levels of parallelism: (i) many search interval can be run independently (no overlap), (ii) the independent inner linear systems can be solved simultaneously on each nodes (using FEAST-MPI), (iii) within a given node, the inner system solver can be solved in parallel (currently with shared memory capability).
Current research:
  • Non-linear problems