Presentation of Degree project C: Linear-scaling recursive expansion of the Fermi-Dirac operator

  • Date:
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Linnea Andersson
  • Contact person: Denis Gaidashev
  • Seminarium

Abstract:  

To assess the electronic structure of a large system of molecules calls for a method to efficiently evaluate the Fermi-Dirac matrix function. A recursive expansion resulting in an implicit expression which can be solved as a linear system of equations is explored and is demonstrated for the first time to achieve linear time complexity with the use of sparse matrix algebra. Two methods, linear conjugate gradient and Newton-Schulz it-eration, are investigated with regards to their performance in solving the linear system at every step in the recursive expansion at finite electronic temperature. At zero temperature the recursive expansion method is com-pared to the second-order spectral projection method, which is known to be one of the most efficient methods.