TY - JOUR

T1 - Electronic structure calculations for plane-wave codes without diagonalization

AU - Jay, Laurent O.

AU - Kim, Hanchul

AU - Saad, Yousef

AU - Chelikowsky, James R.

N1 - Funding Information:
We would like to acknowledge support from the National Science Foundation and from the Minnesota Supercomputing Institute.

PY - 1999/4

Y1 - 1999/4

N2 - We present an algorithm to reduce the computational complexity for plane-wave codes used in electronic structure calculations. The proposed algorithm avoids the diagonalization of large Hermitian matrices arising in such problems. The computational time for the diagonalization procedure typically grows as the cube of the number of atoms, or the number of eigenvalues required. To reduce this computational demand, we approximate directly the occupation operator corresponding to the eigenvectors associated with the occupied states in a certain subspace without actually computing these eigenvectors. A smoothed Chebyshev-Jackson expansion of the Heaviside function of the Hamiltonian matrix is used to represent the occupation operator. This procedure requires only matrix-vector products and is intrinsically parallelizable.

AB - We present an algorithm to reduce the computational complexity for plane-wave codes used in electronic structure calculations. The proposed algorithm avoids the diagonalization of large Hermitian matrices arising in such problems. The computational time for the diagonalization procedure typically grows as the cube of the number of atoms, or the number of eigenvalues required. To reduce this computational demand, we approximate directly the occupation operator corresponding to the eigenvectors associated with the occupied states in a certain subspace without actually computing these eigenvectors. A smoothed Chebyshev-Jackson expansion of the Heaviside function of the Hamiltonian matrix is used to represent the occupation operator. This procedure requires only matrix-vector products and is intrinsically parallelizable.

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U2 - 10.1016/S0010-4655(98)00192-1

DO - 10.1016/S0010-4655(98)00192-1

M3 - Article

AN - SCOPUS:0033115748

SN - 0010-4655

VL - 118

SP - 21

EP - 30

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 1

ER -