Realspace mesh techniques in densityfunctional theory
Abstract
This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finitedifference or finiteelement formulations. The relationship of realspace approaches to linearscaling electrostatics and electronic structure methods is first discussed. Then the basic aspects of realspace representations are presented. Multigrid techniques for solving the discretized problems are covered; these numerical schemes allow for highly efficient solution of the gridbased equations. Applications to problems in electrostatics are discussed, in particular, numerical solutions of Poisson and PoissonBoltzmann equations. Next, methods for solving selfconsistent eigenvalue problems in real space are presented; these techniques have been extensively applied to solutions of the HartreeFock and KohnSham equations of electronic structure, and to eigenvalue problems arising in semiconductor and polymer physics. Finally, realspace methods have found recent application in computations of optical response and excited states in timedependent densityfunctional theory, and these computational developments are summarized. Multiscale solvers are competitive with the most efficient available planewave techniques in terms of the number of selfconsistency steps required to reach the ground state, and they require less work in each selfconsistency update on a uniform grid. Besides excellent efficiencies, the decided advantages of the realspace multiscale approach are (1) the nearlocality of each function update, (2) the ability to handle global eigenfunction constraints and potential updates on coarse levels, and (3) the ability to incorporate adaptive local mesh refinements without loss of optimal multigrid efficiencies.
 Publication:

Reviews of Modern Physics
 Pub Date:
 October 2000
 DOI:
 10.1103/RevModPhys.72.1041
 arXiv:
 arXiv:condmat/0006239
 Bibcode:
 2000RvMP...72.1041B
 Keywords:

 41.20.Cv;
 61.41.+e;
 71.15.Fv;
 71.15.Mb;
 71.10.Li;
 02.30.Hq;
 01.30.Rr;
 02.60.Lj;
 Electrostatics;
 Poisson and Laplace equations boundaryvalue problems;
 Polymers elastomers and plastics;
 Density functional theory local density approximation gradient and other corrections;
 Excited states and pairing interactions in model systems;
 Ordinary differential equations;
 Surveys and tutorial papers;
 resource letters;
 Ordinary and partial differential equations;
 boundary value problems;
 Condensed Matter  Materials Science
 EPrint:
 70 pages, 11 figures. To be published in Reviews of Modern Physics