% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@ARTICLE{Aviat:834629,
      author       = {Aviat, Félix and Levitt, Antoine and Stamm, Benjamin and
                      Maday, Yvon and Ren, Pengyu and Ponder, Jay W. and
                      Lagardère, Louis and Piquemal, Jean-Philip},
      title        = {{T}runcated {C}onjugate {G}radient: {A}n {O}ptimal
                      {S}trategy for the {A}nalytical {E}valuation of the
                      {M}any-{B}ody {P}olarization {E}nergy and {F}orces in
                      {M}olecular {S}imulations},
      journal      = {Journal of chemical theory and computation},
      volume       = {13},
      number       = {1},
      issn         = {1549-9626},
      address      = {Washington, DC},
      reportid     = {FZJ-2017-04537},
      pages        = {180 - 190},
      year         = {2017},
      abstract     = {We introduce a new class of methods, denoted as Truncated
                      Conjugate Gradient(TCG), to solve the many-body polarization
                      energy and its associated forces in molecular simulations
                      (i.e. molecular dynamics (MD) and Monte Carlo). The method
                      consists in a fixed number of Conjugate Gradient (CG)
                      iterations. TCG approaches provide a scalable solution to
                      the polarization problem at a user-chosen cost and a
                      corresponding optimal accuracy. The optimality of the
                      CG-method guarantees that the number of the required
                      matrix-vector products are reduced to a minimum compared to
                      other iterative methods. This family of methods is
                      non-empirical, fully adaptive, and provides analytical
                      gradients, avoiding therefore any energy drift in MD as
                      compared to popular iterative solvers. Besides speed, one
                      great advantage of this class of approximate methods is that
                      their accuracy is systematically improvable. Indeed, as the
                      CG-method is a Krylov subspace method, the associated error
                      is monotonically reduced at each iteration. On top of that,
                      two improvements can be proposed at virtually no cost: (i)
                      the use of preconditioners can be employed, which leads to
                      the Truncated Preconditioned Conjugate Gradient (TPCG); (ii)
                      since the residual of the final step of the CG-method is
                      available, one additional Picard fixed point iteration
                      (“peek”), equivalent to one step of Jacobi Over
                      Relaxation (JOR) with relaxation parameter ω, can be made
                      at almost no cost. This method is denoted by TCG-n(ω).
                      Black-box adaptive methods to find good choices of ω are
                      provided and discussed. Results show that TPCG-3(ω) is
                      converged to high accuracy (a few kcal/mol) for various
                      types of systems including proteins and highly charged
                      systems at the fixed cost of four matrix-vector products:
                      three CG iterations plus the initial CG descent direction.
                      Alternatively, T(P)CG-2(ω) provides robust results at a
                      reduced cost (three matrix-vector products) and offers new
                      perspectives for long polarizable MD as a production
                      algorithm. The T(P)CG-1(ω) level provides less accurate
                      solutions for inhomogeneous systems, but its applicability
                      to well-conditioned problems such as water is remarkable,
                      with only two matrix-vector product evaluations},
      cin          = {IAS-5 / INM-9},
      ddc          = {540},
      cid          = {I:(DE-Juel1)IAS-5-20120330 / I:(DE-Juel1)INM-9-20140121},
      pnm          = {574 - Theory, modelling and simulation (POF3-574)},
      pid          = {G:(DE-HGF)POF3-574},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000391898200017},
      pubmed       = {pmid:28068773},
      doi          = {10.1021/acs.jctc.6b00981},
      url          = {https://juser.fz-juelich.de/record/834629},
}