Toward sharp error analysis of extended Lagrangian molecular dynamics for polarizable force field simulation
Speaker: Michael LINDSEY, CIMS
Location: Warren Weaver Hall 1302
Date: Thursday, September 26, 2019, 11 a.m.
The inertial extended Langrangian self-consistent field iteration-free
(iEL/0-SCF) method was recently introduced as an efficient method for
molecular dynamics simulations of polarizable force field models. These
simulations involve ODEs where the dynamics depend on the solution of a
linear system Ax=b, where A=A(r) and b=b(r) themselves depend on the
current state r. Mathematically, the iEL/0-SCF method introduces a
singularly perturbed Hamiltonian system to solve these ODEs
approximately without performing explicit matrix inversion at each time
step. We prove the convergence of the iEL/0-SCF method provided accurate
initial condition and study the asymptotics of the error in the
parameter \epsilon which controls the perturbation. Sharp asymptotics
depend on the careful analysis of some oscillatory integrals.
Interestingly, it is possible to achieve O(\epsilon) error for the state
r, even though the error for the linear system solution x is only
O(\sqrt(\epsilon)) for certain initializations.