# Analysis Seminar

#### 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.

**Synopsis:**

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.