연세대학교 계산과학공학

Speaker: Prof. Alexander Karl Rothkopf  (University of Stavanger, Norway)

Date: 4pm, Wednesday, Nov 8

Place: ASTC 516 (첨단관 516호)

Title: A discrete variational approach to initial value problems preserving spacetime symmetries

Abstract:

The conventional discretization of space-time entails a breaking of continuum symmetries and spoils the conservation of the associated Noether charges with ramifications for long time stability and accuracy of simulations.

In this work [1] we take first steps towards discretizing classical actions in coordinate space, while retaining continuum symmetries. Our proof-of-principle for a point particle in (1+1)d adopts the action formalism from general relativity, where both space x(\gamma) and time t(\gamma) are dependent variables of a worldline parameter \gamma. Discretizing in \gamma, leaves the values of both x and t continuous and thus the invariance under infinitesimal translations in (1+1)d remains intact. Building upon our previous work on solving initial values on the level of the system action [2] we show that the relativistic approach allows to compute numerically the classical trajectory of a particle under an arbitrary bounded potential, while conserving the relativistic Noether charge for time translation symmetry exactly and at its continuum value in the interior of the simulated domain.

[1] A. Rothkopf, J. Nordström, (arXiv:2307.04490)

[2] A. Rothkopf, J. Nordström, J.Comput.Phys. 477 (2023) 111942 (arXiv:2205.14028)