Exact symmetry conservation and automatic mesh refinement in discrete initial boundary value problems
arXiv:2404.18676 · doi:10.1016/j.jcp.2024.113686
Abstract
We present a novel solution procedure for initial boundary value problems. The procedure is based on an action principle, in which coordinate maps are included as dynamical degrees of freedom. This reparametrization invariant action is formulated in an abstract parameter space and an energy density scale associated with the space-time coordinates separates the dynamics of the coordinate maps and of the propagating fields. Treating coordinates as dependent, i.e. dynamical quantities, offers the opportunity to discretize the action while retaining all space-time symmetries and also provides the basis for automatic adaptive mesh refinement (AMR). The presence of unbroken space-time symmetries after discretization also ensures that the associated continuum Noether charges remain exactly conserved. The presence of coordinate maps in addition provides new freedom in the choice of boundary conditions. An explicit numerical example for wave propagation in dimensions is provided, using recently developed regularized summation-by-parts finite difference operators.
50 pages, 12 figures
References in corpus (11)
- Keldysh Field Theory for Driven Open Quantum Systems
- Review of Summation-by-parts schemes for initial-boundary-value problems
- A catalog of 174 binary black-hole simulations for gravitational-wave astronomy
- The classical mechanics of non-conservative systems
- Hydrodynamic Approaches in Relativistic Heavy Ion Reactions
- D-brane Wess--Zumino actions, T-duality and the cosmological constant
- Quantum versus classical statistical dynamics of an ultracold Bose gas
- Summation-by-parts operators for general function spaces
- Nonlinear Boundary Conditions for Initial Boundary Value Problems with Applications in Computational Fluid Dynamics
- A new variational discretization technique for initial value problems bypassing governing equations
- Summation-by-parts operators for general function spaces: The second derivative