A parallel Eulerian-Lagrangian localized adjoint method

We describe an approach to parallelize Eulerian-Lagrangian localized adjoint methods such that no errors are introduced compared to the sequential case. This parallelization approach fully captures the hyperbolic features of the underlying problem. It uses an overlapping domain decomposition technique, and does not involve the introduction of artificial boundary conditions between subdomains. Implementation details on different parallel architectures are discussed.