Allen's Interval Algebra Makes the Difference

Allen's Interval Algebra constitutes a framework for reasoning about temporal information in a qualitative manner. In particular, it uses intervals, i.e., pairs of endpoints, on the timeline to represent entities corresponding to actions, events, or tasks, and binary relations such as precedes and overlaps to encode the possible configurations between those entities. Allen's calculus has found its way in many academic and industrial applications that involve, most commonly, planning and scheduling, temporal databases, and healthcare. In this paper, we present a novel encoding of Interval Algebra using answer-set programming (ASP) extended by difference constraints, i.e., the fragment abbreviated as ASP(DL), and demonstrate its performance via a preliminary experimental evaluation. Although our ASP encoding is presented in the case of Allen's calculus for the sake of clarity, we suggest that analogous encodings can be devised for other point-based calculi, too.Comment: Part of DECLARE 19 proceeding

Constrained Hyperbolic Divergence Cleaning for Smoothed Particle Magnetohydrodynamics

We present a constrained formulation of Dedner et al's hyperbolic/parabolic divergence cleaning scheme for enforcing the \nabla\dot B = 0 constraint in Smoothed Particle Magnetohydrodynamics (SPMHD) simulations. The constraint we impose is that energy removed must either be conserved or dissipated, such that the scheme is guaranteed to decrease the overall magnetic energy. This is shown to require use of conjugate numerical operators for evaluating \nabla\dot B and \nabla{\psi} in the SPMHD cleaning equations. The resulting scheme is shown to be stable at density jumps and free boundaries, in contrast to an earlier implementation by Price & Monaghan (2005). Optimal values of the damping parameter are found to be {\sigma} = 0.2-0.3 in 2D and {\sigma} = 0.8-1.2 in 3D. With these parameters, our constrained Hamiltonian formulation is found to provide an effective means of enforcing the divergence constraint in SPMHD, typically maintaining average values of h |\nabla\dot B| / |B| to 0.1-1%, up to an order of magnitude better than artificial resistivity without the associated dissipation in the physical field. Furthermore, when applied to realistic, 3D simulations we find an improvement of up to two orders of magnitude in momentum conservation with a corresponding improvement in numerical stability at essentially zero additional computational expense.Comment: 28 pages, 25 figures, accepted to J. Comput. Phys. Movies at http://www.youtube.com/playlist?list=PL215D649FD0BDA466 v2: fixed inverted figs 1,4,6, and several color bar

Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

In this paper we present a full-fledged scheme for the second order accurate, divergence-free evolution of vector fields on an adaptive mesh refinement (AMR) hierarchy. We focus here on adaptive mesh MHD. The scheme is based on making a significant advance in the divergence-free reconstruction of vector fields. In that sense, it complements the earlier work of Balsara and Spicer (1999) where we discussed the divergence-free time-update of vector fields which satisfy Stoke's law type evolution equations. Our advance in divergence-free reconstruction of vector fields is such that it reduces to the total variation diminishing (TVD) property for one-dimensional evolution and yet goes beyond it in multiple dimensions. Divergence-free restriction is also discussed. An electric field correction strategy is presented for use on AMR meshes. The electric field correction strategy helps preserve the divergence-free evolution of the magnetic field even when the time steps are sub-cycled on refined meshes. The above-mentioned innovations have been implemented in Balsara's RIEMANN framework for parallel, self-adaptive computational astrophysics which supports both non-relativistic and relativistic MHD. Several rigorous, three dimensional AMR-MHD test problems with strong discontinuities have been run with the RIEMANN framework showing that the strategy works very well.Comment: J.C.P., figures of reduced qualit