2,723 research outputs found
Adaptive Mesh Refinement Computation of Solidification Microstructures using Dynamic Data Structures
We study the evolution of solidification microstructures using a phase-field
model computed on an adaptive, finite element grid. We discuss the details of
our algorithm and show that it greatly reduces the computational cost of
solving the phase-field model at low undercooling. In particular we show that
the computational complexity of solving any phase-boundary problem scales with
the interface arclength when using an adapting mesh. Moreover, the use of
dynamic data structures allows us to simulate system sizes corresponding to
experimental conditions, which would otherwise require lattices greater that
elements. We examine the convergence properties of our
algorithm. We also present two dimensional, time-dependent calculations of
dendritic evolution, with and without surface tension anisotropy. We benchmark
our results for dendritic growth with microscopic solvability theory, finding
them to be in good agreement with theory for high undercoolings. At low
undercooling, however, we obtain higher values of velocity than solvability
theory at low undercooling, where transients dominate, in accord with a
heuristic criterion which we derive
Efficient maintenance and update of nonbonded lists in macromolecular simulations
Molecular mechanics and dynamics simulations use distance based cutoff approximations for faster computation of pairwise van der Waals and electrostatic energy terms. These approximations traditionally use a precalculated and periodically updated list of interacting atom pairs, known as the “nonbonded neighborhood lists” or nblists, in order to reduce the overhead of finding atom pairs that are within distance cutoff. The size of nblists grows linearly with the number of atoms in the system and superlinearly with the distance cutoff, and as a result, they require significant amount of memory for large molecular systems. The high space usage leads to poor cache performance, which slows computation for large distance cutoffs. Also, the high cost of updates means that one cannot afford to keep the data structure always synchronized with the configuration of the molecules when efficiency is at stake. We propose a dynamic octree data structure for implicit maintenance of nblists using space linear in the number of atoms but independent of the distance cutoff. The list can be updated very efficiently as the coordinates of atoms change during the simulation. Unlike explicit nblists, a single octree works for all distance cutoffs. In addition, octree is a cache-friendly data structure, and hence, it is less prone to cache miss slowdowns on modern memory hierarchies than nblists. Octrees use almost 2 orders of magnitude less memory, which is crucial for simulation of large systems, and while they are comparable in performance to nblists when the distance cutoff is small, they outperform nblists for larger systems and large cutoffs. Our tests show that octree implementation is approximately 1.5 times faster in practical use case scenarios as compared to nblists
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