Parallel-GPU-accelerated adaptive mesh refinement for three-dimensional phase-field simulation of dendritic growth during solidification of binary alloy

In the phase-field simulation of dendrite growth during the solidification of an alloy, the computational cost becomes extremely high when the diffusion length is significantly larger than the curvature radius of a dendrite tip. In such cases, the adaptive mesh refinement (AMR) method is effective for improving the computational performance. In this study, we perform a three-dimensional dendrite growth phase-field simulation in which AMR is implemented via parallel computing using multiple graphics processing units (GPUs), which provide high parallel computation performance. In the parallel GPU computation, we apply dynamic load balancing to parallel computing to equalize the computational cost per GPU. The accuracy of an AMR refinement condition is confirmed through the single-GPU computations of columnar dendrite growth during the directional solidification of a binary alloy. Next, we evaluate the efficiency of dynamic load balancing by performing multiple-GPU parallel computations for three different directional solidification simulations using a moving frame algorithm. Finally, weak scaling tests are performed to confirm the parallel efficiency of the developed code.

Dynamic Averaging Load Balancing on Cycles

We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step $$t\ge 0$$ t ≥ 0 , a random edge is chosen, one unit of load is created, and placed at one of the endpoints. In the same step, assuming that loads are arbitrarily divisible, the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure. Peres et al. (Random Struct Algorithms 47(4):760–775, 2015) studied the variant of this process, where the unit of load is placed in the least loaded endpoint of the chosen edge, and the averaging is not performed. In the case of dynamic load balancing on the cycle of length n the only known upper bound on the expected gap is of order $$\mathcal {O}( n \log n )$$ O ( n log n ) , following from the majorization argument due to the same work. In this paper, we leverage the power of averaging and provide an improved upper bound of $$\mathcal {O} ( \sqrt{n} \log n )$$ O ( n log n ) . We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any $$k \le n/2$$ k ≤ n / 2 . We complement this with a “gap covering” argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We also show that our analysis can be extended to the specific instance of Harary graphs. On the other hand, we prove that the expected second moment of the gap is lower bounded by $$\Omega (n)$$ Ω ( n ) . Additionally, we provide experimental evidence that our upper bound on the gap is tight up to a logarithmic factor.

Hybrid Nearest-Neighbor Ant Colony Optimization Algorithm for Enhancing Load Balancing Task Management

Many computer problems that arise from real-world circumstances are NP-hard, while, in the worst case, these problems are generally assumed to be intractable. Existing distributed computing systems are commonly used for a range of large-scale complex problems, adding advantages to many areas of research. Dynamic load balancing is feasible in distributed computing systems since it is a significant key to maintaining stability of heterogeneous distributed computing systems (HDCS). The challenge of load balancing is an objective function of optimization with exponential complexity of solutions. The problem of dynamic load balancing raises with the scale of the HDCS and it is hard to tackle effectively. The solution to this unsolvable issue is being explored under a particular algorithm paradigm. A new codification strategy, namely hybrid nearest-neighbor ant colony optimization (ACO-NN), which, based on the metaheuristic ant colony optimization (ACO) and an approximate nearest-neighbor (NN) approaches, has been developed to establish a dynamic load balancing algorithm for distributed systems. Several experiments have been conducted to explore the efficiency of this stochastic iterative load balancing algorithm; it is tested with task and nodes accessibility and proved to be effective with diverse performance metrics.