A comparison of the performance of depth-integrated ice-dynamics solvers

In the last decade, the number of ice-sheet models has increased substantially, in line with the growth of the glaciological community. These models use solvers based on different approximations of ice dynamics. In particular, several depth-integrated dynamics approximations have emerged as fast solvers capable of resolving the relevant physics of ice sheets at the continen- tal scale. However, the numerical stability of these schemes has not been studied systematically to evaluate their effectiveness in practice. Here we focus on three such solvers, the so-called Hybrid, L1L2-SIA and DIVA solvers, as well as the well-known SIA and SSA solvers as boundary cases. We investigate the numerical stability of these solvers as a function of grid resolution and the state of the ice sheet. Under simplified conditions with constant viscosity, the maximum stable timestep of the Hybrid solver, like the SIA solver, has a quadratic dependence on grid resolution. In contrast, the DIVA solver has a maximum timestep that is independent of resolution, like the SSA solver. Analysis indicates that the L1L2-SIA solver should behave similarly, but in practice, the complexity of its implementation can make it difficult to maintain stability. In realistic simulations of the Greenland ice sheet with a non-linear rheology, the DIVA and SSA solvers maintain superior numerical stability, while the SIA, Hybrid and L1L2-SIA solvers show markedly poorer performance. At a grid resolution of ∆x = 4 km, the DIVA solver runs approximately 15 times faster than the Hybrid and L1L2-SIA solvers. Our analysis shows that as resolution increases, the ice-dynamics solver can act as a bottleneck to model performance. The DIVA solver emerges as a clear outlier in terms of both model performance and its representation of the ice-flow physics itself.

Garden optimization problems for benchmarking quantum annealers

We benchmark the 5000+ qubit system coupled with the Hybrid Solver Service 2 released by D-Wave Systems Inc. in September 2020 by using a new class of optimization problems called garden optimization problems known in companion planting. These problems are scalable to an arbitrarily large number of variables and intuitively find application in real-world scenarios. We derive their QUBO formulation and illustrate their relation to the quadratic assignment problem. We demonstrate that the system and the new hybrid solver can solve larger problems in less time than their predecessors. However, we also show that the solvers based on the 2000+ qubit system sometimes produce more favourable results if they can solve the problems.

LES/FMDF of turbulent reacting jet in cross-flow

Purpose This study aims to numerically investigate the flow features and mixing/combustion efficiencies in a turbulent reacting jet in cross-flow by a hybrid Eulerian-Lagrangian methodology. Design/methodology/approach A high-order hybrid solver is employed where, the velocity field is obtained by solving the Eulerian filtered compressible transport equations while the species are simulated by using the filtered mass density function (FMDF) method. Findings The main features of a reacting JICF flame are reproduced by the large-eddy simulation (LES)/FMDF method. The computed mean and root-mean-square values of velocity and mean temperature field are in good agreement with experimental data. Reacting JICF’s with different momentum ratios are considered. The jet penetrates deeper for higher momentum ratios. Mixing and combustion efficiency are improved by increasing the momentum ratio. Originality/value The authors investigate the flow and combustion characteristics in subsonic reacting JICFs for which very limited studies are reported in the literature.

A Hybrid GFDM–SBM Solver for Acoustic Radiation and Propagation of Thin Plate Structure Under Shallow Sea Environment

This paper makes the first attempt to propose a novel hybrid collocation solver based on the generalized finite difference method (GFDM) and singular boundary method (SBM) to analyze underwater acoustic radiation and propagation around the thin plate structures excited by simple harmonic force under shallow sea environment. In the proposed hybrid solver, the meshless GFDM is employed to obtain the fluid–structure coupling vibration response of thin plate structure, and then the SBM with Pekeris waveguide Green function is used to calculate the external acoustic field of thin plate structure. The simplified Price–Wu boundary condition is adopted on the surface of plate structure to connect the computational domains between the GFDM and SBM. Three benchmark examples are carried out to demonstrate the accuracy and efficiency of the proposed hybrid GFDM–SBM solver in comparison with the COMSOL simulation for computing underwater acoustic wave fields around the thin plate structures under shallow sea environment.

A hybrid solver for protein multiple sequence alignment problem

In this work, a novel hybrid model called PSOSA for solving multiple sequence alignment (MSA) problem is proposed. The developed approach is a combination between particle swarm optimization (PSO) algorithm and simulated annealing (SA) technique. In our PSOSA approach, PSO is exploited in global search, but it is easily trapped into local optimum and may lead to premature convergence. SA is incorporated as local improvement approach to overcome local optimum problem and intensify the search in local regions to improve solution quality. Numerical results on BAliBASE benchmark have shown the effectiveness of the proposed method and its ability to achieve good quality solutions when compared with those given by other existing methods.