An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory

The improvement of overall uniformity and smoothness of spherical icosahedral grids, the basic framework of atmospheric models, is a key to reducing simulation errors. However, most of the existing grid optimization methods have optimized grid from different aspects and not improved overall uniformity and smoothness of grid at the same time, directly affecting the accuracy and stability of numerical simulation. Although a well-defined grid with more than 12 points cannot be constructed on a sphere, the area uniformity and the interval uniformity of the spherical grid can be traded off to enhance extremely the overall grid uniformity and smoothness. To solve this problem, an overall uniformity and smoothness optimization method of the spherical icosahedral grid is proposed based on the optimal transformation theory. The spherical cell decomposition method has been introduced to iteratively update the grid to minimize the spherical transportation cost, achieving an overall optimization of the spherical icosahedral grid. Experiments on the four optimized grids (the spring dynamics optimized grid, the Heikes and Randall optimized grid, the spherical centroidal Voronoi tessellations optimized grid and XU optimized grid) demonstrate that the grid area uniformity of our method has been raised by 22.60% of SPRG grid, −1.30% of HR grid, 38.30% of SCVT grid and 38.20% of XU grid, and the grid interval uniformity has been improved by 2.50% of SPRG grid, 2.80% of HR grid, 11.10% of SCVT grid and 11.00% of XU grid. Although the grid uniformity of the proposed method is similar with the HR grid, the smoothness of grid deformation has been enhanced by 79.32% of grid area and 24.07% of grid length. To some extent, the proposed method may be viewed as a novel optimization approach of the spherical icosahedral grid which can improve grid overall uniformity and smoothness of grid deformation.

A hybrid SP-QPSO algorithm with parameter free adaptive penalty method for constrained global optimization problems

Most real-life optimization problems involve constraints which require a specialized mechanism to deal with them. The presence of constraints imposes additional challenges to the researchers motivated towards the development of new algorithm with efficient constraint handling mechanism. This paper attempts the suitability of newly developed hybrid algorithm, Shuffled Complex Evolution with Quantum Particle Swarm Optimization abbreviated as SP-QPSO, extended specifically designed for solving constrained optimization problems. The incorporation of adaptive penalty method guides the solutions to the feasible regions of the search space by computing the violation of each one. Further, the algorithm’s performance is improved by Centroidal Voronoi Tessellations method of point initialization promise to visit the entire search space. The effectiveness and the performance of SP-QPSO are examined by solving a broad set of ten benchmark functions and four engineering case study problems taken from the literature. The experimental results show that the hybrid version of SP-QPSO algorithm is not only overcome the shortcomings of the original algorithms but also outperformed most state-of-the-art algorithms, in terms of searching efficiency and computational time.

Impact of Local Grid Refinements of Spherical Centroidal Voronoi Tessellations for Global Atmospheric Models

In order to study the local refinement issue of the horizontal resolution for a global model with Spherical Centroidal Voronoi Tessellations (SCVTs), the SCVTs are set to 10242 cells and 40962 cells respectively using the density function. The ratio between the grid resolutions in the high and low resolution regions (hereafter RHL) is set to 1:2, 1:3 and 1:4 for 10242 cells and 40962 cells, and the width of the grid transition zone (for simplicity, WTZ) is set to 18° and 9° to investigate their impacts on the model simulation. The ideal test cases, i.e. the cosine bell and global steady-state nonlinear zonal geostrophic flow, are carried out with the above settings. Simulation results showthat the larger the RHL is, the larger the resulting error is. It is obvious that the 1:4 ratio gives rise to much larger errors than the 1:2 or 1:3 ratio; the errors resulting from the WTZ is much smaller than that from the RHL. No significant wave distortion or reflected waves are found when the fluctuation passes through the refinement region, and the error is significantly small in the refinement region. Therefore,when designing a local refinement scheme in the global model with SCVT, the RHL should be less than 1:4, i.e., the error is acceptable when the RHL is 1:2 or 1:3.