Smoothing the Boundaries between the Domains of the Surface Computational Mesh

Abstract

For the efficient use of supercomputer computing resources in solving problems of simulation, a high-quality decomposition of the computational meshes is of great importance. Modern computational problems work with huge input data, which makes it impossible to process them on one computational node in a reasonable time. In particular, to carry out calculations on large computational meshes, it is necessary to decompose them into separate domains. In this case, each of the domains is processed at its own computational node, and to maintain the integrity of the problem, computational nodes exchange between themselves computational data that cross the boundaries of the computational mesh domains. The quality of the computational mesh decomposition is characterized by such parameters as the uniformity of the distribution of cells over domains, the maximum length of the boundary between two domains, the total length of all boundaries between all pairs of domains, and many others. The most important indicator of the mesh decomposition quality is the uniformity of the distribution of cells across domains, since the speed of computation of the entire problem is characterized primarily by the speed of processing the largest domain. However, the maximum length of the boundary between pairs of domains is also of high importance, since the value of this parameter determines the speed of data exchanges between computational nodes. With a decrease in the time step in computational problems and an increase in the number of computational nodes (a high degree of parallelization), the proportion of interprocess communications increases significantly, and a decrease in the length of the boundary between domains significantly affects the total time of the computational problem. This article discusses an algorithm for smoothing the boundaries between domains, in the process of which the lengths of the boundaries are reduced, while not impairing the uniformity of the distribution of mesh cells between domains. Numerical experiments have shown that the application of the proposed algorithm leads to a reduction in the lengths of the boundaries between domains by about 10%, which leads to acceleration of data exchange in the course of calculations.

Keywords

• surface unstructured computational mesh
• decomposition
• domain
• supercomputer
• high performance computing
• computation scaling
• mpi exchanges