Al-Athamneh B. Mathematical modeling of geometric objects in parallel computer systems

The thesis is devoted to problems of mathematical modeling of solids in parallel computer systems. There have been described new parallel approaches for meshing, visualization, and formalization of the solids’ representation in computer-aided engineering. The suitable for parallel processing domain-specific language RFL has been developed. The language uses implicit functions and the theory of R-functions to represent solids. Algorithms for parallel processing of an abstract syntax tree have been developed. In these algorithms, the longest independent branches of the abstract syntax tree are processed in parallel. New software QVoxel has been implemented. This software allows to construct mathematical models of solids and to visualize these models using voxels in shared memory parallel architectures.