Memory access optimization for computations on unstructured meshes

Many real-life applications of processor-arrays suffer from memory bandwidth limitations. In many cases an unstructured mesh is given (computation on sensor data, simulations of physical systems — PDEs), where the vertices represent computations with dependencies represented by the edges. Utilization of processing elements (PEs) during these computations is mainly depends on the node indexing of the mesh. If the adjacent nodes are stored close to each other in main memory, the reloading of node data can be significantly decreased. In case of FPGA the memory accesses can be fully determined by the designer. The mesh and an ordering of its nodes, define the graph bandwidth, which determines the minimum size of on-chip memory to avoid reloading of the nodes from the off-chip memory. If the required on-chip memory size is higher than the available resources, the mesh must be divided into parts. In this paper a novel geometry-based method is presented, which constructs reordered parts from a given unstructured mesh, where each part meets some predefined constraints on graph bandwidth.