A plurality of processing elements (PEs) include memory local to at least one of the processing elements in a data packet-switched network interconnecting the processing elements and the memory to enable any of the PEs to access the memory. The network consists of nodes arranged linearly or in a grid to connect the PEs and their local memories to a common controller. The processor performs memory accesses on data stored in the memory in response to control signals sent by the controller to the memory. The local memories share the same memory map or space. The packet-switched network supports multiple concurrent transfers between PEs and memory. Memory accesses include block and/or broadcast read and write operations, in which data can be replicated within the nodes and, according to the operation, written into the shared memory or into the local PE memory.