The accurate subdivision of spatially organized datasets is a complex problem in computer science but specifically important for load balancing in parallel environments. The problem is to (a) find a partitioning where each partition has the same number of elements and (b) the communication between partitions (duplicate members) is minimized. We present a novel parallel load-balancing framework — Sort Balance Split (SBS) — the first to our knowledge to perform accurate parallel partitioning of multidimensional data, while requiring a fixed number of communication steps independent of network size or input data distribution. When compared to the state of the art sampling and parallel partitioning methods adopted by HPC problems, it delivers better load balancing on a shorter time to solution. We analyse four partitioning schemes that SBS can be applied to, and evaluated our method on 4096 nodes of an IBM BlueGene/Q supercomputer partitioning up to 1 trillion elements, and exhibiting almost-linear scaling properties.