The ideal distribution of spatially located heterogeneous workloads is an important problem to address in parallel scientific computing. We investigate the problem of partitioning such workloads (represented as a matrix of positive integers) into rectangles, such that the load of the most loaded rectangle (processor) is minimized. Since finding the optimal arbitrary rectangle-based partition is an NP-hard problem, we investigate particular classes of solutions, namely, rectilinear partitions, jagged partitions and hierarchical partitions. We present a new class of solutions called m-way jagged partitions, propose new optimal algorithms for m-way jagged partitions and hierarchical partitions, propose new heuristic algorithms, and provide worst case performance analyses for some existing and new heuristics. Moreover, the algorithms are tested in simulation on a wide set of instances. Results show that two of the algorithms we introduce lead to a much better load balance than the state-of-the-art algorithms.