We investigate the problem of partitioning finite difference meshes in two dimensions among the processors of a parallel computer. The objective is to achieve a perfect load balance while minimizing the communication cost. There are well-known graph, hypergraph, and geometry-based partitioning algorithms for this problem. The known geometric algorithms have linear running time and obtain the best results for very special mesh sizes and processor numbers. We propose another geometric algorithm. The proposed algorithm is linear; is ap-plicable to much more cases than some well-known alternatives; obtains better results than the graph partitioning algorithms; ob-tains better results than the hypergraph partitioning algorithms almost always. Our algorithm also obtains better results than a known asymptotically-optimal algorithm for some small number of processors. We also catalog related theoretical results.