Hadoop MapReduce vs MPI (vs Spark vs Mahout vs Mesos) - When to use one over the other?

There might be good technical criteria for this decision but I haven't seen anything published on it. There seems to be a cultural divide where it's understood that MapReduce gets used for sifting through data in corporate environments while scientific workloads use MPI. That may be due to underlying sensitivity of those workloads to network performance. Here are a few thoughts about how to find out:

Many modern MPI implementations can run over multiple networks but are heavily optimized for Infiniband. The canonical use case for MapReduce seems to be in a cluster of "white box" commodity systems connected via ethernet. A quick search on "MapReduce Infiniband" leads to http://dl.acm.org/citation.cfm?id=2511027 which suggests that use of Infiniband in a MapReduce environment is a relatively new thing.

So why would you want to run on a system that's highly optimized for Infiniband? It's significantly more expensive than ethernet but has higher bandwidth, lower latency and scales better in cases of high network contention (ref: http://www.hpcadvisorycouncil.com/pdf/IB_and_10GigE_in_HPC.pdf).

If you have an application that would be sensitive to those effects of optimizations for Infiniband that are already baked into many MPI libraries, maybe that would be useful for you. If your app is relatively insensitive to network performance and spends more time on computations that don't require communication between processes, maybe MapReduce is a better choice.

If you have the opportunity to run benchmarks, you could do a projection on whichever system you have available to see how much improved network performance would help. Try throttling your network: downclock GigE to 100mbit or Infiniband QDR to DDR, for example, draw a line through the results and see if the purchase of a faster interconnect optimized by MPI would get you where you want to go.

The link you posted about FEM being done on MapReduce: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6188175&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6188175

uses MPI. It states it right there in the abstract. They combined MPI's programming model (non-embarrassingly parallel) with HDFS to "stage" the data to exploit data locality.

Hadoop is purely for embarrassingly parallel computations. Anything that requires processes to organize themselves and exchange data in complex ways will get crap performance with Hadoop. This can be demonstrated both from an algorithmic complexity point of view, and also from a measurement point of view.