Parallel procedures in Maple

Most of the procedures available in the ALIAS-Maple library have a parallel implementation. They have the same name than the non parallel procedures except that they are prefixed by the word Parallel. Hence ParallelGeneralSolve is the name of the parallel implementation of the procedure GeneralSolve. There is an exception with ParallelContinuationSimplex which exists only in a parallel implementation.

The parallel procedures have the same initial arguments as the normal procedure except that they have at the end two additional arguments:

• a list of strings: this list gives the name of the slave computers. For example ["cygnusx1","molotova"] indicates that the slave computers will be cygnusx1 and molotova.
• a list of pair of integers like [[N1,M1],[N2,M2]]. There must be as many pairs of integers as the number of slave computers. The first number in the pair indicates that the corresponding slave will return approximately N1 new boxes provided that the maximal width of the box given as input for the slave is greater than `ALIAS/diam_switch` and that the mean diameter is larger than `ALIAS/mean_diam_switch`: the exact number of returned boxes is such that right after a bisection process the number of unprocessed boxes is equal or larger than N1. Note that there is a safety mechanism to avoid that a slave has a too large workload: if the number of bisection that has been performed is larger than `ALIAS/max_split` (default value: 10000) and the number of unprocessed boxes is lower or equal to N1, then the slave will return. A good policy is to increase the value of `ALIAS/diam_switch` if you observe that all the computation is done by the slave computers.

  Otherwise if the maximal width of the box given as input for the slave is lower than
  `ALIAS/diam_switch` the slave program will perform at least M bisection (provided that there are still boxes to process after this number of bisection) and will return at most `ALIAS/bisection_slave` (default value: 30). If M S bisections have been done and still the number of unprocessed boxes is larger than `ALIAS/bisection_slave`, then the slave will stop its processing and will return an error code. In that case the master program will bisect the range having the largest width in the initial box, two new boxes will be created and added to the list of unprocessed boxes. The value of S is defined by `ALIAS/safety_factor` with a default value of 2. Clearly the efficiency of the parallel implementation is heavily dependent on the values of N and M and diam_switch. Another way to stop the computation of a slave is to set the flag `ALIAS/time_out` to the maximum number of minutes that a slave may run before sending the processed boxes to the master. By default this value is set to 0 which means that a slave calculation will never be stopped by a time-out signal.