MPI::broadcast() can't deal with more than 2GB of data

[bangerth]

Follow-up to geodynamics/aspect#4484: I looked at Utilities::MPI::broadcast(), and it does this:

      std::vector<char> buffer;
      unsigned int      buffer_size = numbers::invalid_unsigned_int;

      // On the root process, pack the data and determine what the
      // buffer size needs to be.
      if (this_mpi_process(comm) == root_process)
        {
          buffer      = Utilities::pack(object_to_send, false);
          buffer_size = buffer.size();
        }

      // Exchange the size of buffer
      int ierr = MPI_Bcast(&buffer_size, 1, MPI_UNSIGNED, root_process, comm);
      AssertThrowMPI(ierr);

      // If not on the root process, correctly size the buffer to
      // receive the data, then do exactly that.
      if (this_mpi_process(comm) != root_process)
        buffer.resize(buffer_size);

      ierr =
        MPI_Bcast(buffer.data(), buffer_size, MPI_CHAR, root_process, comm);
      AssertThrowMPI(ierr);

The assignment

          buffer_size = buffer.size();

can overflow if we are trying to send large objects, and it will only go downhill from there.

[tjhei]

Well, MPI_Bcast (like all other MPI routines) takes the count as a signed int, so you are limited to 2^31 bytes when compressing or 2^31 objects (doubles/...) if not.
But yes, this routine should check and AssertThrow about this.

This is all related to my work about large MPI IO and Utilities::MPI::create_mpi_data_type_n_bytes

[bangerth]

Ah, yes, crap. So we need that same trick that you did with the large-data output.

[tjhei]

This case is easier, though. We can fall back to a sequence of broadcasts if necessary.

[tjhei]

See #13368