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    TSEvent: refactor and fix bugs, add TSSetPostEventStep() · ca4445c7
    Ilya Fursov authored
        Refactor the core algorithm for resolution of events: TSEventHandler()
        and the helper functions, fixing the existing bugs.
    
        Change event indicator functions from PetscScalar to PetscReal.
        Change the API of TSSetEventHandler(): in the user `indicator()` callback,
        the 'fvalue' argument type changed from PetscScalar[] to PetscReal[].
    
        Add TSSetPostEventStep(), deprecate TSSetPostEventIntervalStep().
        Deprecate option -ts_event_post_eventinterval_step.
    
        Fix bugs in interaction of TSEvent with tspan.
        Add six new test examples.
    
        Below are the examples of bugs fixed by this patch.
        The source codes (ex3.c, ex3span.c, ex4.c, ex5.c) can be found
        in src/ts/event/tests. To run them with the older Petsc versions,
        one would need to comment out "#define NEW_VERSION".
        Behaviour for three library versions is reported below:
        * ORIG: current Petsc version, before the proposed patch.
        * 6688: independently of the proposed patch, Merge Request 6688 was
          developed, which fixed some bugs with zero-crossing directions.
        * NEW : the proposed patch.
    
        ./ex3 -ts_monitor -ts_event_monitor -ts_view -ts_type beuler \
        -ts_adapt_type basic -flg -V 1e9 -ts_adapt_dt_min 1e-6 -change5 1 -dir 1
        * ORIG: fails to resolve 5 out of 6 events, and resolves 23 incorrect events.
        * 6688: fails to exit the TSEvent iteration via the step size (bracket size)
          criterion.
        * NEW : ok, resolves all 6 events.
    
        ./ex4 -ts_adapt_type basic -ts_type rk -ts_dt 0.25 -ts_event_tol 1e-8 \
        -dir 0 -ts_adapt_dt_min 1e-10 -ts_view -ts_monitor -ts_event_monitor
        * ORIG: only reaches t = 0.0300236 after 10000 TS steps.
        * 6688: only reaches t = 0.0300236 after 10000 TS steps.
        * NEW : ok, reaches the final time t = 4.0 after 96 TS steps, resolving
          all 16 events.
    
        ./ex5 -ts_monitor -ts_event_monitor -ts_type rk -ts_adapt_type basic \
        -ts_view -ts_dt 0.25 -flg -dir 0
        * ORIG: only reaches t = 4.0 after 10000 TS steps, erroneously reports
          event at t = 4.0 around 5000 times.
        * 6688: only reaches t = 4.0 after 10000 TS steps.
        * NEW : ok, reaches the final time t = 10.0 after 99 TS steps, resolving
          all 34 events.
    
        ./ex5 -ts_monitor -ts_event_monitor -ts_type rk -ts_adapt_type basic \
        -ts_view -ts_dt 0.25 -flg -dir 1
        * ORIG: fails, starts taking negative time steps, no events are correctly
          resolved.
        * 6688: ok, but slower: 90 TS steps to resolve all 17 events.
        * NEW : ok, and faster: 48 TS steps to resolve all 17 events.
    
        ./ex5 -ts_monitor -ts_event_monitor -ts_type rk -ts_adapt_type basic \
        -ts_view -ts_dt 0.25 -flg -dir -1
        * ORIG: fails, starts taking 'nan' time steps.
        * 6688: mostly fails, only reaches t = 4.99993 after 10000 TS steps.
        * NEW : ok, reaches the final time t = 10.0 after 74 TS steps, resolving
          all 17 events.
    
        The same run in parallel:
        mpirun -n 2 ./ex5 -ts_monitor -ts_event_monitor -ts_type rk \
        -ts_adapt_type basic -ts_view -ts_dt 0.25 -flg -dir -1
        * ORIG: fails, starts taking negative time steps, exits with runtime error.
        * 6688: mostly fails, only reaches t = 3, besides, the parallel run is not
          consistent with the serial run (see above).
        * NEW : ok, reaches the final time t = 10.0 after 74 TS steps, resolving
          all 17 events.
    
        ./ex3span -ts_monitor -ts_event_monitor
        * ORIG: (confused by events) misses tspan points: 4.02, 4.21, 4.98, 5.01,
          5.21, 5.98, 6, 6.01, 6.02, 6.21, 6.99, 7.21, 8.01, 8.21, 9.01.
        * 6688: (confused by events) misses tspan points: 4.02, 4.21, 4.98, 5.01,
          5.21, 5.98, 6, 6.01, 6.02, 6.21, 6.99, 7.21, 8.01, 8.21, 9.01.
        * NEW : ok.
    
        ./ex3span -ts_monitor -ts_event_monitor -ts_event_post_event_step 0.5
        * ORIG: misses the majority of tspan points (except 0.01 and 0.21),
          and also resolves the last event location at wrong time t = 9.21.
        * 6688: misses the majority of tspan points (except 0.01 and 0.21),
          and also resolves the last event location at wrong time t = 9.21.
        * NEW : ok.
    ca4445c7