Allow single-step backward Euler integrator (#1773)

now if you add `integrator.do_single_step=1` then `BackwardEuler`  will ignore the tolerances and just do a single step.

Author: chongchonghe

Docs/source/ode_integrators.rst

@@ -27,7 +27,9 @@ Presently, allowed integrators are:
 * ``BackwardEuler``: an implicit first-order accurate backward-Euler
   method.  An error estimate is done by taking 2 half steps and
   comparing to a single full step.  This error is then used to control
-  the timestep by using the local truncation error scaling.
+  the timestep by using the local truncation error scaling. Optionally, the
+  user can disable error estimation and force a single-step backward-Euler
+  integration by setting `integrator.do_single_step = 1`.
 
 * ``ForwardEuler``: an explicit first-order forward-Euler method.  This is
   meant for testing purposes only.  No Jacobian is needed.

integration/BackwardEuler/_parameters

@@ -5,3 +5,6 @@ max_iter                                 int             25
 
 # tolerance for the Newton solve
 tol                                      real            1.e-10
+
+# toggle single-step BackwardEuler integration and ignoring error tolerance
+do_single_step                           int             0

integration/BackwardEuler/be_integrator.H

@@ -181,6 +181,15 @@ int be_integrator (BurnT& state, BeT& be)
 
     int ierr;
 
+    if (integrator_rp::do_single_step == 1) {
+        // Do a single step to the final time
+        const amrex::Real dt_single_step = be.tout - be.t;
+        ierr = single_step(state, be, dt_single_step);
+        be.t = be.tout;
+        ++be.n_step;
+        return ierr;
+    }
+
     // estimate the timestep
 
     amrex::Array1D<amrex::Real, 1, int_neqs> ydot;