Add thread safety for when multiple threads are failing point inversion

Refs a failure that briefly cropped up on idaholab/moose#29700
and that I can get to trigger 100% of the time with a build with
thread sanitizer

Author: lindsayad

include/fe/fe_map.h

@@ -1042,6 +1042,11 @@ class FEMap
    * Work vector for compute_affine_map()
    */
   std::vector<const Node *> _elem_nodes;
+
+  /**
+   * A mutex for locking the error stream for failed point inversions
+   */
+  static Threads::spin_mutex _point_inv_err_mutex;
 };
 
 

src/fe/fe_map.C

@@ -40,6 +40,7 @@
 
 namespace libMesh
 {
+Threads::spin_mutex FEMap::_point_inv_err_mutex;
 
 FEFamily
 FEMap::map_fe_type(const Elem & elem)
@@ -892,10 +893,11 @@ void FEMap::compute_single_point_map(const unsigned int dim,
                 // Don't call print_info() recursively if we're already
                 // failing.  print_info() calls Elem::volume() which may
                 // call FE::reinit() and trigger the same failure again.
-                static bool failing = false;
+                thread_local bool failing = false;
                 if (!failing)
                   {
                     failing = true;
+                    Threads::spin_mutex::scoped_lock lock(_point_inv_err_mutex);
                     elem->print_info(libMesh::err);
                     failing = false;
                     if (calculate_xyz)