diff --git a/include/ginkgo/core/base/mpi.hpp b/include/ginkgo/core/base/mpi.hpp
index 862f145ae16..b9221c59745 100644
--- a/include/ginkgo/core/base/mpi.hpp
+++ b/include/ginkgo/core/base/mpi.hpp
@@ -513,10 +513,7 @@ class communicator {
      *
      * @return  if the two comm objects are equal
      */
-    bool operator==(const communicator& rhs) const
-    {
-        return compare(rhs.get());
-    }
+    bool operator==(const communicator& rhs) const { return is_identical(rhs); }
 
     /**
      * Compare two communicator objects for non-equality.
@@ -525,6 +522,39 @@ class communicator {
      */
     bool operator!=(const communicator& rhs) const { return !(*this == rhs); }
 
+    /**
+     * Checks if the rhs communicator is identical to this communicator.
+     *
+     * @return  true if rhs is identical to this
+     */
+    bool is_identical(const communicator& rhs) const
+    {
+        if (!get() || !rhs.get()) {
+            return get() == rhs.get();
+        }
+        int flag;
+        GKO_ASSERT_NO_MPI_ERRORS(MPI_Comm_compare(get(), rhs.get(), &flag));
+        return flag == MPI_IDENT;
+    }
+
+    /**
+     * Checks if the rhs communicator is congruent to this communicator.
+     *
+     * Congruent communicators are defined as having identical rank members and
+     * rank ordering.
+     *
+     * @return  true if rhs is congruent to this
+     */
+    bool is_congruent(const communicator& rhs) const
+    {
+        if (!get() || !rhs.get()) {
+            return get() == rhs.get();
+        }
+        int flag;
+        GKO_ASSERT_NO_MPI_ERRORS(MPI_Comm_compare(get(), rhs.get(), &flag));
+        return flag == MPI_CONGRUENT;
+    }
+
     /**
      * This function is used to synchronize the ranks in the communicator.
      * Calls MPI_Barrier
@@ -1492,13 +1522,6 @@ class communicator {
         GKO_ASSERT_NO_MPI_ERRORS(MPI_Comm_size(this->get(), &size));
         return size;
     }
-
-    bool compare(const MPI_Comm& other) const
-    {
-        int flag;
-        GKO_ASSERT_NO_MPI_ERRORS(MPI_Comm_compare(get(), other, &flag));
-        return flag == MPI_IDENT;
-    }
 };