Flattening hierarchical XML in SQL using the nodes

I have a Stored Procedure that takes an XML document as a parameter similar in a structure to the following:

<grandparent name="grandpa bob">
  <parent name="papa john">
    <children>
      <child name="mark" />
      <child name="cindy" />
    </children>
  </parent>
  <parent name="papa henry">
    <children>
      <child name="mary" />
    </children>
  </parent>
</grandparent>

My requirement is to "flatten" this data so that it can be inserted into a temporary table and manipulated further down the procedure, so the above XML becomes:

Grandparent Name Parent Name     Child Name
---------------- --------------- ---------------
grandpa bob      papa john       mark
grandpa bob      papa john       cindy
grandpa bob      papa henry      mary

This is currently being done using SQL Server XML Nodes:

SELECT
    VIRT.node.value('../../../@name','varchar(15)') 'Grandparent Name',
    VIRT.node.value('../../@name','varchar(15)') 'Parent Name',
    VIRT.node.value('@name','varchar(15)') 'Child Name'
FROM
    @xmlFamilyTree.nodes('/grandparent/parent/children/child') AS VIRT(node)

This works great until I start throwing large amounts of data at the procedure (i.e. 1000+ child nodes), at which point this grinds to a halt and takes between 1 and 2 minutes to execute. I think this may be due to the fact that I am starting off at the lowest level (<child) and then traversing back up the XML document for each occurance. Would splitting this single query into 3 chunks (one per node that I need data from) improve performance here? Given that none of these nodes have "keys" on them that I could use to join back up with, could anyone offer any pointers how I might be able to go about doing this?

I seem to have answered my own question after a bit more looking around online:

SELECT
    grandparent.gname.value('@name', 'VARCHAR(15)'),
    parent.pname.value('@name', 'VARCHAR(15)'),
    child.cname.value('@name', 'VARCHAR(15)')
FROM
    @xmlFamilyTree.nodes('/grandparent') AS grandparent(gname)
CROSS APPLY
    grandparent.gname.nodes('*') AS parent(pname)
CROSS APPLY
    parent.pname.nodes('children/*') AS child(cname)

Using CROSS APPLY I can select the top-level grandparent node and use this to select the child parent nodes and so on. Using this method I have taken my query from executing in around 1 minute 30 seconds down to around 6 seconds.

Interestingly though, if I use the "old" OPEN XML method to retrieve the same data, the query executes in 1 second!

It seems like you may have to approach the use of these two techniques on a case-by-case basis depending on the expected size/complexity of the document being passed in.