The accepted answer gave me a good start, but brought in more classes and more processing than I would have liked; so this is my interpretation:
$xml_reader = new XMLReader;
$xml_reader->open($feed_url);
// move the pointer to the first product
while ($xml_reader->read() && $xml_reader->name != 'product');
// loop through the products
while ($xml_reader->name == 'product')
{
// load the current xml element into simplexml and we’re off and running!
$xml = simplexml_load_string($xml_reader->readOuterXML());
// now you can use your simpleXML object ($xml).
echo $xml->element_1;
// move the pointer to the next product
$xml_reader->next('product');
}
// don’t forget to close the file
$xml_reader->close();