you can use querySelectorAll to get partial attributes, including ID:
document.querySelectorAll("[id^='this_div_id']")
the ^ next to the equal sign means "starts with", you can use * instead, but it is prone to false positives.
, ( ) comapare querySelectorAll; jQuery , .
: :
document.querySelectorAll("[id^='this_div_id']:not([id$='_test_field'])");
not() -, "_test_field" .
/: http://pagedemos.com/partialmatch/