Find Largest Building in each Parcel (largest feature in each groupby set)

Question

I have a question similar to this one, but the proposed approach doesn't seem to work. For context, I am new to qgis.

Given a set of parcels, each with 0 or more buildings, I want to select only the largest building in each parcel.

There are about 200k parcels and 320k thousand buildings.

Example

Building A:
 parcel_APN: 1 (ParcelNumber)
 SHAPE_Area: 100 

Building B:
 parcel_APN: 1
 SHAPE_Area: 500

Building C:
 parcel_APN: 2
 SHAPE_Area: 50

>>> LargestBuildings: [B, C]

I tried two approaches:

SQL Query DB Manager

Seems like this should work, but I let it run for 2 hours and it did not finish. Dataset is big, but seems to be shouldn't take that long for a SQL join. A simpler SELECT with MAX area and groupby but without the join take less than 5 seconds.

The approach is to first group by APN to find the largest shape area, then do inner join using id and max area , with the same table, to retrieve the largest buildings.

SELECT * FROM
 ( 
   SELECT 
     parcel_APN,
     MAX(SHAPE_Area) as max_shape
   FROM buildings as t0
   GROUP BY parcel_APN
 ) as t1
JOIN buildings as t2
ON t1.parcel_APN = t2.parcel_APN and max_shape = t2.SHAPE_area

Using Attribute Expression

This is the approach suggested in the SO mentioned above:

maximum("SHAPE_Area", group_by:="parcel_APN")

I let this run last night, this morning was still running and eventually QGIS crashed.

Questions

Do these approach seem correct? Is there an easier way to go about this? Are the file sizes too big for something like this in QGIS? And maybe I need to work in subsets or work with the data outside?

---

Update

I created a small subset to test, and the attribute expression method does not seem to work - selects all buildings:

Update 2

DB Manager Query seems to work! I guess now I just need to find a way to run it without crashing QGIS, or load it into PostGIS to run it.

Answer 1

While a SQL approach with DB Manager and Virtual layers inside QGIS worked with small samples, it would run for hours or crash agains the entire datates.

As suggested by @DSSPatial, I loaded the data into PostGIS and it worked really well, and fast. Here is the final query:

INSERT INTO main_buildings
SELECT 
    t2.*
FROM
 ( 
   SELECT 
     t0."parcel_APN",
     MAX(t0."SHAPE_Area") as max_shape
   FROM main_buildings as t0
   GROUP BY t0."parcel_APN"
 ) as t1
INNER JOIN main_buildings as t2
ON t1."parcel_APN" = t2."parcel_APN" and max_shape = t2."SHAPE_Area";

Not perfect but this is what I was looking for.