NEW metod idea
HI just have new idea of metod its bit advenced

but I mean that can be fast
1 STEP
Just easy solve 2x2x3 block like whit petrus
2 STEP
solve the corner and opposite edge like with keyhole trick

you will see in example solve

next
3 STEP A
Next you have to solve last edge to cross and this is advenced you have to twist edges to have orient 3 edges on top
3 STEP B
now you have to like with keyhole trick solve last pair to f2l but you have to look to edges on top and dont destroy it to have cross on top after it
4 STEP
now you have to do all coll alg. to solve last layer and that just do U perms or Z or H perm

its fast
Example solve :F2 R2 D' U' B2 U' B2 L2 D B2 R2 F' R' D B F2 U R' D F L2 U2
orient: x2 y
2x2x3 block: R Ui Ri yi U2 r Ui ri y Ri Fi R
Corner+Edge: y R2 U Ri U R Ui Ri
Edges orient : y U Mi U M
Keyhole: Di Li U2 L U2 Li U L D
Last layer R U Ri U R U2 Ri and then Z perm
its not best but you can try it I mean it that sometime its good solve like I have on it time like 14 sec