  Methodological progress is reported in the challenging direction of a
black-box-type variational solution of the (ro)vibrational Schr\"odinger
equation applicable to floppy, polyatomic systems with multiple large-amplitude
motions. This progress is achieved through the combination of (i) the numerical
kinetic-energy operator (KEO) approach of [E. M\'atyus, G. Czak\'o, and A. G.
Cs\'asz\'ar, J. Chem. Phys. 130, 134112 (2009)] and (ii) the Smolyak
non-product grid method of [G. Avila and T. Carrington, Jr., J. Chem. Phys.
131, 174103 (2009)]. The numerical representation of the KEO makes it possible
to choose internal coordinates and a body-fixed frame best suited for the
molecular system. The Smolyak scheme reduces the size of the direct-product
grid representation by orders of magnitude, while retaining some of the useful
features of it. As a result, multi-dimensional (ro)vibrational states are
computed with system-adapted coordinates, a compact basis- and
grid-representation, and an iterative eigensolver. Details of the
methodological developments and the first numerical applications are presented
for the CH$_4\cdot$Ar complex treated in full (12D) vibrational dimensionality.
