  Fully numerical mesh solutions of 2D and 3D quantum equations of Schroedinger
and Hartree-Fock type allow us to work with wavefunctions which possess a very
flexible geometry. This flexibility is especially important for calculations of
atoms and molecules in strong external fields where neither the external field
nor the internal interactions can be considered as a perturbation. In the
framework of this method we present various approaches to calculations of
quasi-steady states of these systems in strong electric fields. These
approaches are aimed at obtaining precise complex wavefunctions and
corresponding eigenvalues in the form E = E_0 - i\Gamma/2, where E_0 is the
real part of the energy and the value \Gamma/2 determines the lifetime of the
state in relation to escape of electrons from the system. The applications for
single-electron systems include correct solutions of the Schroedinger equation
for the H_2^+ ion (energies and decay rates) and the hydrogen atom in strong
parallel electric and magnetic fields. Some results for the helium atom in
strong electric fields are announced.
