  Super-Yang-Mills theory (SYM) is a central building block for supersymmetric
extensions of the Standard Model of particle physics. Whereas the weakly
coupled subsector of the latter can be treated within a perturbative setting,
the strongly coupled subsector must be dealt with a non-perturbative approach.
Such an approach is provided by the lattice formulation. Unfortunately a
lattice regularization breaks supersymmetry and consequently the mass
degeneracy within a supermultiplet. In this article we investigate the
properties of $\mathcal{N}=1$ supersymmetric SU(3) Yang-Mills theory with a
lattice Wilson Dirac operator with an additional parity mass, similar as in
twisted mass lattice QCD. We show that a special $45^\circ$ twist effectively
moves the mass splitting of the chiral partners. Thus, at finite lattice
spacing both chiral and supersymmetry are enhanced resulting in an improved
continuum extrapolation. Furthermore, we show that for the non-interacting
theory at $45^\circ$ twist discretization errors of order $\mathcal{O}(a)$ are
suppressed, suggesting that the same happens for the interacting theory as
well. As an aside, we demonstrate that the DD$\alpha$AMG multigrid algorithm
accelerates the inversion of the Wilson Dirac operator considerably. On a
$16^3\times 32$ lattice, speed-up factors of up to 20 are reached if commonly
used algorithms are replaced by the DD$\alpha$AMG.
