  In this paper, we investigate the stochastic evolution equations (SEEs)
driven by $\log$-Whittle-Mat$\acute{{\mathrm{e}}}$rn (W-M) random diffusion
coefficient field and $Q$-Wiener multiplicative force noise. First, the
well-posedness of the underlying equations is established by proving the
existence, uniqueness, and stability of the mild solution. A sampling approach
called approximation circulant embedding with padding is proposed to sample the
random coefficient field. Then a spatio-temporal discretization method based on
semi-implicit Euler-Maruyama scheme and finite element method is constructed
and analyzed. An estimate for the strong convergence rate is derived. Numerical
experiments are finally reported to confirm the theoretical result.
