We consider a particle undergoing diffusion with stochastic resetting in a bounded
domain U ⊂ Rd for d = 2, 3. The domain is perforated by a set of partially absorbing spherical targets
within which the particle may be absorbed at a rate κ. Each target is assumed to be much smaller
than |U|, which allows us to use asymptotic and Green’s function methods to solve the diffusion
equation in Laplace space. In particular, we construct an inner solution within the interior and local
exterior of each target and match it with an outer solution in the bulk of U. This yields an asymptotic
expansion of the Laplace transformed flux into each target in powers of ν = −1/ ln (d = 2) and
(d = 3), respectively, where is the nondimensionalized target size. The fluxes determine how the
mean first passage time (MFPT) to absorption depends on the reaction rate κ and the resetting rate
r. For a range of parameter values, the MFPT is a unimodal function of r, with a minimum at an
optimal resetting rate ropt that depends on κ and the target configuration.