General perturbative approach to the diffusion equation in the presence of absorbing defects: frequency-domain and time-domain results

In this work, based on our previously proposed perturbation theory for the diffusion equation, we present new theoretical results in time and frequency domains. More specifically, we have developed a fourth order perturbation theory of the diffusion equation for absorbing defects. The method of Padé Approximants is used to extend the validity of the proposed theory to a wider range of absorbing contrasts between defects and background medium. The results of the theory are validated by comparisons with Monte Carlo simulations. In the frequency domain, the discrepancy between theoretical and Monte Carlo results for amplitude (AC) data are less than 10% up to an absorption contrast of Δμa ≤ 0.2 mm-1, whereas the discrepancy of phase data is less than 1° up to Δμa ≤ 0.1 mm-1. In the time domain, the average discrepancy is around 2-3% up to Δμa ≤ 0.06 mm-1. The proposed method is an effective and fast forwardproblem solver that has the potential to find general applicability in a number of situations.