A perturbation method for computing quick estimates of the echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit is presented. The perturbation basis involves (relatively few) dipole distributions on the boundaries generating a small perturbation matrix in O(s^2) time, where s denotes the number of boundary elements. Several approximate eigenvalues and eigenfunctions to the diffusion operator are retrieved. The method is applied to 1-D and 2-D systems with Neumann boundary conditions.
@article{arxiv.1104.2310,
title = {A mixed basis approach in the SGP-limit},
author = {Matias Nordin and Martin Nilsson Jacobi and Magnus Nydén},
journal= {arXiv preprint arXiv:1104.2310},
year = {2015}
}