A mixed basis approach in the SGP-limit
This work provides a faster computational approach for NMR diffusion experiments, but it is an incremental improvement over existing methods for a specific domain.
The paper presents a perturbation method for computing echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit, achieving O(s^2) time complexity where s is the number of boundary elements. The method retrieves approximate eigenvalues and eigenfunctions for 1-D and 2-D systems with Neumann boundary conditions.
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.