A mixed basis approach in the SGP-limit

TL;DR

This paper introduces a perturbation-based method for rapidly estimating echo decay in pulsed spin echo NMR diffusion experiments within the short gradient pulse limit, using a mixed basis approach involving boundary dipole distributions.

Contribution

It presents a novel perturbation basis method that efficiently computes approximate eigenvalues and eigenfunctions for diffusion operators in NMR experiments, reducing computational complexity.

Findings

Effective in 1-D and 2-D systems with Neumann boundary conditions.

Computes eigenvalues and eigenfunctions with small perturbation matrices.

Achieves O(s^2) computational time for boundary element number s.

Abstract

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.