The FMM relations are most easily derived using Cartesian coordinates.
The FMM presented in this article uses the standard translation operator for translating multipole/local expansions.
The FMM scheme is more memory efficient and more flexible then the FFT scheme.
The FMM and subspace combinations provide stable and robust results on highly diverse media (Rawlinson et al. 2010).
The FMM kernels M2L, M2M, and L2L (equations (3b), (3d), (3e)) all require O ( p 4 ) operations.
The FMM handles the interactions among the surface charge elements and directly outputs surface integrals of the fields over each individual element.
The FMM relations of Section 2 and Appendix A (using the rotation-accelerated M2L kernel of Appendix A.6 when faster) have been implemented in computer code.
The FMM negative binomial models demonstrated non-convergence.
The FMM represents the velocity response as several strain-rate dependent variables which all decay with time.
The FMM also has a circumferential titanium fiber-mesh surface located proximally, identical to the FMT, but has a polished distal part with splines and flutes.
The FMM pattern in men with CMM appeared more heterogeneous, with a majority showing a FMM extent larger than the range found in controls.
