User:Hidayetoglu/sandbox

The Multilevel Fast Multipole Algorithm (MLFMA) is used along with Method of Moments (MoM) a numerical computational method of solving linear partial differential equations which have been formulated as integral equations  of large objects almost faster without loss in accuracy. This method is an alternative formulation of the technology behind the MoM and is applicable to much larger structures like radar cross-section (RCS) analysis, antenna integration on large structures, reflector antenna design, finite size antenna arrays, etc., making full-wave current-based solutions of such structures a possibility.

Method
The MLFMA is based on the Method of Moments (MoM), but reduces the computational complexity from $$\mathcal{O}(N^3)$$ or $$\mathcal{O}(IN^2)$$ to $$\mathcal{O}(I N \log N)$$, where $$N$$ represents the number of unknowns and $$I$$ represents the number of iterations for the solution. For volumetric problems, MLFMA computational complexity is $$\mathcal{O}(I N)$$, however, $$N$$ is much larger because of the curse of dimensionality. This method subdivides the Boundary Element mesh into different clusters and if two clusters are in each other's far field, all calculations that would have to be made for every pair of nodes can be reduced to the midpoints of the clusters with almost no loss of accuracy. For clusters not in the far field, the traditional Boundary Element Method (BEM) has to be applied. That is, MLFMA introduces different levels of clustering (clusters made out of smaller clusters - is the idea of multilevel clustering) to additionally enhance computational speedup.

== Historical background ==