Strebel approach

A completely different approach to the problem is due to Lekner [11] and Sperb [12,13]. Although the method in the original Lekner formulation has (N ) complexity, Strebel and Sperb have developed a factorization approach which yields an 0 NlogN) algorithm [14], called MMM The Strebel approach can also be adapted for partially periodic systems [15] however, the method becomes computationally more expensive. 

Loos M, Schipper AM, Schlink U, Strebel K, Ragas AMJ. 2010. Receptor-oriented approaches in wildlife and human exposure modelling a comparative study. Environ Model Software 25 369-382. 

Another approach to tackle the conditionally convergent Coulomb sum is used by Strebel and Sperb [15] and called the MMM method. Instead of defining the summation order, the sum is made convergent by means of a convergence factor ... 

The limit E exists and has as its value that of the Ewald method minus the dipole term [16]. Starting from this convergence factor approach, Strebel and Sperb constructed a method of computational order 0(A / ) or, with a more clever algorithm, (P(AllogAl), MMM [15]. Unlike the particle mesh Ewald methods, no mesh is introduced, so that no interpolation errors occur, and it is comparatively easy to find error estimates for the method. Consequently, this method allows much higher precisions compared to P M or (S)PME. 

Starting from this convergence factor approach along the lines of the Lekner sum, R. Strebel and R. Sperb constructed a method of computational order O (N log N), MMM [54]. The favorable scaling is obtained, very much as in the Ewald case, by technical tricks in the calculation of the far formula. The far formula has a product decomposition and can be evaluated hierarchically, similar in spirit to the fast multipole methods. 

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See also in sourсe #XX -- [ ]

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