A wide variety of special techniques for handling long-range forces are explained in this chapter. This includes the traditional Ewald sum, and the particle-mesh methods that use a discrete Fourier transform. A number of techniques based on spherical truncation such as the Wolf method, the isotropic periodic sum and the reaction field are also considered. Techniques for larger systems such as the fast-multipole method, the multilevel summation approach, and the direct solution of Maxwell’s equations, are explained. The advantages and disadvantages of the different approaches are reviewed, and a number of methods for tackling long-range forces in inhomogeneous systems, particularly in a slab geometry, are presented.
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