Fast multipole method for three‐dimensional systems with periodic boundary condition in two directions

2020 ◽  
Vol 41 (9) ◽  
pp. 940-948
Author(s):  
Noriyuki Yoshii ◽  
Yoshimichi Andoh ◽  
Susumu Okazaki
Keyword(s):  
Boundary Condition ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fast Multipole Method ◽  
Three Dimensional ◽  
Fast Multipole ◽  
Multipole Method

Periodic boundary conditions and the fast multipole method

1997 ◽  
Vol 107 (23) ◽  
pp. 10131-10140 ◽  
Author(s):  
Matt Challacombe ◽  
Chris White ◽  
Martin Head-Gordon
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Fast Multipole Method ◽  
Periodic Boundary Conditions ◽  
Fast Multipole ◽  
Multipole Method

Error estimates for the fast multipole method. II. The three-dimensional case

1995 ◽  
Vol 448 (1934) ◽  
pp. 401-418 ◽  
Keyword(s):  
Error Estimates ◽  
Fast Multipole Method ◽  
Three Dimensional ◽  
Analytic Form ◽  
Dimensional Case ◽  
Fast Multipole ◽  
Complicated Form ◽  
Long Range Interactions ◽  
Multipole Method ◽  
Simple Analytic Form

The fast multipole method is a new and interesting method for computing long range interactions in particle systems. Although the method already has been implemented and compared to traditional and other methods with respect to accuracy and speed, no accurate error estimates of the fast multipole method have been given. In this paper we develop an explicit though complicated form for the error in the three dimensional case, and derive an estimate for it. The estimate has a simple analytic form which will allow its use in tuning the method for best efficiency and for comparison of the method with other methods at the same accuracy.

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