Commit 42443d3f by COULAUD Olivier

### Improvements for Ewal

parent f8d11ba6
 ... ... @@ -118,6 +118,19 @@ can have a complexity reduced from O(n2) to O(n). But many physical problem could also have the need to compute periodic simulations. Many analytical methods have been developed but none of them is using the power of the FMM to compute the periodicity. The potential at particle $x_i$ computed by ScalFMM code is given by $$V(x_i) = \sum_{j=0,i\neq j}^{N}{\frac{q_j}{\|x_i-x_j\|}}$$ and the force on atom $x_i$ $$f(x_i) = \sum_{j=0,i\neq j}^{N}{q_j\frac{x_i-x_j}{\|x_i-x_j\|^3}}.$$ Finally, the total energy of the system writes $$U = \frac{1}{2}\sum_{i=0}^{N}{q_i V(x_i)}.$$ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{State of the art} ... ... @@ -392,15 +405,20 @@ f(x_i) = -\frac{q_0^2}{4 \pi\epsilon_0 l_0^2} q_i \sum_{j=0,i\neq j}^{N}{q_j\fra  The Energy conversion factor is $\gamma_0 = \frac{q_0^2}{4 \pi\epsilon_0 l_0}/E_0 = 138935.4835$. The energy unit is in Joules and if you want $kcal mol^{-1}$ unit the the factor becomes $\gamma_0/418.400$. To compare with the molecular dynamics code, the forces and the energy is multiplied by $C_{force}$ ($C_{energy}$ respectively). \begin{center} \begin{tabular}{|l|c|c|c|c|c|} \hline & \multicolumn{2}{|c|}{Energy} & \multicolumn{2}{c|}{Force} \\ units& $kcal\, mol^{-1}$& & &\\ \hline $C_{energy}$& & & &\\ $C_{force}$& & & &\\ $C_{force}$& -138935.4835/418.400& & &\\ \hline \end{tabular} \end{center} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Conclusion} A new approach has been proposed to compute a periodic FMM. ... ...
 ... ... @@ -189,7 +189,7 @@ public: else{ *inPhysicalValue = FReal(-0.41); *inIndex = HW; std::cerr << "Atom type not defined"<< std::endl; std::cerr << "Atom type not defined "<< type << std::endl; exit(-1); } } ... ...
 ... ... @@ -16,8 +16,8 @@ #include "FMath.hpp" // Constant values const FReal FMath::FPi = FReal(M_PI); const FReal FMath::FTwoPi = FReal(2.0*M_PI); const FReal FMath::FPi = FReal(M_PI); const FReal FMath::FTwoPi = FReal(2.0*M_PI); const FReal FMath::FPiDiv2 = FReal(M_PI_2); const FReal FMath::Epsilon = FReal(0.00000000000000000001); ... ...
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