Section: New Results

Incremental algorithms for long-range interactions

Participants : Semeho Edorh, Stephane Redon.

We have started a PhD to develop incremental algorithms for calculating long-range molecular interactions. Numerical simulation of molecular dynamics are very expensive in terms of CPU resources, especially because of the evaluation of the interaction potential. In large crystalline ionic systems, Ewald summation is the most popular method for computing Coulombic interactions. It rewrites the interaction potential $\phi$ as the sum of two terms: $\phi \left(r\right)={\phi }_{dir}\left(r\right)+{\phi }_{rec}\left(r\right)$. The so-called “short-range” contribution ${\phi }_{dir}$ can be easily calculated in a direct space , where as the “long-range” contribution ${\phi }_{rec}$ is calculated using a Fourier transform.

Direct evaluation of the Ewald summation is an order $N^2$ computational problem. Over the past three decades, many techniques were developed and reduced the evaluation of the potential to an order $Nlog\left(N\right)$ problem. We want to develop a new approach that can reduce the computational cost by using incremental algorithms. The key idea is to use, at each time step of the simulation, information that has been computed in previous steps.