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FMM vs Treecode structure. Left: FMM cluster-cluster interaction list; Right: treecode particle-cluster interaction (R is the distance from the charge to the blue cluster's center; r c is the radius of the blue cluster c which is the farthest particle inside c to the center of c.
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The Poisson-Boltzmann model is an effective and popular approach for modeling solvated biomolecules in continuum solvent with dissolved electrolytes. In this paper, we report our recent work in developing a Galerkin boundary integral method for solving the Poisson-Boltzmann (PB) equation. The solver has combined advantages in accuracy, efficiency,...
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... we found it to be useful for the computation of the free solvation energy (25), where the source and evaluation points are different and zero or limited near field calculations are required. The direct computation of the solvation energy as interactions between N boundary elements and N c atomic centers has O(N c N ) complexity. This is shown in Fig. 2b, in which a charge located at x n will interact with induced charges (φ 1 or ∂φ 1 ∂ν ) located at the center of each panel. These interactions consist of near field particle-particle interaction by direction summation and far field particle-cluster interaction controlled by maximum acceptance criterion (MAC) as specified below. For ...
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This article presents a fast direct solver, termed Algebraic Inverse Fast Multipole Method (from now on abbreviated as AIFMM), for linear systems arising out of $N$-body problems. AIFMM relies on the following three main ideas: (i) Certain sub-blocks in the matrix corresponding to $N$-body problems can be efficiently represented as low-rank matrice...
