A Fast Adaptive Multipole Algorithm for Calculating Screened Coulomb (Yukawa) Interactions

X-ray free-electron lasers (XFELs) are a promising tool for the structural determination of macro-and biomolecules, using coherent diffractive imaging. During imaging, the intense XFEL pulses also efficiently ionize the molecules, so it is important to estimate how the charged environment within the molecule modifies atomic properties, in comparison to the case of an isolated atom. Here, we apply the XATOM toolkit to obtain predictions on the modified ionization thresholds and rates of some photoinduced processes in carbon. The Hartree-Fock-Slater model is extended to include the electron screening and ion correlation effects, induced by external charges. With this extended model, we obtain predictions on modifications of orbital energies, photoabsorption cross sections, Auger decay rates, fluorescence emission rates, and atomic scattering factors as a function of the density and temperature of the surrounding charges. Our results have implications for the studies of dynamics within XFEL irradiated samples, in particular for those dedicated to coherent diffraction imaging.

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“…The Debye-screened Coulomb potential in Eq. (5) can be expanded in terms of modified Bessel functions and spherical harmonics [54,55] as…”

Section: B Debye Screeningmentioning

confidence: 99%

Effect of screening by external charges on the atomic orbitals and photoinduced processes within the Hartree-Fock-Slater atom

et al. 2012

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“…Finally, we note that the computational and storage complexities will scale linearly for matrix or inhomogeneous kernels. For example, for the Stokes kernel in (12), the number of coefficients, p, scales as a results of the matrix kernel size to p = 9(n 3 p − (n p − 2) 3 ). For the modified Helmholtz kernel in (11), the inhomogeneous nature of the kernel results in an increased storage complexity, which varies depending on the number of different levels in the tree.…”

Section: Harper Langston Leslie Greengard and Denis Zorinmentioning

confidence: 99%

A free-space adaptive FMM-Based PDE solver in three dimensions

Langston

Greengard

Zorin

2011

CAMCoS

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We present a kernel-independent, adaptive fast multipole method (FMM) of arbitrary order accuracy for solving elliptic PDEs in three dimensions with radiation and periodic boundary conditions. The algorithm requires only the ability to evaluate the Green's function for the governing equation and a representation of the source distribution (the right-hand side) that can be evaluated at arbitrary points. The performance is accelerated in three ways. First, we construct a piecewise polynomial approximation of the right-hand side and compute far-field expansions in the FMM from the coefficients of this approximation. Second, we precompute tables of quadratures to handle the near-field interactions on adaptive octree data structures, keeping the total storage requirements in check through the exploitation of symmetries. Third, we employ shared-memory parallelization methods and load-balancing techniques to accelerate the major algorithmic loops of the FMM. We present numerical examples for the Laplace, modified Helmholtz and Stokes equations.

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“…For a review of FMM-type methods and a more thorough discussion of the literature, we refer the reader to [10]. We should note here, however, the recent work of Boschitsch et al [3], who give (to the best of our knowledge) the first detailed description of an FMM for (2). Their scheme, however, does not take into account the plane wave representation and relies on classical expansions.…”

Section: Introductionmentioning

confidence: 96%

“…in R 3 . Such calculations arise in various problems in physics, chemistry, and biology when Coulomb forces are damped by screening effects.…”

Section: Introductionmentioning

confidence: 97%

A New Version of the Fast Multipole Method for Screened Coulomb Interactions in Three Dimensions

Greengard

Huang

2002

Journal of Computational Physics

118

107

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A Fast Adaptive Multipole Algorithm for Calculating Screened Coulomb (Yukawa) Interactions

Cited by 36 publications

References 69 publications

Effect of screening by external charges on the atomic orbitals and photoinduced processes within the Hartree-Fock-Slater atom

Effect of screening by external charges on the atomic orbitals and photoinduced processes within the Hartree-Fock-Slater atom

A free-space adaptive FMM-Based PDE solver in three dimensions

A New Version of the Fast Multipole Method for Screened Coulomb Interactions in Three Dimensions

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