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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Real-space quadrature: A convenient, efficient representation for multipole expansions

Multipoles are central to the theory and modeling of polarizable and nonpolarizable molecular electrostatics. This has made a representation in terms of point charges a highly sought after goal, since rotation of multipoles is a bottleneck in molecular dynamics implementations. All known point charge representations are orders of magnitude less efficient than spherical harmonics due to either using too many fixed charge locations or due to nonlinear fitting of fewer charge locations. We present the first complete solution to this problem—completely replacing spherical harmonic basis functions by a dramatically simpler set of weights associated to fixed, discrete points on a sphere. This representation is shown to be space optimal. It reduces the spherical harmonic decomposition of Poisson’s operator to pairwise summations over the point set. As a corollary, we also shows exact quadrature-based formulas for contraction over trace-free supersymmetric 3D tensors. Moreover, multiplication of spherical harmonic basis functions translates to a direct product in this representation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Multipole expansion method for supernova neutrino oscillations

Here, we demonstrate a multipole expansion method to calculate collective neutrino oscillations in supernovae using the neutrino bulb model. We show that it is much more efficient to solve multi-angle neutrino oscillations in multipole basis than in angle basis. The multipole expansion method also provides interesting insights into multi-angle calculations that were accomplished previously in angle basis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Atom-partitioned multipole expansions for electrostatic potential boundary conditions

Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Multipole Expansion of Atomic Electron Density Fluctuation Interactions in the Density-Functional Tight-Binding Method

The accuracy of the density-functional tight-binding (DFTB) method in describing noncovalent interactions is limited due to its reliance on monopole-based spherical charge densities. In this study, we present a multipole-extended second-order DFTB (mDFTB2) method that takes into account atomic dipole and quadrupole interactions. Furthermore, we combine the multipole expansion with the monopole-based third-order contribution, resulting in the mDFTB3 method. To assess the accuracy of mDFTB2 and mDFTB3, we evaluate their performance in describing noncovalent interactions, proton transfer barriers, and dipole moments. Here, our benchmark results show promising improvements even when using the existing electronic parameters optimized for the original DFTB3 model. Both mDFTB2 and mDFTB3 outperform their monopole-based counterparts, DFTB2 and DFTB3, in terms of accuracy. While mDFTB2 and mDFTB3 perform comparably for neutral and positively charged systems, mDFTB3 exhibits superior performance over mDFTB2 when dealing with negatively charged systems and proton transfers. Overall, the incorporation of the multipole expansion significantly enhances the accuracy of the DFTB method in describing noncovalent interactions and proton transfers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Exchange splitting of the interaction energy and the multipole expansion of the wave function

The exchange splitting J of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula J{sub surf}[Φ], the volume-integral formula of the symmetry-adapted perturbation theory J{sub SAPT}[Φ], and a variational volume-integral formula J{sub var}[Φ]. The calculations are based on the multipole expansion of the wave function Φ, which is divergent for any internuclear distance R. Nevertheless, the resulting approximations to the leading coefficient j{sub 0} in the large-R asymptotic series J(R) = 2e{sup −R−1}R(j{sub 0} + j{sub 1}R{sup −1} + j{sub 2}R{sup −2} + ⋯) converge with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the J{sub var}[Φ], J{sub surf}[Φ], and J{sub SAPT}[Φ] formulas are used, respectively. Additionally, we observe that also the higher j{sub k} coefficients are predicted correctly when the multipole expansion is used in the J{sub var}[Φ] and J{sub surf}[Φ] formulas. The symmetry adapted perturbation theory formula J{sub SAPT}[Φ] predicts correctly only the first two coefficients, j{sub 0} and j{sub 1}, gives a wrong value of j{sub 2}, and diverges for higher j{sub n}. Since the variational volume-integral formula can be easily generalized to many-electron systems and evaluated with standard basis-set techniques of quantum chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1999

A Multipole Expansion Method for Analyzing Lightning Field Changes

Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q model) or a point dipole (the P model). The Q model has four unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P model has six unknown parameters and describes many intracloud (IC) discharges. In this paper we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a dme-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer-simulated sources and on natural lightning at the NASA Kennedy Space Center and U.S. Air Force Eastern Range.

Koshak, William J.↗
NASA NTRS1998

A Multipole Expansion Method for Analyzing Lightning Field Changes

Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q-model) or a point dipole (the P-model). The Q-model has 4 unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P-model has 6 unknown parameters and describes many intracloud (IC) discharges. In this paper, we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a 3-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer simulated sources and on natural lightning at the NASA Kennedy Space Center and USAF Eastern Range.

Koshak, William J.↗
DOE OSTI2015

Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved—up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations

Recently, a novel approach to hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations has been suggested [Schwörer et al., J. Chem. Phys. 138, 244103 (2013)]. Here, the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10{sup 3}-10{sup 5} molecules as negative gradients of a DFT/PMM hybrid Hamiltonian. The electrostatic interactions are efficiently described by a hierarchical fast multipole method (FMM). Adopting recent progress of this FMM technique [Lorenzen et al., J. Chem. Theory Comput. 10, 3244 (2014)], which particularly entails a strictly linear scaling of the computational effort with the system size, and adapting this revised FMM approach to the computation of the interactions between the DFT and PMM fragments of a simulation system, here, we show how one can further enhance the efficiency and accuracy of such DFT/PMM-MD simulations. The resulting gain of total performance, as measured for alanine dipeptide (DFT) embedded in water (PMM) by the product of the gains in efficiency and accuracy, amounts to about one order of magnitude. We also demonstrate that the jointly parallelized implementation of the DFT and PMM-MD parts of the computation enables the efficient use of high-performance computing systems. The associated software is available online.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Approximate recalculation of the {alpha}(Z{alpha}){sup 5} contribution to the self-energy effect on hydrogenic states with a multipole expansion

A contribution of virtual electron states with large wave numbers to the self-energy of an electron bound in the weak Coulomb field is analyzed in the context of the evaluation method suggested in the previous paper. The contribution is of the order {alpha}(Z{alpha}){sup 5}. The same value for this contribution is found here as the one found in the previous calculations using different evaluation methods. When we add the remaining terms of the order {alpha}(Z{alpha}){sup 5} to the calculation of the self-energy effect in hydrogen-like ions presented in the previous paper we find a very good agreement with numerical evaluations. The relative difference between present and numerical evaluations ranges from 2 parts in 10{sup 6} for Z=1 up to 6 parts in 10{sup 4} for Z=10. - Highlights: Black-Right-Pointing-Pointer The complete terms of the order {alpha}(Z{alpha}){sup 5} are identified. Black-Right-Pointing-Pointer The accuracy of the result for the ground state of the hydrogen is 2 ppm. Black-Right-Pointing-Pointer The separation into the low and high energy regions and their matching is avoided.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1995

Sensitivity analysis in multipole-accelerated panel methods for potential flow

In the design of an airframe, the effect of changing the geometry on resulting computations is necessary for design optimization. The geometry is defined in terms of a series of design variables, including design variables to define the wing planform, tail, canard, pylon, and nacelle. Design optimization in this research is based on how these design variable affect the potential flow. The potential flow is computed as a function of the geometry and location of a series of panels describing the airframe, which are in turn a function of the design variables. Multipole accelerated panel methods improve the computational complexity of the problem and thus are an attractive approach. To utilize the methods in design optimization, it was necessary to define the appropriate sensitivity derivatives. The overhead incurred from finding the sensitivity derivatives in conjunction with the original computation should be small. This research developed the background for multipole-accelerated panel methods and the framework for finding sensitivity derivatives in the methods. Potential flow panel codes are commonly used for powered-lift aerodynamic predictions for three dimensional geometries. Given an airframe which has been discretized into a series of panels to define the airframe geometry, potential is computed as a function of the influence of all panels on all other panels. This is a computationally intensive problem for which efficient solutions are desired to improve the computational time and to allow greater resolution by use of more panels. One such solution is the use of hierarchical multipole methods which entail approximations of the effects of far-field terms. Hierarchical multipole methods have become prevalent in molecular dynamics and gravitational physics, and have been introduced into the fields of capacitance calculations, computational fluid dynamics, and electromagnetics. The methods utilize multipole expansions to describe the effect of bodies (i.e. particles, astrophysical bodies, panels, etc.) within a sphere on points distant from the sphere, where the influence diminishes as a function of distance. The expansions are exact with infinite series, however, for practical computations, the series are truncated and accuracy is selected based on the number of terms retained in the expansions. A hierarchical tree structure groups bodies together based on proximity to allow definition of multipole expansions for each group. The multipole expansions are then used to compute the effect of the bodies in a group on distant bodies.

Leathrum, James F., Jr.↗
NASA NTRS1994

Accelerated panel methods using the fast multipole method

Panel methods are commonly used in computational fluid dynamics for the solution of potential flow problems. The methods are a numerical technique based on the surface distribution of singularity elements. The solution is the process of finding the strength of the singularity elements distributed over the body's surface. This process involves the solution of the matrix problem Pq = p' for a set of unknowns q. The Fast Multipole Method is used to directly compute q without using matrix solvers. The algorithm works in O(N) time for N points, a great improvement over standard matrix solvers. In panel methods, the surface of a body is divided into a series of quadrilateral panels. The methods involve the computation of the influence of all other panels on each individual panel. The influence is based on the surface distribution, though this can be approximated by the area for distant panels. An alternative approximation, though with arbitrary accuracy, is to develop a multipole expansion about the center of the panel to describe the effect of a given panel on distant points in space. The expansion is based on the moments of the panel, thus allow the use of various surface distributions without changing the basic algorithm, just the computation of the various moments. The expansions are then manipulated in a tree walk to develop Taylor series expansions about a point in space which describe the effect of all distant panels on any point within a volume of convergence. The effect of near panels then needs to be computed directly, but the effect of all distant panels can be computed by simply evaluating the resulting expansion. The Fast Multipole Method has been applied to panel methods for the solution of source and doublet distributions. A major feature of the algorithm is that the algorithm does not change to derive the potential and velocity for sources and doublets. The same expansions can be used for both sources and doublets. Since the velocity is related to the potential, and the doublet potential is related to the z-component of the source velocity, all values can be derived from the same expansion by taking a series of partial derivatives. This requires more expansion terms to be kept since terms are lost in the process of taking partial derivatives. Thus to maintain accuracy for the doublet computation, more terms are required than if just evaluating for sources. The resulting Fast Multipole code should then parallelize better than classical panel methods due to the locality of data dependencies found in the Fast Multipole Method. Theoretically the parallelized code should execute in O(log N) time with O(N) processors, though this is not practical. Ongoing work includes implementing the parallel accelerated panel method, including methods to improve the load balancing of the problem by taking advantage of the known geometry of panels, and to encorporate sensitivity analysis into the algorithm.

Leathrum, James F., Jr.↗
DOE OSTI2013

An improved multipole approximation for self-gravity and its importance for core-collapse supernova simulations

Self-gravity computation by multipole expansion is a common approach in problems such as core-collapse and Type Ia supernovae, where single large condensations of mass must be treated. The standard formulation of multipole self-gravity in arbitrary coordinate systems suffers from two significant sources of error, which we correct in the formulation presented in this article. The first source of error is due to the numerical approximation that effectively places grid cell mass at the central point of the cell, then computes the gravitational potential at that point, resulting in a convergence failure of the multipole expansion. We describe a new scheme that avoids this problem by computing gravitational potential at cell faces. The second source of error is due to sub-optimal choice of location for the expansion center, which results in angular power at high multipole l values in the gravitational field, requiring a high—and expensive—value of multipole cutoff l {sub max}. By introducing a global measure of angular power in the gravitational field, we show that the optimal coordinate for the expansion is the square-density-weighted mean location. We subject our new multipole self-gravity algorithm, implemented in the FLASH simulation framework, to two rigorous test problems: MacLaurin spheroids for which exact analytic solutions are known, and core-collapse supernovae. We show that key observables of the core-collapse simulations, particularly shock expansion, proto-neutron star motion, and momentum conservation, are extremely sensitive to the accuracy of the multipole gravity, and the accuracy of their computation is greatly improved by our reformulated solver.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Full radiator-perturber interaction in computer simulations of hydrogenic spectral line broadening by plasmas

Spectral line broadening by plasmas can be computed by solving the equation of motion for the dipole of the radiating system perturbed by a fluctuating potential obtained from computer simulations. Such calculations have relied on the multipole expansion of the radiator-plasma interaction often keeping only the dipole term. With increasing density, however, higher multipoles as well as plasma perturbers overlapping the bound electron wave functions are expected to become important. For hydrogenic systems, the atomic matrix elements of the full Coulomb and screened Coulomb interactions are given by analytical formulas. Using these results, a computer simulation approach that accounts for the full radiator-plasma interaction is developed. One benefit is the removal of inherent strong collision divergences in the multipole expansion approximation. Furthermore, it yields the plasma polarization shift produced by perturbers penetrating the wave function of the radiator bound electrons. Here, the model was applied to hydrogenic argon Ly-α , Ly- β , and Ly-$\gamma$ spectral lines in a dense argon plasma at free electron densities of 10 24 or 10 25 cm ⁻3 and temperature of $800$ $eV$ relevant to plasma diagnostic techniques for inertial confinement fusion implosions.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

The Lagrangian-space Effective Field Theory of large scale structures

Here, we introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of extended objects in Lagrangian space. In LEFT the resulting finite size effects are described using a multipole expansion parameterized by a set of time dependent coefficients and organized in powers of the ratio of the wavenumber of interest k over the non-linear scale k NL . The multipoles encode the effects of the short distance modes on the long-wavelength universe and absorb UV divergences when present. There are no IR divergences in LEFT. Some of the parameters that control the perturbative approach are not assumed to be small and can be automatically resummed. We present an illustrative one-loop calculation for a power law universe. We describe the dynamics both at the level of the equations of motion and through an action formalism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗