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147 results on '"Umrigar, C. J."'

101. Energy landscape of silicon systems and its description by force fields, tight binding schemes, density functional methods, and quantum Monte Carlo methods

Author

Ghasemi, S. Alireza, primary, Amsler, Maximilian, additional, Hennig, Richard G., additional, Roy, Shantanu, additional, Goedecker, Stefan, additional, Lenosky, Thomas J., additional, Umrigar, C. J., additional, Genovese, Luigi, additional, Morishita, Tetsuya, additional, and Nishio, Kengo, additional

Published
2010
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124. Monte Carlo Eigenvalue Methods in Quantum Mechanics and Statistical Mechanics

Author

RHODE ISLAND UNIV KINGSTON DEPT OF PHYSICS, Nightingale, M. P., Umrigar, C. J., RHODE ISLAND UNIV KINGSTON DEPT OF PHYSICS, Nightingale, M. P., and Umrigar, C. J.

Abstract

In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the underlying mathematics is quite similar in that they are stochastic implementations of the power method. In all cases, optimized trial states can be used to reduce the errors of Monte Carlo estimates., Sponsored in part by National Science Foundation Grants DMR-9725080 and CHE-9625498. Final version published in Monte Carlo Methods in Chemistry, edited by David M. Ferguson, J. Ilja Siepmann, and Donald G. Truhlar, Advances in Chemical Physics, V105, John Wiley & Sons, New York, 1999. Available online 1 Feb 2008.

Published
1998

146. Comparison of polynomial approximations to speed up planewave-based quantum Monte Carlo calculations

Author

F. R. Petruzielo, Richard G. Hennig, Cyrus Umrigar, John W. Wilkins, Dario Alfè, William Parker, Parker, William D., Umrigar, C. J., Alfè, Dario, Petruzielo, F. R., Hennig, Richard G., and Wilkins, John W.

Subjects
Quantum Monte Carlo, Numerical Analysis, Basis (linear algebra), Physics and Astronomy (miscellaneous), Applied Mathematics, Lagrange polynomial, Computer Science Applications1707 Computer Vision and Pattern Recognition, Basis function, Computer Science Applications, Computational Mathematics, symbols.namesake, B-spline, Modeling and Simulation, Quantum mechanics, symbols, Applied mathematics, Slater determinant, Variational Monte Carlo, Laplace operator, Smoothing, Mathematics
Abstract

The computational cost of quantum Monte Carlo (QMC) calculations of realistic periodic systems depends strongly on the method of storing and evaluating the many-particle wave function. Previous work by Williamson et al. (2001) 35 and Alfe and Gillan, (2004) 36 has demonstrated the reduction of the O ( N 3 ) cost of evaluating the Slater determinant with planewaves to O ( N 2 ) using localized basis functions. We compare four polynomial approximations as basis functions - interpolating Lagrange polynomials, interpolating piecewise-polynomial-form (pp-) splines, and basis-form (B-) splines (interpolating and smoothing). All these basis functions provide a similar speedup relative to the planewave basis. The pp-splines have eight times the memory requirement of the other methods. To test the accuracy of the basis functions, we apply them to the ground state structures of Si, Al, and MgO. The polynomial approximations differ in accuracy most strongly for MgO, and smoothing B-splines most closely reproduce the planewave value for of the variational Monte Carlo energy. Using separate approximations for the Laplacian of the orbitals increases the accuracy sufficiently to justify the increased memory requirement, making smoothing B-splines, with separate approximation for the Laplacian, the preferred choice for approximating planewave-represented orbitals in QMC calculations.

Published
2015
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147. Reducing the time-step errors in diffusion Monte Carlo.

Author

Anderson TA, Per MC, and Umrigar CJ

Abstract

We modify the reweighting factor of the projector used in diffusion Monte Carlo to reduce the time-step error of the total energy. Furthermore, we present a reweighting scheme that has the desirable feature that it is exactly size-consistent, i.e., the energy of a system containing widely separated fragments is the same as the sum of the energies of the individual fragments. The practical utility of the latter improvement is that it reduces the time-step error of the binding energies of some weakly interacting systems., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Published
2024
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