16,136 research outputs found
Quantum Monte Carlo for minimum energy structures
We present an efficient method to find minimum energy structures using energy
estimates from accurate quantum Monte Carlo calculations. This method involves
a stochastic process formed from the stochastic energy estimates from Monte
Carlo that can be averaged to find precise structural minima while using
inexpensive calculations with moderate statistical uncertainty. We demonstrate
the applicability of the algorithm by minimizing the energy of the H2O-OH-
complex and showing that the structural minima from quantum Monte Carlo
calculations affect the qualitative behavior of the potential energy surface
substantially.Comment: 7 pages, 4 figure
Stochastic collocation on unstructured multivariate meshes
Collocation has become a standard tool for approximation of parameterized
systems in the uncertainty quantification (UQ) community. Techniques for
least-squares regularization, compressive sampling recovery, and interpolatory
reconstruction are becoming standard tools used in a variety of applications.
Selection of a collocation mesh is frequently a challenge, but methods that
construct geometrically "unstructured" collocation meshes have shown great
potential due to attractive theoretical properties and direct, simple
generation and implementation. We investigate properties of these meshes,
presenting stability and accuracy results that can be used as guides for
generating stochastic collocation grids in multiple dimensions.Comment: 29 pages, 6 figure
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