The Unreasonable Usefulness of Approximation by Linear Combination
Through the exploitation of data-sparsity ---a catch all term for savings gained from a variety of approximations--- it is possible to reduce the computational cost of accurate electronic structure calculations to linear. Meaning, that the total time to solution for the calculation grows at...
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Virginia Tech
2018
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| Online Access: | http://hdl.handle.net/10919/83866 |
| Summary: | Through the exploitation of data-sparsity ---a catch all term for savings
gained from a variety of approximations--- it is possible to reduce the
computational cost of accurate electronic structure calculations to linear.
Meaning, that the total time to solution for the calculation grows at the same
rate as the number of particles that are correlated. Multiple techniques for
exploiting data-sparsity are discussed, with a focus on those that can be
systematically improved by tightening numerical parameters such that as the
parameter approaches zero the approximation becomes exact.
These techniques are first applied to Hartree-Fock theory and then we attempt
to design a linear scaling massively parallel electron correlation strategy
based on second order perturbation theory. === Ph. D. |
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