Tree codes

Postprocessing cutset information such as cutset acronyms and cutset searches is performed by REPORT (BNL written to aid in preparation of NUREG/CR-4207). A standard output format for the fault tree codes would facilitate postprocessing,... 

Challacombe, M., Schwegler, E., Almlof, J., 1996, Fast Assembly of the Coulomb Matrix A Quantum Chemical Tree Code , J. Chem. Phys., 104, 4685. 

Challacombe, M. E. Schwegler, and J. Almlof. 1996. Fast assembly of the Coulomb matrix A quantum chemical tree code. J. Chem. Phys. 104,4686. 

Giese, T. J., and York, D. M. (2008). Extension of adaptive tree code and fast multipole methods to high angular momentum particle charge densities,/. Comput Chem. 29(12), 1895-1904. 

As mentioned in Sect. 2.5, in principle the FMM, multigrid methods, or tree codes can handle this situation, but they are much too slow for the normally only small number of charges involved, and error estimates are not easy to obtain. Also, a modified Ewald method in which the summation of the reciprocal-space vectors was modified [70], similar to the one used by Kawata and Mikami [71] exists, but also here the approximations made seem hard to control which render the method rather useless. 

The quantum-chemical tree code (QCTC) [M. Challacombe and E. Schwegler, J. Chem. Phys., 106, 5526 (1997)] is a modification of the classical tree-code method. The QCTC method allows calculation of the matrix elements of the Coulomb matrix J for large molecules in a time that is proportional to the number of basis functions b this calculation is 0 b), and one says that the calculation exhibits linear scaling with size of the molecule. Challacombe and Schwegler used the QCTC method to do an ab initio SCE MO calculation on the 698-atom monomer of the P53 protein at a fixed geometry (obtained from a protein data bank) using the 3-21G basis set (3836 basis functions). They then calculated the molecular electrostatic potential (Section 15.7) of the P53 monomer. (The P53 protein is a tetramer and acts as a tumor suppressor. Mutations in the gene for this protein are found in half of human cancers.)... 

FMM = fast tnultipole method RBM = recursive bisection method TC = tree code. 

A problem similar to the evaluation of J[p, p ] is encountered in simulations of systems of classical particles (point charges), where the particle-particle interaction also has a quadratic O(N ) scaling. For this problem, three algorithms with linear or near-linear scaling have been introduced recently the Fast Multipole Method (FMM), Tree Codes (TC), and the Recursive Bisection Method (RBM). The success of these three methods has prompted its application to the 7[p, p ] problem. ... 

We can increase the efficiency of RBM by keeping all the multipole expansions in memory, instead of recomputing them every time. This is, in plain words, the idea behind the so-called tree codes. ... 

Assembly of the Coulomb Matrix A Quantum Chemical Tree Code. 

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