Numerical optimization of computing algorithms of the variational nodal method

Numerical schemes have been developed for improving the computational efficiency of the variational nodal method (VNM). Reordering and orthogonal transformation schemes for nodal unknowns have been found for reducing the coefficient matrices of VNM into block-diagonal forms. The resulting block-diagonal forms of coefficient matrices make it possible to eliminate the unnecessary operations in matrix manipulations and hence reduce the computational time. These new schemes have been incorporated within the algorithms currently used in the variational nodal code VARIANT at Argonne National Laboratory. All primary algorithms ranging from the generation of response matrices to the iterative solution scheme for the response matrix equations have been modified to implement the new schemes. The efficiency of the new schemes has been tested on eigenvalue problems by comparing the computation times of the new and existing schemes. Three-dimensional calculations were performed in hexagonal and Cartesian geometry for various spatial and angular approximations. The test results show that very significant gains can be obtained especially for the coupling coefficient calculations in higher angular approximations. Almost an order of magnitude for the total computing time is achieved in the best case.