2 results about "Matrix function" patented technology

The application provides a linear scale electronic structure calculation method and system based on a dyeing superposition state and a terminal, based on the dyeing superposition state, and is used for solving sparse operator or matrix functions with spatial locality or limited correlation length, such as a density matrix, an inverse square root of an overlap matrix, and an operator required by an orthogonal representation transformation, which are involved in a Kohn-Sham self-consistent process under a local basis representation. On the premise of maintaining linear scale complexity, the application breaks through the dependence of a traditional algorithm on sparse matrix-sparse matrix multiplication (SpMSpM), and reconstructs core calculation into regular sparse matrix-dense matrix multiplication (SpMM). Through transformation of a bottom layer calculation paradigm, the regularity of Kohn-Sham electronic structure self-consistent calculation and the parallel adaptation ability of a bottom layer hardware are significantly improved, and inherent bottlenecks, such as a large pre-factor and low hardware execution efficiency, caused by the limitation of a core operator (SpMSpM) in a traditional linear scale algorithm are fundamentally relieved.

The application provides a metal scatterer electromagnetic scattering analysis method based on an electric field integral equation, triangular surface patch units are used to discretize a target surface, and RWG base functions are defined to expand and approximate surface currents; the expanded and approximated surface current is substituted into the electric field integral equation, the equation is tested by using a RWG-based test function, a discrete electric field integral equation matrix system is obtained; a Gram matrix corresponding to the RWG base function is constructed, according to a matrix function theory, Chebyshev polynomial approximation expansion suitable for a scalar inverse square root is extended to Chebyshev polynomial approximation expansion suitable for a matrix inverse square root, and numerical calculation of the Gram matrix inverse square root is realized; the Gram matrix inverse square root is used to precondition the discrete electric field integral equation matrix system, a correlation between a solution vector of a preconditioned matrix equation system and a solution vector of an original matrix equation system is established, and a spatial scattering field of the metal scatterer is obtained. The application improves the electromagnetic scattering analysis efficiency of the metal scatterer.