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Quantum three body problem: an overview of numerical computation

project	explain	remarks
High precision numerical integration	DE integration method	Calculate the Coulomb potential energy matrix : Implicitly calculate matrix and vector multiplication
Iteratively solve super large sparse matrix	The corresponding matrix of kinetic energy operator can be decomposed into two sparse matrices and , use CGS+ Preprocessor method iterative solution	The main matrix of the kinetic energy operator is a super tridiagonal matrix , Can be expressed as Kronecker Tensor form , use LU decompose , Or direct Gauss elimination can be solved , Used as a CGS Preprocessing matrix in M
ARPACK/PARPACK Iteratively solve eigenvalues	Solve the maximum eigenvalue by iterative method	Matrix display form is not required , Provide matrix x Vector operation is enough , Support MPI Parallel mode
Coulomb matrix x vector	utilize Jacobi Polynomial recurrence relation and DE Integral implicit calculation	There is no need to display calculations
Convergence analysis	Extrapolate and interpolate the increasing truncated eigenvalue results , Get high-precision results	Find the progressive law of sequence , use E Algorithm extrapolation
Hybrid accuracy calculation strategy	With low accuracy (REAL(4)) Calculate the approximate eigenvector , With high precision (REAL(8)/REAL(16)) correct	It can significantly accelerate the calculation efficiency
GPU Acceleration strategy	use GPU Calculate the vector multiplication of Coulomb matrix	Jacobi Polynomial recurrence relation 、 Block matrix multiplication

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