TY - GEN

T1 - Solving the Three-Dimensional Faddeev–Merkuriev Equations via Spline Collocation and Tensor Product Preconditioning

AU - Яковлев, Сергей Леонидович

AU - Градусов, Виталий Александрович

AU - Руднев, Владимир Александрович

AU - Яревский, Евгений Александрович

PY - 2023

Y1 - 2023

N2 - We present an efficient computational approach to solving the Faddeev-Merkuriev equations for quantum three-body systems. The efficiency of our approach stems from the following three key factors. The appropriate treatment of the three-body dynamics due to the use of the Faddeev-Merkuriev equations, which results in the simplification of the solution. The advanced partial-wave analysis based on the Wigner functions decomposition of the solutions that leads to a model-free reduction of the six dimensional problem to a three-dimensional one. The elaborated numerical scheme that makes extensive use of the structure of the equations. The numerical approach is based on the spline collocation method and uses the tensor product form of discretized operators. For solving the linear equations we worked out the preconditioning scheme which is based on the Matrix Decomposition Algorithm. We show that this numerical scheme outperforms the general-purpose direct sparse linear system solvers in both time and memory requirements. The numerical approach demonstrated also clear advantages over the generic scheme that we implemented in earlier research. The approach has been applied to high-precision calculations of bound states and scattering states of several three-body systems.

AB - We present an efficient computational approach to solving the Faddeev-Merkuriev equations for quantum three-body systems. The efficiency of our approach stems from the following three key factors. The appropriate treatment of the three-body dynamics due to the use of the Faddeev-Merkuriev equations, which results in the simplification of the solution. The advanced partial-wave analysis based on the Wigner functions decomposition of the solutions that leads to a model-free reduction of the six dimensional problem to a three-dimensional one. The elaborated numerical scheme that makes extensive use of the structure of the equations. The numerical approach is based on the spline collocation method and uses the tensor product form of discretized operators. For solving the linear equations we worked out the preconditioning scheme which is based on the Matrix Decomposition Algorithm. We show that this numerical scheme outperforms the general-purpose direct sparse linear system solvers in both time and memory requirements. The numerical approach demonstrated also clear advantages over the generic scheme that we implemented in earlier research. The approach has been applied to high-precision calculations of bound states and scattering states of several three-body systems.

KW - Faddeev–Merkuriev equations

KW - Spline collocation

KW - Tensor product preconditioner

UR - https://www.mendeley.com/catalogue/ed8f0c5d-27e1-330f-8408-a30089a9dbcb/

U2 - 10.1007/978-3-031-38864-4_5

DO - 10.1007/978-3-031-38864-4_5

M3 - Conference contribution

SN - 978-3-031-38863-7

T3 - Communications in Computer and Information Science

SP - 63

EP - 77

BT - Parallel Computational Technologies.

A2 - Sokolinsky, Leonid

A2 - Zimber, Mikhail

PB - Springer Nature

T2 - Parallel Computational Technologies. : 17th International Conference,

Y2 - 28 March 2023 through 30 March 2023

ER -