arXiv subjects

Yuan-Yuan Huang

Publications and source records attributed to Yuan-Yuan Huang.

8 recordsLinked to original sources

arXiv2026

Constraining DVCS Compton Form Factors Using Lattice QCD informed Neural Network

The lattice QCD calculation of generalized form factors are exploited to determine the subtraction constants through all order dispersion relations of Deeply Virtual Compton Scattering (DVCS). The leading order relation is found to constrain significantly the real part of the Compton Form Factors (CFFs), and the higher order one reduces considerably both the real and imaginary part of CFFs in a global analysis of proton data. This is realized by a synthesis of the DVCS data and LQCD calculations within a neural network framework, whose architecture is specifically designed for a reliable extrapolation to unmeasured kinematic regime. By leveraging dispersion relations beyond leading order, our framework allows for adding higher moments of generalized parton distributions (GPDs) from LQCD into the extraction of CFFs from DVCS data.

hep-ph↗

arXiv2026

Assessing the impact of the electron ion collider in China on Deeply Virtual Compton Scattering

We assess the impact of future measurements of deeply virtual Compton scattering (DVCS) off protons using the planned detector at the Electron-Ion Collider in China (EicC), proposed as an upgrade to the High Intensity heavy-ion Accelerator Facility (HIAF). We develop a neural-network architecture to flexibly parameterize the Compton Form Factors (CFFs), extrapolate reliably into unmeasured kinematic regions, and provide robust uncertainty estimates through the replica method. The framework is fitted to the available worldwide DVCS data using the Gepard software. We find a significant reduction in the uncertainties of all CFFs after incorporating pseudo-data from single and double polarization asymmetries at the EicC, with particularly strong improvements in the sea-quark region.

hep-ph↗

arXiv2026

Optimal preconditioning techniques for finite volume approximation of three-dimensional conservative space-fractional diffusion equations

A Crank-Nicolson finite volume approximation for three-dimensional conservative space-fractional diffusion equation results in large and dense three-level Toeplitz discrete linear systems. Preconditioned Krylov subspace methods with sine transform-based preconditioners are developed to solve these systems, including the preconditioned conjugate gradient (PCG) method for the symmetric case and the preconditioned generalized minimal residual (PGMRES) method for the non-symmetric case. Moreover, we provide detailed analysis of the convergence of these Krylov subspace methods. Specifically, for the symmetric case, we prove the spectra of the preconditioned matrices are uniformly bounded in the open interval (1/2, 3/2), which results in a linear convergence rate of the PCG method. For the non-symmetric case, we demonstrate that the PGMRES method also achieves a linear convergence rate independent of discretization stepsizes from the residual point of view. These results imply that the iteration counts of the PCG and PGMRES methods are uniformly bounded and independent of the matrix sizes. Numerical experiments in both symmetric and non-symmetric cases in two- and three-dimensions are conducted to confirm the optimal performance of the proposed preconditioned Krylov subspace methods.

math.NA↗

arXiv2025

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients

In this paper, we propose an efficient method for solving multi-dimensional Riesz space fractional diffusion equations with variable coefficients. The Crank-Nicolson (CN) method is used for temporal discretization, while the fourth-order fractional centered difference (4FCD) method is employed for spatial discretization. Using a novel technique, we show that the CN-4FCD scheme for the multi-dimensional case is unconditionally stable and convergent, achieving second-order accuracy in time and fourth-order accuracy in space with respect to the discrete L2-norm. Moreover, leveraging the symmetric multi-level Toeplitz-like structure of the coefficient matrix in the discrete linear systems, we enhance the computational efficiency of the proposed scheme with a sine transform-based preconditioner, ensuring a mesh-size-independent convergence rate for the conjugate gradient method. Finally, two numerical examples validate the theoretical analysis and demonstrate the superior performance of the proposed preconditioner compared to existing methods.

math.NA↗

arXiv2025

Upwind-and-shifted numerical scheme for fractional convection equation

Fundamental solution of a space fractional convection equation of order $α$ is the probability density function of Lévy flights with long-tailed $α$-stable jump length distribution. By studying an upwind second-order implicit finite difference scheme for the equation with $α\in(0,1)$, an upwind-and-shifted scheme with order $3-α$ is obtained in this paper, and the scheme is shown to be unconditionally stable for a wide range of $α$. Numerical examples, including simulations on a probability density function, are presented showing the effectiveness of the numerical schemes.

math.NA↗

arXiv2024

Optimal preconditioners for nonsymmetric multilevel Toeplitz systems with application to solving non-local evolutionary partial differential equations

Preconditioning for multilevel Toeplitz systems has long been a focal point of research in numerical linear algebra. In this work, we develop a novel preconditioning method for a class of nonsymmetric multilevel Toeplitz systems, which includes the all-at-once systems that arise from evolutionary partial differential equations. These systems have recently garnered considerable attention in the literature. To further illustrate our proposed preconditioning strategy, we specifically consider the application of solving a wide range of non-local, time-dependent partial differential equations in a parallel-in-time manner. For these equations, we propose a symmetric positive definite multilevel Tau preconditioner that is not only efficient to implement but can also be adapted as an optimal preconditioner. In this context, the proposed preconditioner is optimal in the sense that it enables mesh-independent convergence when using the preconditioned generalized minimal residual method. Numerical examples are provided to critically analyze the results and underscore the effectiveness of our preconditioning strategy.

math.NA↗

arXiv2024

An efficient preconditioner for evolutionary partial differential equations with $θ$-method in time discretization

In this study, the $θ$-method is used for discretizing a class of evolutionary partial differential equations. Then, we transform the resultant all-at-once linear system and introduce a novel one-sided preconditioner, which can be fast implemented in a parallel-in-time way. By introducing an auxiliary two-sided preconditioned system, we provide theoretical insights into the relationship between the residuals of the generalized minimal residual (GMRES) method when applied to both one-sided and two-sided preconditioned systems. Moreover, we show that the condition number of the two-sided preconditioned matrix is uniformly bounded by a constant that is independent of the matrix size, which in turn implies that the convergence behavior of the GMRES method for the one-sided preconditioned system is guaranteed. Numerical experiments confirm the efficiency and robustness of the proposed preconditioning approach.

math.NA↗

arXiv2024

A novel fourth-order scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equations and its optimal preconditioned solver

A novel fourth-order finite difference formula coupling the Crank-Nicolson explicit linearized method is proposed to solve Riesz space fractional nonlinear reaction-diffusion equations in two dimensions. Theoretically, under the Lipschitz assumption on the nonlinear term, the proposed high-order scheme is proved to be unconditionally stable and convergent in the discrete $L_2$-norm. Moreover, a $τ$-matrix based preconditioner is developed to speed up the convergence of the conjugate gradient method with an optimal convergence rate (a convergence rate independent of mesh sizes) for solving the symmetric discrete linear system. Theoretical analysis shows that the spectra of the preconditioned matrices are uniformly bounded in the open interval $(3/8,2)$. To the best of our knowledge, this is the first attempt to develop a preconditioned iterative solver with a mesh-independent convergence rate for the linearized high-order scheme. Numerical examples are given to validate the accuracy of the scheme and the effectiveness of the proposed preconditioned solver.

math.NA↗