arXiv subjects

Changhui Yao

Publications and source records attributed to Changhui Yao.

4 recordsLinked to original sources

arXiv2026

Robust Block Preconditioning for 3D nonlinear steady-state radiation transport equations

In this work, based on the discrete ordinate method, we propose a robust block preconditioning strategy for the 3D nonlinear steady-state radiation transport equation with heat diffusion term. The presence of the diffusive term of the temperature equation prevents its elimination into a single equation for the radiation intensity. To overcome this difficulty, all physical variables are assembled into a single monolithic linear system. The heat flux and temperature are treated as independent variables in a mixed $H(\mathrm{div})$-conforming finite element formulation. The equation for radiation intensity is discretised by a discontinuous Galerkin method with upwind flux, where a vectorial finite element space is used to couples the radiation intensity in different directions within each element. We then construct a Newton-Krylov iterative solver to solve the nonlinear equations, for which the core part is efficient preconditioning. To accelerate the convergence of Krylov's method, three block preconditioners are constructed, corresponding to different levels of approximation of the coupling between the temperature and radiation intensity. $P_{\mathrm{Schur}}$ retains the full coupling. $P_{\mathrm{Split}}$ drops the conductive contribution to the radiation block. $P_{\mathrm{BJ}}$ neglects the radiation-to-temperature coupling, retaining only the temperature-to-radiation coupling. Numerical experiments demonstrate the mesh independence and robustness of the proposed preconditioners.

math.NA↗

arXiv2026

Optimal error estimate of an isoparametric upwind discontinuous Galerkin method for radiation transport equation on curved domains

In recent years, high-order finite element methods on high-order meshes have attracted considerable attention. This work investigates the isoparametric upwind discontinuous Galerkin method for the radiation transport equation on a bounded domain with a piecewise $C^{k+1}$ smooth curved boundary. We use the isoparametric mapping to approximate the curved domain and construct a curved upwind discontinuous Galerkin scheme. The first-order hyperbolic nature and the complexity introduced by non-affine transformation, lead to additional difficulties for geometric approximation, numerical stability and the optimal error estimate. To address these issues, with the help of an isoparametric auxiliary operator, we first prove that the bilinear form is continuous with respect to the DG norm when its first argument is the isoparametric projection error. Then the geometric approximation error of inflow boundary of original domain is precisely estimated. The error order between discrete normal vectors and the continuous ones are also proven. Finally, the rigorous analysis yields an optimal convergence rate in the DG norm. Two- and three-dimensional numerical tests are conducted to support the theoretical results.

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arXiv2017

Finite Element Methods For Wave Propagation With Debye Polarization In Nonlinear Dielectric Materials

In this paper, we consider the wave propagation with Debye polarization in nonlinear dielectric materials. For this model, the Rother's method is employed to derive the well-posedness of the electric fields and the existence of the polarized fields by monotonicity theorem as well as the boundedness of the two fields are established. Then, the time errors are derived for the semi-discrete solutions by the order $O(\Delta t)$. Subsequently, decoupled the full-discrete scheme of the Euler in time and Raviart-Thomas-N$\acute{e}$d$\acute{e}$lec element $k\geq 2$ in spatial is established. Based on the truncated error, we present the convergent analysis with the order $O(\Delta t+h^s) $ under the technique of a-prior $L^\infty$ assumption. For the $k=1$, we employ the superconvergence technique to ensure the a-prior $L^\infty$ assumption. In the end, we give some numerical examples to demonstrate our theories.

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arXiv2017

The Solvability Of Magneto-heating Coupling Model With Turbulent Convection Zone And The Flow Fields

In this paper, the magneto-heating coupling model is studied in details, with turbulent convection zone and the flow field involved. Our main work is to analyze the well-posed property of this model with the regularity techniques. For the magnetic field, we consider the space $H_0(curl)\cap H(div_0)$ and for the heat equation, we consider the space $H_0^1(\Omega)$. Then we present the weak formulation of the coupled magneto-heating model and establish the regularity problem. Using Roth's method, monotone theories of nonlinear operator, weak convergence theories, we prove that the limits of the solutions from Roth's method converge to the solutions of the regularity problem with proper initial data. With the help of the spacial regularity technique, we derive the results of the well-posedness of the original problems when the regular parameter $\epsilon\longrightarrow 0$. Moreover, with additional regularity assumption for both the magnetic field and temperature variable, we prove the uniqueness of the solutions.

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