arXiv subjects

Wenqi Yao

Publications and source records attributed to Wenqi Yao.

3 recordsLinked to original sources

arXiv2026

A Globally Conservative Compact Framework for Conservation Laws: Fourth-Order Schemes with Enhanced Resolution and Stability

The compact finite difference method is a powerful tool for discretizing conservation laws, owing to its inherent flexibility in developing high-resolution and highly stable schemes. In this paper, we propose a framework for the design of genuine globally conservative compact finite difference schemes, which addresses a critical requirement in conservation laws. Within our framework, we rigorously establish that the discrete conservation law maintains strict conservation for flux functions in polynomial spaces with optimal algebraic order, i.e., the discrete scheme achieves an optimal algebraic precision.Our work advances the existing conservative compact finite difference schemes, which rely on approaches to maintaining global conservation that are fundamentally consistent with the method proposed by Lele [Lele, J. Comput. Phys., 1992]. As an application, we propose an algorithm for designing globally conservative fourth-order schemes, aimed at optimizing resolution and asymptotic stability. Three schemes are generated using the algorithm, with their excellent performance across multiple aspects validated through numerical experiments.

math.NA↗

arXiv2024

High Order Finite Difference Schemes for the Transparent Boundary Conditions and Their Applications in the 1D Schrödinger-Poisson Problem

The 1D Schrödinger equation closed with the transparent boundary conditions(TBCs) is known as a successful model for describing quantum effects, and is usually considered with a self-consistent Poisson equation in simulating quantum devices. We introduce discrete fourth order transparent boundary conditions(D4TBCs), which have been proven to be essentially non-oscillating when the potential vanishes, and to share the same accuracy order with the finite difference scheme used to discretize the 1D Schrödinger equation. Furthermore, a framework of analytic discretization of TBCs(aDTBCs) is proposed, which does not introduce any discretization error, thus is accurate. With the accurate discretizations, one is able to improve the accuracy of the discretization for the 1D Schrödinger problem to arbitrarily high levels. As numerical tools, two globally fourth order compact finite difference schemes are proposed for the 1D Schrödinger-Poisson problem, involving either of the D4TBCs or the aDTBCs, respectively, and the uniqueness of solutions of both discrete Schrödinger problems are rigorously proved. Numerical experiments, including simulations of a resistor and two nanoscale resonant tunneling diodes, verify the accuracy order of the discretization schemes and show potential of the numerical algorithm introduced for the 1D Schrödinger-Poisson problem in simulating various quantum devices.

math.NA↗

arXiv2019

A Deuflhard-type exponential integrator Fourier pseudospectral method for the "Good" Boussinesq equation

We propose an exponential integrator Fourier pseudospectral method DEI-FP for solving the "Good" Boussinesq (GB) equation. The numerical scheme is based on a Deuflhard-type exponential integrator and a Fourier pseudospectral method for temporal and spatial discretizations, respectively. The scheme is fully explicit and efficient due to the fast Fourier transform. Rigorous error estimates are established for the method without any CFL-type condition constraint. In more details, the method converges quadratically and spectrally in time and space, respectively. Extensive numerical experiments are reported to confirm the theoretical analysis and to demonstrate rich dynamics of the GB equation.

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