arXiv subjects

Xuping Wang

Publications and source records attributed to Xuping Wang.

10 recordsLinked to original sources

arXiv2026

A solid-solution approach for room-temperature bulk plasticity in KTa1-xNbxO3

Dislocations are being engineered into perovskite oxides to harvest versatile functional properties. One major bottleneck, however, persists: perovskite oxides that can be engineered with dislocations, particularly via mechanical deformation at room temperature in bulk scale, have so far been limited to only three materials: SrTiO3 (2001, Brunner et al.), KNbO3 (2016, Mark et al.), and KTaO3 (2024, Fang & Zhang et al.). Here, we propose a simple and effective approach by using solid solution to significantly extend the range of materials. We showcase KTa1-xNbxO3 (0<x<1) perovskite oxides for their bulk plasticity at room temperature by constructing a closed-loop validation workflow that includes crystal growth, Brinell indentation, bulk compression, and transmission electron microscopy characterization. Our findings are expected to unlock the materials toolbox for dislocation-tuned functionality of perovskite oxides.

cond-mat.mtrl-sci↗

arXiv2026

Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using General Multipliers

A unified framework is proposed to establish the energy dissipation of implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, based on general multipliers that are linear combinations of first-order differences of numerical solutions. A generalized Dahlquist's theory is developed to establish the energy dissipation of IMEX-LMMs. It is shown that given an IMEX-LMM, to find a multiplier ensuring the energy dissipation is relaxed to solve a linear programming that can be easily solved. Within this framework, two specific multipliers are discovered to establish the energy dissipation of the sixth-order IMEX backward differentiation formula (IMEX-BDF6) method and a seventh-order IMEX weighted and shifted BDF method, and a new eighth-order energy-dissipative IMEX-LMM is provided. To the best of our knowledge, these are the first energy-dissipation results for the IMEX-BDF6 method and the IMEX-LMMs of order higher than six. In addition, this framework can be used directly to establish the $L^2$- or $H^1$-stability of general LMMs for linear parabolic problems. Numerical experiments illustrate the temporal accuracy and energy dissipation of these methods.

math.NA↗

arXiv2026

Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using a Simple Multiplier

This paper proposes a theoretical framework for establishing the energy dissipation of general implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, by constructing a dissipative modified energy consisting of the original energy and a non-negative quadratic modification. We first test IMEX-LMMs with a simple multiplier, the first-order time difference of numerical solutions. Then, it is shown that the associated non-negative quadratic modification can be constructed if and only if two generating polynomials (corresponding to the LMM) are positive on $[-1,1]$. Based on this, the modified energy is proved to decay over time under a mild time-step restriction depending on the lower bounds of the associated generating polynomials. As a consequence, the energy dissipation of the well-known backward differentiation formula methods up to fifth order can be obtained straightforwardly. Furthermore, we construct for the first time (to the best of our knowledge) a sixth-order energy-dissipative IMEX-LMM and also prove the sixth-order barrier of energy-dissipative IMEX-LMMs when testing the simple multiplier. Some numerical experiments are conducted to verify our theoretical results.

math.NA↗

arXiv2026

Long-time stability of implicit-explicit Runge-Kutta methods for two-dimensional incompressible flows

High-order adaptive time-stepping algorithms are of significant practical value and theoretical interest for accelerating long-time fluid-flow simulations and resolving complex dynamical behaviors. While several high-order implicit-explicit schemes have been proposed in the literature, their long-time stability properties remain largely unexplored. We develop a family of long-time stable implicit-explicit Runge-Kutta (IERK) methods, up to fourth-order temporal accuracy, for the two-dimensional incompressible Navier-Stokes equations in vorticity-stream function formulation. By combining a convolution-type H\"{o}lder inequality with a damping-type multistage Gr\"{o}nwall inequality, we establish a unified analytical framework that proves long-time stability in both the $L^2$ and $H^1$ norms. A key component of the analysis is a mathematical-induction argument that ensures stage-wise boundedness of the vorticity in the $H^\delta$ norm for some $\delta>0$. To the best of our knowledge, this is the first work to establish large-time stability results for high-order IERK algorithms for the two-dimensional incompressible Navier-Stokes equations. Our IERK schemes employ stiffly accurate diagonally implicit Runge-Kutta approximations for the linear diffusive term together with explicit Runge-Kutta approximations for the nonlinear advection term. By exploiting the specific structure of the Navier-Stokes model, we derive a reduced set of order conditions-requiring only 5 and 11 conditions for the third- and fourth-order methods, respectively, in contrast to the classical 6 and 18-allowing the construction of a parameterized family of efficient schemes. These IERK methods are particularly well suited for adaptive time-stepping, as they permit significantly enlarged step sizes in actual computations.

math.NA↗

arXiv2024

A class of refined implicit-explicit Runge-Kutta methods with robust time adaptability and unconditional convergence for the Cahn-Hilliard model

One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of stage solutions without the global Lipschitz continuity assumption of nonlinear bulk. With the help of discrete orthogonal convolution kernels, an updated time-space splitting technique is developed to establish the uniform boundedness of stage solutions for a refined class of IERK methods in which the associated differentiation matrices and the average dissipation rates are always independent of the time-space discretization meshes. This makes the refined IERK methods highly advantageous in self-adaptive time-stepping procedures as some larger adaptive step-sizes in actual simulations become possible. From the perspective of optimizing the average dissipation rate, we construct some parameterized refined IERK methods up to third-order accuracy, in which the involved diagonally implicit Runge-Kutta methods for the implicit part have an explicit first stage and allow a stage-order of two such that they are not necessarily algebraically stable. Then we are able to establish, for the first time, the original energy dissipation law and the unconditional $L^2$ norm convergence. Extensive numerical tests are presented to support our theory.

math.NA↗

arXiv2024

A unified framework on the original energy laws of three effective classes of Runge-Kutta methods for phase field crystal type models

The main theoretical obstacle to establish the original energy dissipation laws of Runge-Kutta methods for phase-field equations is to verify the maximum norm boundedness of the stage solutions without assuming global Lipschitz continuity of the nonlinear bulk. We present a unified theoretical framework for the energy stability of three effective classes of Runge-Kutta methods, including the additive implicit-explicit Runge-Kutta, explicit exponential Runge-Kutta and corrected integrating factor Runge-Kutta methods, for the Swift-Hohenberg and phase field crystal models. By the standard discrete energy argument, it is proven that the three classes of Runge-Kutta methods preserve the original energy dissipation laws if the associated differentiation matrices are positive definite. Our main tools include the differential form with the associated differentiation matrix, the discrete orthogonal convolution kernels and the principle of mathematical induction. Many existing Runge-Kutta methods in the literature are revisited by evaluating the lower bound on the minimum eigenvalues of the associated differentiation matrices. Our theoretical approach paves a new way for the internal nonlinear stability of Runge-Kutta methods for dissipative semilinear parabolic problems.

math.NA↗

arXiv2024

Average energy dissipation rates of additive implicit-explicit Runge-Kutta methods for gradient flow problems

A unified theoretical framework is suggested to examine the energy dissipation properties at all stages of additive implicit-explicit Runge-Kutta (IERK) methods up to fourth-order accuracy for gradient flow problems. We construct some parameterized IERK methods by applying the so-called first same as last method, that is, the diagonally implicit Runge-Kutta method with the explicit first stage and stiffly-accurate assumption for the linear stiff term, and applying the explicit Runge-Kutta method for the nonlinear term. The main part of the novel framework is to construct the differential forms and the associated differentiation matrices of IERK methods by using the difference coefficients of method and the so-called discrete orthogonal convolution kernels. As the main result, we prove that an IERK method can preserve the original energy dissipation law unconditionally if the associated differentiation matrix is positive semi-definite. The recent indicator, namely average energy dissipation rate, is also adopted for these multi-stage methods to evaluate the overall energy dissipation rate of an IERK method such that one can choose proper parameters in some parameterized IERK methods. It is found that the selection of method parameters in the IERK methods is at least as important as the selection of different IERK methods. Extensive numerical experiments are also included to support our theory.

math.NA↗

arXiv2024

Original energy dissipation preserving corrections of integrating factor Runge-Kutta methods for gradient flow problems

Explicit integrating factor Runge-Kutta methods are attractive and popular in developing high-order maximum bound principle preserving time-stepping schemes for Allen-Cahn type gradient flows. However, they always suffer from the non-preservation of steady-state solution and original energy dissipation law. To overcome these disadvantages, some new integrating factor methods are developed by using two classes of difference correction, including the telescopic correction and nonlinear-term translation correction, enforcing the preservation of steady-state solution. Then the original energy dissipation properties of the new methods are examined by using the associated differential forms and the differentiation matrices. As applications, some new integrating factor Runge-Kutta methods up to third-order maintaining the original energy dissipation law are constructed by applying the difference correction strategies to some popular explicit integrating factor methods in the literature. Extensive numerical experiments are presented to support our theory and to demonstrate the improved performance of new methods.

math.NA↗

arXiv2024

Average energy dissipation rates of explicit exponential Runge-Kutta methods for gradient flow problems

We propose a unified theoretical framework to examine the energy dissipation properties at all stages of explicit exponential Runge-Kutta (EERK) methods for gradient flow problems. The main part of the novel framework is to construct the differential form of EERK method by using the difference coefficients of method and the so-called discrete orthogonal convolution kernels. As the main result, we prove that an EERK method can preserve the original energy dissipation law unconditionally if the associated differentiation matrix is positive semi-definite. A simple indicator, namely average dissipation rate, is also introduced for these multi-stage methods to evaluate the overall energy dissipation rate of an EERK method such that one can choose proper parameters in some parameterized EERK methods or compare different kinds of EERK methods. Some existing EERK methods in the literature are evaluated from the perspective of preserving the original energy dissipation law and the energy dissipation rate. Some numerical examples are also included to support our theory.

math.NA↗

arXiv2012

On exterior calculus and curvature in piecewise-flat manifolds

Simplicial, piecewise-flat discretizations of manifolds provide a clear path towards curvature analysis on discrete geometries and for solutions of PDE's on manifolds of complex topologies. In this manuscript we review and expand on discrete exterior calculus methods using hybrid domains. We then analyze the geometric structure of curvature operators in a piecewise-flat lattice.

math.DG↗