In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic Runge-Kutta method(SRK). Two ...In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic Runge-Kutta method(SRK). Two fully implicit schemes are presented and their stability qualities are discussed. And the numerical report illustrates the better numerical behavior.展开更多
A parallel diagonally iterated Runge Kutta (PDIRK) method is constructed to solve stiff initial value problems for delay differential equations. The order and stability of this PDIRK method has been analyzed, and the ...A parallel diagonally iterated Runge Kutta (PDIRK) method is constructed to solve stiff initial value problems for delay differential equations. The order and stability of this PDIRK method has been analyzed, and the iteration parameters of the method are tuned in such a way that fast convergence to the value of corrector is achieved.展开更多
The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in ma...The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in many scale-resolving simulations of interests in computational science and engineering.The physical domain-based DGmethod can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on non-affinemeshes.When using the quadraturebased DG method,these advantages are overshadowed by severe computational costs on mixed-curved meshes,making implicit scale-resolving simulations unaffordable.To address this issue,the quadrature-free direct reconstruction method(DRM)is extended to the implicit DG method.In this approach,the generalized reconstruction approximates non-linear flux functions directly in the physical domain,making the computing-intensive numerical integrations precomputable at a preprocessing step.The DRM operator is applied to the residual computation in the matrix-free method.The DRM operator can be further extended to the system matrix computation for the matrix-explicit Krylov subspace method and preconditioning.Finally,the A-stable Rosenbrock-type Runge–Kutta methods are adopted to achieve high-order accuracy in time.Extensive verification and validation from the manufactured solution to implicit large eddy simulations are conducted.The computed results confirm that the proposed method significantly improves computational efficiency compared to the quadrature-based method while accurately resolving detailed unsteady flow features that are hardly captured by scale-modeled simulations.展开更多
Presents a study which dealt with stability of the implicit Runge-Kutta methods for the numerical solutions of the systems of delay differential equations. Stability behavior of the methods; Exponential solutions of t...Presents a study which dealt with stability of the implicit Runge-Kutta methods for the numerical solutions of the systems of delay differential equations. Stability behavior of the methods; Exponential solutions of the equations.展开更多
文摘In this paper, the Ito-Taylor expansion of stochastic differential equation is briefly introduced. The colored rooted tree theory is applied to derive strong order 1.0 implicit stochastic Runge-Kutta method(SRK). Two fully implicit schemes are presented and their stability qualities are discussed. And the numerical report illustrates the better numerical behavior.
基金Supported by Projects from NSF of China(10571147)Specialized Research Fund for Doctoral Programof Higher Education of China(20094301110001)+1 种基金NSF of Hunan Province (09JJ3002)Hunan Provincial Innovation Foundation for Postgraduate(S2008yjscx02)
文摘A parallel diagonally iterated Runge Kutta (PDIRK) method is constructed to solve stiff initial value problems for delay differential equations. The order and stability of this PDIRK method has been analyzed, and the iteration parameters of the method are tuned in such a way that fast convergence to the value of corrector is achieved.
基金the financial support provided by the Defense Acquisition Program Administration(DAPA)under Grant UD200046CD(Data-driven Flow Modeling Research Laboratory)the Korea Research Institute for defense Technology planning and advancement(KRIT)under Grant KRIT-CT-22-030(Reusable Unmanned Space Vehicle Research Center,2023)supported by the program of the National Research Foundation of Korea(NRF-2021R1A2C2008348).
文摘The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in many scale-resolving simulations of interests in computational science and engineering.The physical domain-based DGmethod can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on non-affinemeshes.When using the quadraturebased DG method,these advantages are overshadowed by severe computational costs on mixed-curved meshes,making implicit scale-resolving simulations unaffordable.To address this issue,the quadrature-free direct reconstruction method(DRM)is extended to the implicit DG method.In this approach,the generalized reconstruction approximates non-linear flux functions directly in the physical domain,making the computing-intensive numerical integrations precomputable at a preprocessing step.The DRM operator is applied to the residual computation in the matrix-free method.The DRM operator can be further extended to the system matrix computation for the matrix-explicit Krylov subspace method and preconditioning.Finally,the A-stable Rosenbrock-type Runge–Kutta methods are adopted to achieve high-order accuracy in time.Extensive verification and validation from the manufactured solution to implicit large eddy simulations are conducted.The computed results confirm that the proposed method significantly improves computational efficiency compared to the quadrature-based method while accurately resolving detailed unsteady flow features that are hardly captured by scale-modeled simulations.
文摘Presents a study which dealt with stability of the implicit Runge-Kutta methods for the numerical solutions of the systems of delay differential equations. Stability behavior of the methods; Exponential solutions of the equations.
