The phase-field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) a...
The phase-field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to address the mesh size dependency of the model. However, existing AFEM approaches for this application frequently rely on heuristic adjustments and empirical parameters for mesh refinement. In this paper, we introduce an adaptive finite element method based on a recovery type posteriori error estimates approach grounded in theoretical analysis. This method transforms the gradient of the numerical solution into a smoother function space, using the difference between the recovered gradient and the original numerical gradient as an error indicator for adaptive mesh refinement. This enables the automatic capture of crack propagation directions without the need for empirical parameters. We have implemented this adaptive method for the Hybrid formulation of the phase-field model using the open-source software package FEALPy. The accuracy and efficiency of the proposed approach are demonstrated through simulations of classical 2D and 3D brittle fracture examples, validating the robustness and effectiveness of our implementation.
Due to the successful applications in engineering,physics,biology,finance,etc.,there has been substantial interest in fractional diffusion equations over the past few decades,and literatures on developing and analyzin...
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Due to the successful applications in engineering,physics,biology,finance,etc.,there has been substantial interest in fractional diffusion equations over the past few decades,and literatures on developing and analyzing efficient and accurate numerical methods for reliably simulating such equations are vast and fast *** paper gives a concise overview on finite element methods for these equations,which are divided into time fractional,space fractional and time-space fractional diffusion ***,we also involve some relevant topics on the regularity theory,the well-posedness,and the fast algorithm.
The research of two-level overlapping Schwarz (TL-OS) method based on constrained energy minimizing coarse space is still in its infancy, and there exist some defects, e.g. mainly for second order elliptic problem and...
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To address the limitations of the FDNA approach, in this paper, we analyze the dependency of the receiver node on the feeder nodes as well as the impact of the node's operability level on the system effectiveness,...
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In this paper we propose a new scaling method to study the Schur complements of SDD1 matrices. Its core is related to the non-negative property of the inverse M-matrix, while numerically improving the Quotient formula...
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In this paper, we present an arbitrarily high-order numerical scheme for the two-component Camassa–Holm system, ensuring the preservation of three invariants: energy and two Casimir functions. The spatial discretizat...
In this paper, we present an arbitrarily high-order numerical scheme for the two-component Camassa–Holm system, ensuring the preservation of three invariants: energy and two Casimir functions. The spatial discretization is achieved using Fourier–Galerkin methods, resulting in a semi-discrete system which retains a Hamiltonian structure and approximates the invariants of the original continuous system. Subsequently, an energy-preserving Runge–Kutta method, such as Hamiltonian boundary value methods, is applied to the semi-discrete system, yielding a fully discrete scheme of arbitrarily high order. The proposed scheme is validated through numerical simulations, demonstrating its accuracy and capability in capturing different types of solutions of the two-component Camassa–Holm equation.
In this paper, some new results on time-varying missile against a stationary target using pure proportional navigation (PPN) are developed in the planar interception problem. First, the relative motion equation is est...
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This paper considers a class of discontinuous Galerkin method,which is constructed by Wong-Zakai approximation with the orthonormal Fourier basis,for numerically solving nonautonomous Stratonovich stochastic delay dif...
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This paper considers a class of discontinuous Galerkin method,which is constructed by Wong-Zakai approximation with the orthonormal Fourier basis,for numerically solving nonautonomous Stratonovich stochastic delay differential *** prove that the discontinuous Galerkin scheme is strongly convergent:globally stable and analogously asymptotically stable in mean square *** addition,this method can be easily extended to solve nonautonomous Stratonovich stochastic pantograph differential *** tests indicate that the method has first-order and half-order strong mean square convergence,when the diffusion term is without delay and with delay,respectively.
The Hm-conforming virtual elements of any degree k on any shape of polytope in n with m, n ≥ 1 and k ≥ m are recursively constructed by gluing conforming virtual elements on faces in a universal way. For the lowest ...
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The concept of the spacecraft Reachable Domain (RD) has garnered significant scholarly attention due to its crucial role in space situational awareness and on-orbit service applications. While the existing research ha...
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The concept of the spacecraft Reachable Domain (RD) has garnered significant scholarly attention due to its crucial role in space situational awareness and on-orbit service applications. While the existing research has largely focused on single-impulse RD analysis, the challenge of Multi-Impulse RD (MIRD) remains a key area of interest. This study introduces a methodology for the precise calculation of spacecraft MIRD. The reachability constraints specific to MIRD are first formulated through coordinate transformations. Two restricted maneuvering strategies are examined. The derivation of two extremum conditions allows for determining the accessible orientation range and the nodes encompassing the MIRD. Subsequently, four nonlinear programming models are developed to address two types of MIRD by skillfully relaxing constraints using scale factors. Numerical results validate the robustness and effectiveness of the proposed approach, showing substantial agreement with Monte Carlo simulations and confirming its applicability to spacecraft on various elliptical orbits.
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