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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This paper focuses on designing a lowest-order divergence-free virtual element method for solving Navier-Stokes equations with a nonlinear damping term on polygonal meshes. The exact divergence-free property of virtua...
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This paper focuses on designing a lowest-order divergence-free virtual element method for solving Navier-Stokes equations with a nonlinear damping term on polygonal meshes. The exact divergence-free property of virtual space preserves the mass-conservation of the system. With the application of Helmholtz projection, we provide stability estimates regarding the velocity. An optimal convergence estimate is derived, showing that the error estimate for the velocity in energy norm is pressure-independent. Finally, we perform various numerical simulations to validate the accuracy of our theoretical findings.
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.
Although existing deep learning compressed-sensing-based Magnetic Resonance Imaging (CS-MRI) methods have achieved considerably impressive performance, explainability and generalizability continue to be challenging fo...
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In this paper, we develop a residual-type a posteriori error estimation for an interior penalty virtual element method (IPVEM) for the Kirchhoff plate bending problem. Building on the work in Feng and Yu (2024), we ad...
In this paper, we develop a residual-type a posteriori error estimation for an interior penalty virtual element method (IPVEM) for the Kirchhoff plate bending problem. Building on the work in Feng and Yu (2024), we adopt a modified discrete variational formulation that incorporates the H 1 -elliptic projector in the jump and average terms. This allows us to simplify the numerical implementation by including the H 1 -elliptic projector in the computable error estimators. We derive the reliability and efficiency of the a posteriori error bound by constructing an enriching operator and establishing some related error estimates that align with C 0 -continuous interior penalty finite element methods. As observed in the a priori analysis, the interior penalty virtual elements exhibit similar behaviors to C 0 -continuous elements despite its H 1 -nonconforming. This observation extends to the a posteriori estimate since we do not need to account for the jumps of the function itself in the discrete scheme and the error estimators. As an outcome of the error estimator, an adaptive VEM is introduced by means of the mesh refinement strategy with the one-hanging-node rule. Numerical results from several benchmark tests confirm the robustness of the proposed error estimators and show the efficiency of the resulting adaptive VEM.
This article focuses on the development of high-order energy stable schemes for the multi-length-scale incommensurate phase-field crystal model which is able to study the phase behavior of aperiodic structures. These ...
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