Proximal gradient-based optimization is one of the most common strategies to solve inverse problem of images, and it is easy to implement. However, these techniques often generate heavy artifacts in image reconstructi...
详细信息
We propose a spectral viewpoint for grain boundaries that are generally quasiperiodic. To accurately capture the spectra computationally, it is crucial to adopt the projection method for quasiperiodic functions. Armed...
详细信息
Traditional transform optical devices are designed from anisotropic magnetic materials which are difficult to fabricate. In this paper, we design and simulate a conformal carpet invisible cloak and bending waveguide d...
详细信息
In this paper, we study the global optimality of polynomial portfolio optimization (PPO). The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters. We introduce a ...
详细信息
In [Dai et al, Multi. Model. Simul., 2020], a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn–Sham density functional theory, based on which a linearized method was dev...
详细信息
In this paper,we design a collocation method to solve the fractional Ginzburg-Landau equation.A Jacobi collocation method is developed and implemented in two ***,we space-discretize the equation by the Jacobi-Gauss-Lo...
详细信息
In this paper,we design a collocation method to solve the fractional Ginzburg-Landau equation.A Jacobi collocation method is developed and implemented in two ***,we space-discretize the equation by the Jacobi-Gauss-Lobatto collocation(JGLC)method in one-and two-dimensional *** equation is then converted to a system of ordinary differential equations(ODEs)with the time variable based on *** second step applies the Jacobi-Gauss-Radau collocation(JGRC)method for the time ***,we give a theoretical proof of convergence of this Jacobi collocation method and some numerical results showing the proposed scheme is an effective and high-precision algorithm.
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.
Among various algorithms of multifractal analysis (MFA) for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally ...
详细信息
Among various algorithms of multifractal analysis (MFA) for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive for MFA of large-scale networks with tens of millions of nodes. It is also not clear whether MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of networks, our CESA employs the compressed sparse row format of the adjacency matrix and the breadth-first search technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic to linear. Then the CESA is demonstrated to be effective, efficient, and feasible through the MFA results of (u,v)-flower model networks from the fifth to the 1.th generations. It enables us to study the multifractality of networks of the size of about 1. million nodes with a normal desktop computer. Furthermore, we have also found that increasing the size of (u,v)-flower model network does improve the accuracy of MFA results. Finally, our CESA is applied to a few typical real-world networks of large scale.
Image registration has played an important role in image processing problems, especially in medical imaging applications. It is well known that when the deformation is large, many variational models cannot ensure diff...
详细信息
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...
详细信息
暂无评论