We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probabil...
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We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probability of the explosion of fragments and the probability function of the velocity change of a surviving particle satisfy the corresponding physical conditions. Although the nonrelativistic Boltzmann-like equation modeling the universe fireworks is mathematically easy, this article leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness of the solution by means of methods taken from the famous work by DiPerna ＆ Lions about the Boltzmann equation. We also show both the regularity and the time-asymptotic behavior of solution to the Cauchy problem.
Understanding and predicting the properties of inorganic materials is crucial for accelerating advancements in materials science and driving applications in energy, electronics, and beyond. Integrating material struct...
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In this paper, we propose a new smooth function that possesses a property not satisfied by the existing smooth functions. Based on this smooth function, we discuss the existence and continuity of the smoothing path fo...
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In this paper, we propose a new smooth function that possesses a property not satisfied by the existing smooth functions. Based on this smooth function, we discuss the existence and continuity of the smoothing path for solving the P0 function nonlinear complementarity problem (NCP). Using the characteristics of the new smooth function, we investigate the boundedness of the iteration sequence generated by the non-interior continuation methods for solving the P0 function NCP under the assumption that the solution set of the NCP is nonempty and bounded. We show that the assumption that the solution set of the NCP is nonempty and bounded is weaker than those required by a few existing continuation methods for solving the NCP.
In this paper,we consider a kind of coupled nonlinear problem with Signorini contact *** solve this problem,we discuss a new coupling of finite element and boundary element by adding an auxiliary *** first derive an a...
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In this paper,we consider a kind of coupled nonlinear problem with Signorini contact *** solve this problem,we discuss a new coupling of finite element and boundary element by adding an auxiliary *** first derive an asymptotic error estimate of the approximation to the coupled FEM-BEM variational *** we design an iterative method for solving the coupled system,in which only three standard subproblems without involving any boundary integral equation are *** will be shown that the convergence speed of this iteration method is independent of the mesh size.
作者：
Shuo ZhangLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences
University of Chinese Academy of SciencesBeijing 100049China
This paper presents a nonconforming finite element scheme for the planar biharmonic equation,which applies piecewise cubic polynomials(P_(3))and possesses O(h^(2))convergence rate for smooth solutions in the energy no...
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This paper presents a nonconforming finite element scheme for the planar biharmonic equation,which applies piecewise cubic polynomials(P_(3))and possesses O(h^(2))convergence rate for smooth solutions in the energy norm on general shape-regular *** Dirichlet and Navier type boundary value problems are *** basis for the scheme is a piecewise cubic polynomial space,which can approximate the H^(4) functions with O(h^(2))accuracy in the broken H^(2) ***,a discrete strengthened Miranda-Talenti estimate(▽^(2)_(h)·,▽^(2)_(h)·)=(Δh·,Δh·),which is usually not true for nonconforming finite element spaces,is *** finite element space does not correspond to a finite element defined with Ciarlet’s triple;however,it admits a set of locally supported basis functions and can thus be implemented by the usual *** notion of the finite element Stokes complex plays an important role in the analysis as well as the construction of the basis functions.
作者：
Xuying ZhaoZhong-Ci ShiLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingNCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences
Capital Normal UniversityBeijing 100048China
Nonconforming grids with hanging nodes are frequently used in adaptive finite element comput at *** all earlier works on such methods,proper cons train ts should be enforced on degrees of freedom on edges/faces with h...
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Nonconforming grids with hanging nodes are frequently used in adaptive finite element comput at *** all earlier works on such methods,proper cons train ts should be enforced on degrees of freedom on edges/faces with hanging nodes to keep continuity,which yield numerical computations much *** 2014,Zhao et al.(2014)presented quadrilateral constraint-free finite element methods on quadrilateral grids with hanging *** paper further develops a hexahedral constraint-free finite element method on hexahedral grids with hanging nodes,which is of greater challenge than the two-dimensional ***-based a posteriori error reliability and efficiency are also established in this paper.
A conservative modification to the ghost fluid method(GFM)is developed for compressible multiphase *** motivation is to eliminate or reduce the conservation error of the GFM without affecting its *** track the conserv...
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A conservative modification to the ghost fluid method(GFM)is developed for compressible multiphase *** motivation is to eliminate or reduce the conservation error of the GFM without affecting its *** track the conservative variables near the material interface and use this information to modify the numerical solution for an interfacing cell when the interface has passed the *** modification procedure can be used on the GFM with any base *** this paper we use the fifth order finite difference WENO scheme for the spatial discretization and the third order TVD Runge-Kutta method for the time *** level set method is used to capture the *** experiments show that the method is at least mass and momentum conservative and is in general comparable in numerical resolution with the original GFM.
We propose Monte Carlo Nonlocal physics-informed neural networks(MC-Nonlocal-PINNs),which are a generalization of MC-fPINNs in *** et al.(*** ***.400(2022),115523)for solving general nonlocal models such as integral e...
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We propose Monte Carlo Nonlocal physics-informed neural networks(MC-Nonlocal-PINNs),which are a generalization of MC-fPINNs in *** et al.(*** ***.400(2022),115523)for solving general nonlocal models such as integral equations and nonlocal *** to MC-fPINNs,our MC-Nonlocal-PINNs handle nonlocal operators in a Monte Carlo way,resulting in a very stable approach for high dimensional *** present a variety of test problems,including high dimensional Volterra type integral equations,hypersingular integral equations and nonlocal PDEs,to demonstrate the effectiveness of our approach.
作者：
Xiaoying DaiLiwei ZhangAihui ZhouLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences
University of Chinese Academy of SciencesBeijing 100049China
To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure *** this paper,we propose and analyze a class of iteration schemes for the di...
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To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure *** this paper,we propose and analyze a class of iteration schemes for the discretized Kohn-Sham Density Functional Theory model,with which the iterative approximations are guaranteed to converge to the Kohn-Sham orbitals without any orthogonalization as long as the initial orbitals are orthogonal and the time step sizes are given *** addition,we present a feasible and efficient approach to get suitable time step sizes and report some numerical experiments to validate our theory.
作者：
Wensheng ZhangLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesP.O.Box Beijing 2719P.R.China
Simulation of elastic wave propagation has important applications in many areas such as inverse problemand geophysical *** this paper,stability conditions for wave simulation in 3-D anisotropic media with the pseudosp...
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Simulation of elastic wave propagation has important applications in many areas such as inverse problemand geophysical *** this paper,stability conditions for wave simulation in 3-D anisotropic media with the pseudospectral method are *** can be expressed explicitly by elasticity constants which are easy to be applied in *** 3-Dwave simulation for two typical anisotropic media,transversely isotropic media and orthorhombic media,are carried *** results demonstrate some satisfactory behaviors of the pseudospectral method.
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