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stability conditions AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS

Acta Mathematica Scientia 2023年第3期43卷 1007-1030页

作者：卢文轩 School of Mathematics and Statistics Yunnan UniversityKunming650091China

We study the space of stability conditions on K3 surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds(moduli). We find certain highly non-generic behaviors of marginal stability walls(a key notion in the study of wall crossings)in the space of stability conditions. These correspond via mirror symmetry to some nongeneric behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of the homological mirror conjecture and SYZ mirror conjecture.

关键词： mirror symmetry stability conditions K3 surfaces attractor mechanism

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stability conditions for Wave Simulation in 3-D Anisotropic Media with the Pseudospectral Method

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Communications in Computational Physics 2012年第8期12卷 703-720页

作者： Wensheng Zhang LSEC 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 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.

关键词： Wave simulation stability conditions 3-D anisotropic media pseudospectral method

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ON DISPERSION-CONTROLLED PRINCIPLES FOR NON-OSCILLATORY SHOCK-CAPTURING SCHEMES

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Acta Mechanica Sinica 2004年第1期20卷 1-15页

作者：姜宗林 Key Laboratory of High Temperature Gas Dynamics Chinese Academy of SciencesInstitute of MechanicsBeijing 100080China

The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long *** is only during the last two decades that extensive studies on the dispersion-controlled dissipative(DCD)schemes were *** studies have demonstrated that this kind of the schemes is distinct from conventional dissipation-based schemes in which the dispersion term of the modified equation is not considered in scheme construction to avoid nonphysical oscillation occurring in shock wave *** principle of the dispersion controlled aims at removing nonphysical oscillations by making use of dispersion characteristics instead of adding artificial viscosity to dissipate the oscillation as the conventional schemes *** progresses on the dispersion- controlled principles are reviewed in this paper,including the exploration of the role of dispersions in numerical simulations,the development of the dispersion-controlled principles,efforts devoted to high-order dispersion-controlled dissipative schemes,the extension to both the finite volume and the finite element methods,scheme verification and solution validation,and comments on several aspects of the schemes from author's viewpoint.

关键词： DCD schemes stability conditions numerical methods CFD validation

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Practical Absorbing Boundary conditions forWave Propagation on Arbitrary Domain

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Advances in Applied Mathematics and Mechanics 2020年第6期12卷 1384-1415页

作者： Fengru Wang Jerry Zhijian Yang Cheng Yuan School of Mathematics and Statistics Wuhan UniversityWuhanHubei 430072China Computational Science Hubei Key Laboratory Wuhan UniversityWuhanHubei 430072China

This paper presents an absorbing boundary conditions(ABCs)for wave propagations on arbitrary computational *** purpose of ABCs is to eliminate the unwanted spurious reflection at the artificial boundaries and minimize the finite size *** methods are usually complicate in theoretical derivation and implementation and work only for very limited types of boundary *** contrast to other existing methods,our emphasis is placed on the ease of *** particular,we propose a method for which the implementation can be done by fitting or learning from the simulation data in a larger domain,and it is insensitive to the geometry and space dimension of the computational ***,a stability criterion is imposed to ensure the stability of the proposed *** results are presented to demonstrate the effectiveness of our method.

关键词： Absorbing boundary condition wave equations stability conditions

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