In geologically complex regions, the prestack depth migration is necessary in order to obtain accurate structure images. In this report, we discuss the prestack depth migration by finite-difference (FD) method and Fou...
作者：
秦孟兆李洪伟LSEC
Institute of Computational Mathematics and Scientific/Engineering Computing the Academy of Mathematics and Systems Sciences the Chinese Academy of Sciences Beijing China
In this article, we analyze and study under what conditions a source-free system has volumepreserving RK schemes. For linear systems, we give a comparatively thorough discussion about RK methods to be phase volume pr...
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In this article, we analyze and study under what conditions a source-free system has volumepreserving RK schemes. For linear systems, we give a comparatively thorough discussion about RK methods to be phase volume preserving integrators. We also analyze the relationship between volume-preserving integrators and symplectic integrators.
Based on the dual mixed variational formulation with three variants (stress, displacement, displacement on contact boundary) and the unilateral beaming problem of finite element discretization, an Uzawa type iterative...
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Based on the dual mixed variational formulation with three variants (stress, displacement, displacement on contact boundary) and the unilateral beaming problem of finite element discretization, an Uzawa type iterative algorithm is presented. The convergence of this iterative algorithm is proved, and then the efficiency of the algorithm is tested by a numerical example.
Given the power of large language and large vision models, it is of profound and fundamental interest to ask if a foundational model based on data and parameter scaling laws and pre-training strategies is possible for...
Deconvolution problem is a main topic in signal processing. Many practical applications are re-quired to solve deconvolution problems. An important example is image reconstruction. Usually, researcherslike to use regu...
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Deconvolution problem is a main topic in signal processing. Many practical applications are re-quired to solve deconvolution problems. An important example is image reconstruction. Usually, researcherslike to use regularization method to deal with this problem. But the cost of computation is high due to thefact that direct methods are used. This paper develops a trust region-cg method, a kind of iterative methodsto solve this kind of problem. The regularity of the method is proved. Based on the special structure of thediscrete matrix, FFT can be used for calculation. Hence combining trust region-cg method with FFT is suitablefor solving large scale problems in signal processing.
The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the i...
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The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the initialproblem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initialproblems of Nizhnich and the Nizhnich-Novikov-Veselov equations are solved by using this approach.
The three-dimensional compressible Navier-Stokes equations are approximated by a fifth order upwind compact and a sixth order symmetrical compact difference relations combined with three-stage Ronge-Kutta method. The ...
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The three-dimensional compressible Navier-Stokes equations are approximated by a fifth order upwind compact and a sixth order symmetrical compact difference relations combined with three-stage Ronge-Kutta method. The computed results are presented for convective Mach numberMc = 0.8 andRe = 200 with initial data which have equal and opposite oblique waves. From the computed results we can see the variation of coherent structures with time integration and full process of instability, formation of A -vortices, double horseshoe vortices and mushroom structures. The large structures break into small and smaller vortex structures. Finally, the movement of small structure becomes dominant, and flow field turns into turbulence. It is noted that production of small vortex structures is combined with turning of symmetrical structures to unsymmetrical ones. It is shown in the present computation that the flow field turns into turbulence directly from initial instability and there is not vortex pairing in process of transition. It means that for large convective Mach number the transition mechanism for compressible mixing layer differs from that in incompressible mixing layer.
The simulation of wave propagation has important applications in many problems such as in computational seismology. Here, we focus on boundary absorbing computations in wave simulation with the finite element method o...
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作者：
GUO YixiaoMING PingbingLSEC
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
The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architectu...
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The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.
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