This paper reveals the inner links between two known frameworks of multisplitting relaxation methods as completely as possible. By meticulously investigating the specific structures of these two frameworks, the asympt...
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Abstract This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are give...
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Abstract This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are given to illustrate the efficiency of the method.
The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produ...
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The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.
A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplec...
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A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler-Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.
The "Large Scale scientific Computation (LSSC) Research"project is one of the state Major Basic Research projects funded by the Chinese Ministry of Science and Technology in the field ofinformation scien...
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The "Large Scale scientific Computation (LSSC) Research"project is one of the state Major Basic Research projects funded by the Chinese Ministry of Science and Technology in the field ofinformation science and technology.……
In this paper, we propose a new trust region affine scaling method for nonlinear programming with simple bounds. Our new method is an interior-point trust region method with a new scaling technique. The scaling matrix...
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Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of n...
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Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of nonmonotone line search is used. Under mildassumptions, we prove the global convergence of the method. Some numerical results arealso presented.
This paper is concerned with the construction of high order mass-lumping finite elements on simplexes and a program for computing mass-lumping finite elements on triangles and *** polynomial spaces for mass-lumping fi...
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This paper is concerned with the construction of high order mass-lumping finite elements on simplexes and a program for computing mass-lumping finite elements on triangles and *** polynomial spaces for mass-lumping finite elements,as proposed in the literature,are presented and *** particular,the unisolvence problem of symmetric point-sets for the polynomial spaces used in mass-lumping elements is addressed,and an interesting property of the unisolvent symmetric point-sets is observed and *** its theoretical proof is still lacking,this property seems to be true in general,and it can greatly reduce the number of cases to consider in the computations of mass-lumping elements.A program for computing mass-lumping finite elements on triangles and tetrahedra,derived from the code for computing numerical quadrature rules presented in [7],is *** mass-lumping finite elements on triangles found using this program with higher orders,namely 7,8 and 9,than those available in the literature are reported.
Two Armijo-type line searches are proposed in this paper for nonlinear conjugate gradient methods. Under these line searches, global convergence results are established for several famous conjugate gradient methods, i...
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Two Armijo-type line searches are proposed in this paper for nonlinear conjugate gradient methods. Under these line searches, global convergence results are established for several famous conjugate gradient methods, including the Fletcher-Reeves method, the Polak-Ribiere-Polyak method, and the conjugate descent method.
According to Lorenz, chaotic dynamic systems have sensitive dependence on initial conditions(SDIC), i.e., the butterfly-effect: a tiny difference on initial conditions might lead to huge difference of computer-gene...
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According to Lorenz, chaotic dynamic systems have sensitive dependence on initial conditions(SDIC), i.e., the butterfly-effect: a tiny difference on initial conditions might lead to huge difference of computer-generated simulations after a long time. Thus, computer-generated chaotic results given by traditional algorithms in double precision are a kind of mixture of "true"(convergent) solution and numerical noises at the same level. Today, this defect can be overcome by means of the "clean numerical simulation"(CNS) with negligible numerical noises in a long enough interval of time. The CNS is based on the Taylor series method at high enough order and data in the multiple precision with large enough number of digits, plus a convergence check using an additional simulation with even smaller numerical noises. In theory, convergent(reliable) chaotic solutions can be obtained in an arbitrary long(but finite) interval of time by means of the CNS. The CNS can reduce numerical noises to such a level even much smaller than micro-level uncertainty of physical quantities that propagation of these physical micro-level uncertainties can be precisely investigated. In this paper, we briefly introduce the basic ideas of the CNS, and its applications in long-term reliable simulations of Lorenz equation, three-body problem and Rayleigh-Bénard turbulent flows. Using the CNS, it is found that a chaotic three-body system with symmetry might disrupt without any external disturbance, say, its symmetry-breaking and system-disruption are "self-excited", i.e., out-of-nothing. In addition, by means of the CNS, we can provide a rigorous theoretical evidence that the micro-level thermal fluctuation is the origin of macroscopic randomness of turbulent flows. Naturally, much more precise than traditional algorithms in double precision, the CNS can provide us a new way to more accurately investigate chaotic dynamic systems.
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