We combine the newly constructed Galerkin difference basis with the energy-based discontinuous Galerkin method for wave equations in second-order *** approximation properties of the resulting method are excellent and ...
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We combine the newly constructed Galerkin difference basis with the energy-based discontinuous Galerkin method for wave equations in second-order *** approximation properties of the resulting method are excellent and the allowable time steps are large compared to traditional discontinuous Galerkin *** one drawback of the combined approach is the cost of inversion of the local mass *** demonstrate that for constant coefficient problems on Cartesian meshes this bottleneck can be removed by the use of a modified Galerkin difference *** variable coefficients or non-Cartesian meshes this technique is not possible and we instead use the preconditioned conjugate gradient method to iteratively invert the mass *** a careful choice of preconditioner we can demonstrate optimal complexity,albeit with a larger constant.
Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a...
Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: we reached about 5 x 10(4) simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reach the second order phase transition point, where the correlation length grows to infinity. We varied the gravitational constant, and we found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). We studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths. The heavy propagator geodesic appeared to be much smoother, so that the scaling laws were found, corresponding to finite fractal dimensions: D+ approximately 2.3 in the gravity phase and D- approximately 4.6 in the antigravity phase. Similar, but somewhat lower numbers were obtained from the heat kernel singularity. The influence of the alpha-R2 terms in 2, 3 and 4 dimensions is discussed.
The simplex algorithm is a widely used method for solving a linear programming problem (LP) which is first presented by George B. Dantzig. One of the important steps of the simplex algorithm is applying an appropriate...
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ISBN:
(纸本)9789881925336
The simplex algorithm is a widely used method for solving a linear programming problem (LP) which is first presented by George B. Dantzig. One of the important steps of the simplex algorithm is applying an appropriate pivot rule, the rule to select the entering variable. An effective pivot rule can lead to the optimal solution of LP with the small number of iterations. In a minimization problem, Dantzig's pivot rule selects an entering variable corresponding to the most negative reduced cost. The concept is to have the maximum improvement in the objective value per unit step of the entering variable. However, in some problems, Dantzig's rule may visit a large number of extreme points before reaching the optimal solution. In this paper, we propose a pivot rule that could reduce the number of such iterations over the Dantzig's pivot rule. The idea is to have the maximum improvement in the objective value function by trying to block a leaving variable that makes a little change in the objective function value as much as possible. Then we test and compare the efficacy of this rule with Dantzig' original rule.
The reproducing kernel particle method （RKPM） has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modele...
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The reproducing kernel particle method （RKPM） has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advectiondiffusion equation （FADE）, which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.
Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely t...
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Presents a study that investigated the asymptotic behavior of discrete solutions in comparison to the case of continuous solutions. Numerical representation of the problem; Details on the solution of explicit differen...
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Presents a study that investigated the asymptotic behavior of discrete solutions in comparison to the case of continuous solutions. Numerical representation of the problem; Details on the solution of explicit difference scheme for the corresponding nonlinear elliptic equations; Results and discussion.
We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independen...
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We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independent compensated Poisson random measure. A semi-discrete scheme is developed for discrete time approximation, which is constituted by a classic scheme for the forward SDE [20, 28] and a novel scheme for the backward SDE. Under some reasonable regularity conditions, we prove that the semi-discrete scheme can achieve second-order convergence in approximating the FBSDEs of interest; and such convergence rate does not require jump-adapted temporal discretization. Next, to add in spatial discretization, a fully discrete scheme is developed by designing accurate quadrature rules for estimating the involved conditional mathematical expectations. Several numerical examples are given to illustrate the effectiveness and the high accuracy of the proposed schemes.
A simplified relativistic configuration interaction method is used to study the dielectronic satellite transition processes,in which the whole high-n dielectronic satellite transition processes can be treated convenie...
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A simplified relativistic configuration interaction method is used to study the dielectronic satellite transition processes,in which the whole high-n dielectronic satellite transition processes can be treated conveniently in the frame of quantum defect *** theoretical results for heliumlike iron are in good agreement with the experimental measurements.
The Chahine-Twomey relaxation method for inversion of the atmospheric radiative transfer equation is extended to provide an inverse solution to Barrick's equation describing second order scatter of high frequency ...
The Chahine-Twomey relaxation method for inversion of the atmospheric radiative transfer equation is extended to provide an inverse solution to Barrick's equation describing second order scatter of high frequency (HF) radio waves from the ocean surface. The success of the method is demonstrated here using synthesised radar Doppler spectra obtained by solving the direct problem with wave buoy directional spectrum measurements. Wave buoy measurements are limited in the range of directional characteristics that can be measured. The results presented here suggest that HF radar is capable of providing a more general measurement of the directional spectrum.
Theoretically describing feature learning in neural networks is crucial for understanding their expressive power and inductive biases, motivating various approaches. Some approaches describe network behavior after tra...
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