Numerical Analysis and Applications最新文献

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Monte Carlo Method for Numerical Simulation of Solar Energy Radiation Transfer in Crystal Clouds 蒙特卡洛法数值模拟晶体云中的太阳能辐射传输

IF 0.3 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications

Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020046

B. A. Kargin, E. G. Kablukova, Q. Mu, S. M. Prigarin

Abstract

The paper deals with numerical simulations related to radiation transfer in ice clouds. A mathematical model of crystal particles of irregular shape and an algorithm for modeling such particles based on constructing a convex hull of a set of random points are considered. Two approaches to simulating radiation transfer in optically anisotropic clouds are studied. One approach uses pre-calculated scattering phase functions for crystals of various shapes and orientations. In the other approach, no knowledge of phase functions is required; the radiation scattering angle is simulated directly at interaction of a photon with faces of crystal. This approach enables simple adjustment of the input parameters of the problem to changing microphysical characteristics of the environment, including the shape, orientation, and transparency of particles and roughness of their boundaries, and does not require time-consuming pre-calculations. The impact of flutter on the radiation transfer by the cloud layer and angular distributions of the reflected and transmitted radiation are studied.

摘要本文涉及与冰云中辐射传递有关的数值模拟。文中考虑了不规则形状晶体颗粒的数学模型，以及基于构建一组随机点凸壳的此类颗粒建模算法。研究了模拟光学各向异性云中辐射传递的两种方法。一种方法使用预先计算好的不同形状和方向晶体的散射相位函数。另一种方法则不需要相位函数知识，而是直接模拟光子与晶体表面相互作用时的辐射散射角。这种方法可以根据不断变化的环境微物理特性（包括颗粒的形状、取向和透明度以及颗粒边界的粗糙度）对问题的输入参数进行简单调整，而且不需要耗时的预先计算。研究了飘动对云层辐射传输以及反射和透射辐射角度分布的影响。

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引用次数: 0

Monte Carlo Simulation of Wide-Angle Lidar Signals 宽角度激光雷达信号的蒙特卡罗模拟

IF 0.3 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications

Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020083

S. M. Prigarin, D. E. Mironova

Abstract

The paper deals with Monte Carlo modeling of spatiotemporal signals of wide-angle lidars for probing atmospheric clouds. Using computational experiments, we study the features of lidar signals for monostatic and bistatic sensing schemes which make it possible to analyze the optical and microphysical properties of the cloud environment. When probing thin cloud layers, the lidar signal looks like an expanding and attenuating light ring. It is shown that for a bistatic scheme a second ring, which appears for a short time inside the main one, is characteristic of the lidar signal.

摘要本文涉及用于探测大气云层的广角激光雷达时空信号的蒙特卡罗建模。通过计算实验，我们研究了单静态和双静态传感方案下激光雷达信号的特征，这使得分析云环境的光学和微物理特性成为可能。在探测薄云层时，激光雷达信号看起来像一个膨胀和衰减的光环。研究表明，在双静态方案中，激光雷达信号的特征是在主光环内短时间出现第二个光环。

引用次数: 0

On the Influence of Random Environmental Factors on Heat Transfer Processes in Aircraft 随机环境因素对飞机传热过程的影响

IF 0.3 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications

Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020034

S. A. Gusev, V. N. Nikolaev

Abstract

The main goal of the work is to simulate heat transfer in structural elements of an aircraft under random temperature changes of its outer surface due to rapid changes in environmental parameters. In this case, to model the heat transfer a one-dimensional boundary value problem of the third kind is taken for the heat conduction equation. Random disturbances are specified at the boundary corresponding to the outer surface. The numerical solution is based on an application of a Galerkin method. Modeling the random disturbances of the external environment is carried out using a Wiener integral in a system of differential equations written in integral form. Calculations for a problem with a known exact solution show that when moving away from the boundary with random disturbances, the numerical solution of the boundary value problem with disturbances converges to the known exact solution of the undisturbed boundary value problem. Based on an expansion of the solution to the boundary value problem in trigonometric functions, theoretical estimates are obtained for the influence of a disturbance on the outer surface as a function of the wall thickness and the disturbance magnitude.

摘要这项工作的主要目标是模拟飞机外表面温度因环境参数快速变化而发生随机变化时结构元件的热传导情况。在这种情况下，热传导方程采用第三类一维边界值问题来模拟热传导。在与外表面相对应的边界上指定了随机扰动。数值解法基于 Galerkin 方法的应用。外部环境随机扰动的建模是在以积分形式书写的微分方程系统中使用维纳积分进行的。对已知精确解的计算表明，当远离有随机扰动的边界时，有扰动边界值问题的数值解趋近于未受扰动边界值问题的已知精确解。根据三角函数对边界值问题解的扩展，得到了扰动对外表面影响的理论估计值，它是壁厚和扰动大小的函数。

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引用次数: 0

Efficiently Realized Approximate Models of Random Functions in Stochastic Problems of the Theory of Particle Transfer 粒子转移理论随机问题中高效实现的随机函数近似模型

IF 0.3 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications

Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020058

G. A. Mikhailov, G. Z. Lotova, I. N. Medvedev

Abstract

The paper presents efficiently realized approximations of random functions, which have been developed by the authors and are numerically simulated for study of stochastic processes of particle transfer, including the problems of process criticality fluctuations in random media with multiplication. Efficient correlation-randomized algorithms are constructed for approximating an ensemble of particle trajectories using a correlation function or only a correlation scale of medium. A simple grid model of an isotropic random field is formulated, which reproduces a given average correlation length. This ensures high accuracy in solving stochastic transfer problems for a small correlation scale. The algorithms are tested by solving a test problem of photon transfer and a problem of estimating the overexponential average particle flux in a random medium with multiplication.

摘要本文介绍了有效实现的随机函数近似值，这些近似值由作者开发并进行了数值模拟，用于研究粒子转移的随机过程，包括随机介质中的过程临界波动问题。构建了高效的相关随机算法，用于使用相关函数或仅使用介质的相关尺度来近似粒子轨迹集合。还制定了各向同性随机场的简单网格模型，该模型可再现给定的平均相关长度。这确保了在解决小相关尺度随机转移问题时的高精确度。通过解决光子传输的测试问题和估计随机介质中超指数平均粒子通量的乘法问题，对算法进行了测试。

引用次数: 0

Rosenbrock-Type Methods for Solving Stochastic Differential Equations 求解随机微分方程的罗森布洛克式方法

IF 0.3 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications

Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020010

T. A. Averina, K. A. Rybakov

Abstract

This paper reviews recent publications that describe mathematical models with stochastic differential equations (SDEs) and applications in various fields. The purpose of this paper is to briefly describe Rosenbrock-type methods for approximate solution of SDEs. It shows how the performance of the numerical methods can be improved and the accuracy of calculations can be increased without increasing the implementation complexity too much. The paper also proposes a new Rosenbrock-type method for SDEs with multiplicative non-commutative noise. Its testing is carried out by modeling rotational diffusion.

摘要本文回顾了最近发表的有关随机微分方程（SDE）数学模型及其在各个领域应用的文章。本文旨在简要介绍用于近似求解 SDE 的 Rosenbrock 型方法。它说明了如何在不增加太多实现复杂性的情况下，改善数值方法的性能并提高计算精度。论文还针对具有乘法非交换噪声的 SDE 提出了一种新的 Rosenbrock 型方法。通过建立旋转扩散模型对该方法进行了测试。

引用次数: 0

Stochastic Simulation Algorithm for Solving the System of Lame Equations for Two- and Three-Dimensional Domains by Combining the Slobodianskii Representation, the Method of Fundamental Solutions and a Stochastic Projection Method 结合斯洛博迪安斯基表示法、基本解法和随机投影法求解二维和三维域拉姆方程组的随机模拟算法

IF 0.3 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications

Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020095

K. K. Sabelfeld, D. D. Smirnov

Abstract

In this paper, a new stochastic algorithm for solving the system of Lame equations based on the Slobodianskii representation is proposed, in which the recovery of boundary conditions for the harmonic functions involved is carried out implicitly using the method of fundamental solutions, while the unknown coefficients in this method are calculated using a stochastic projection method. Results of numerical experiments for several examples of two- and three-dimensional boundary value problems are presented, which demonstrate the high efficiency of the proposed method.

摘要本文提出了一种基于 Slobodianskii 表示法求解 Lame 方程系统的新随机算法，其中利用基解法隐式地恢复所涉及谐函数的边界条件，而该方法中的未知系数则利用随机投影法计算。文中给出了几个二维和三维边界值问题实例的数值实验结果，证明了所提方法的高效性。

引用次数: 0

Analyzing the Semilocal Convergence of a Fourth-Order Newton-Type Scheme with Novel Majorant and Average Lipschitz Conditions 分析四阶牛顿式方案的半局部收敛与新的主要和平均 Lipschitz 条件

IF 0.3 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications

Pub Date : 2024-03-13 DOI: 10.1134/s1995423924010026

J. P. Jaiswal

Abstract

The main focus of this paper is the analysis of the semilocal convergence (S.C.) of a three-step Newton-type scheme (TSNTS) used for finding the solution of nonlinear operators in Banach spaces (B.S.). A novel S.C. analysis of the TSNTS is introduced, which is based on the assumption that a generalized Lipschitz condition (G.L.C.) is satisfied by the first derivative of the operator. The findings contribute to the theoretical understanding of TSNTS in B.S. and have practical implications in various applications, such as integral equation further validating our results.

摘要本文的重点是分析用于寻找巴拿赫空间（B.S.）中非线性算子解的三步牛顿型方案（TSNTS）的半局部收敛性（S.C.）。本文引入了对 TSNTS 的新颖 S.C. 分析，该分析基于算子一阶导数满足广义 Lipschitz 条件 (G.L.C.) 的假设。这些发现有助于从理论上理解 B.S.中的 TSNTS，并在各种应用中具有实际意义，例如积分方程进一步验证了我们的结果。

引用次数: 0

Sensitivity of Functionals to Input Data in a Variational Assimilation Problem for a Sea Thermodynamics Model 海洋热力学模型变量同化问题中函数对输入数据的敏感性

IF 0.3 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications

Pub Date : 2024-03-13 DOI: 10.1134/s1995423924010087

V. P. Shutyaev, E. I. Parmuzin

Abstract

A problem of variational data assimilation for a sea thermodynamics model is considered, with the aim to reconstruct sea surface heat fluxes taking into account the covariance matrices of input data errors. The sensitivity of some solution functionals to input data in this problem of variational assimilation is studied, and the results of numerical experiments for a model of dynamics of the Baltic Sea are presented.

摘要考虑了海洋热力学模型的变异数据同化问题，目的是在考虑输入数据误差协方差矩阵的情况下重建海面热通量。研究了变分同化问题中某些解函数对输入数据的敏感性，并介绍了波罗的海动力学模型的数值实验结果。

引用次数: 0

A Difference Scheme for Wave Equation 波方程的差分方案

IF 0.3 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications

Pub Date : 2024-03-13 DOI: 10.1134/s1995423924010063

A. F. Mastryukov

Abstract

The paper deals with a numerical solution of a wave equation. The solution algorithm uses optimal parameters which are obtained by using Laguerre transform in time for the wave equation. Additional parameters are introduced into a difference scheme of 2nd-order approximation for the equation. The optimal values of these parameters are obtained by minimizing the error of a difference approximation of the Helmholtz equation. Applying the inverse Laguerre transform in the equation for harmonics, a differential-difference wave equation with the optimal parameters is obtained. This equation is difference in the spatial variables and differential in time. An iterative algorithm for solving the differential-difference wave equation with the optimal parameters is proposed. The results of numerical calculations of the differential-difference equations for 2-dimensional and 1-dimensional versions of the equation are presented. It is shown that the difference schemes with the optimal parameters give an increase in the accuracy of solving the equations.

摘要本文涉及波方程的数值求解。求解算法使用了通过对波方程进行拉盖尔时间变换而获得的最佳参数。方程的二阶近似差分方案中引入了附加参数。这些参数的最佳值是通过最小化亥姆霍兹方程差分近似的误差获得的。在谐波方程中应用反拉盖尔变换，就能得到具有最佳参数的微分-差分波方程。该方程在空间变量上是差分的，在时间上是微分的。提出了一种求解具有最佳参数的微分-差分波方程的迭代算法。介绍了二维和一维微分-差分方程的数值计算结果。结果表明，采用最优参数的差分方案提高了方程的求解精度。

引用次数: 0

On the Fourth Order Accurate Interpolation Operator for the Difference Solution of the 3-Dimensional Laplace Equation 论三维拉普拉斯方程差分解的四阶精确插值算子

IF 0.3 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications

Pub Date : 2024-03-13 DOI: 10.1134/s1995423924010038

A. A. Dosiyev, E. Celiker

Abstract

A three-dimensional (3D) matching operator is proposed for the fourth-order accurate solution of the Dirichlet problem of Laplace’s equation in a rectangular parallelepiped. The operator is constructed based on homogeneous, orthogonal-harmonic polynomials in three variables, and employs the cubic grid difference solution of the problem for the approximate solution inbetween the grid nodes. The difference solution on the nodes used by the interpolation operator is calculated by a novel formula, developed on the basis of the discrete Fourier transform. This formula can be applied on the required nodes directly, without requiring the solution of the whole system of difference equations. The fourth-order accuracy of the constructed numerical tools are demonstrated further through a numerical example.

摘要提出了一种三维（3D）匹配算子，用于四阶精确求解矩形平行六面体中拉普拉斯方程的 Dirichlet 问题。该算子基于三变量的同次正交谐波多项式构建，并采用问题的立方网格差分解作为网格节点之间的近似解。插值算子使用的节点上的差分解是通过一个基于离散傅立叶变换的新公式计算出来的。该公式可直接应用于所需节点，而无需求解整个差分方程系统。通过一个数值示例，进一步证明了所构建的数值工具的四阶精度。

引用次数: 0

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