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A New Approach to Analytical Modeling of Mars’s Magnetic Field 火星磁场分析建模的新方法
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2022-01-04 DOI: 10.1080/17415977.2021.2018427
I. E. Stepanova, T. Gudkova, A. Salnikov, A. Batov
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引用次数: 1
Recovery of thermal load parameters by means of the Monte Carlo method with fixed and meshless random walks 用蒙特卡罗方法恢复固定和无网格随机漫步的热负荷参数
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-12-24 DOI: 10.1080/17415977.2021.2016738
S. Milewski
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引用次数: 0
Solution of the Cauchy problem for the wave equation using iterative regularization 用迭代正则化方法求解波动方程的柯西问题
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-12-23 DOI: 10.1080/17415977.2021.1949590
M. Alosaimi, D. Lesnic, B. Johansson
We propose a regularization method based on the iterative conjugate gradient method for the solution of a Cauchy problem for the wave equation in one dimension. This linear but ill-posed Cauchy problem consists of finding the displacement and flux on a hostile and inaccessible part of the medium boundary from Cauchy data measurements of the same quantities on the remaining friendly and accessible part of the boundary. This inverse boundary value problem is recast as a least-squares minimization problem that is solved by using the conjugate gradient method whose iterations are stopped according to the discrepancy principle for obtaining stable reconstructions. The objective functional associated is proved Fréchet differentiable and a formula for its gradient is derived. The well-posed direct, adjoint and sensitivity problems present in the conjugate gradient method are solved by using a finite-difference method. Two numerical examples to illustrate the accuracy and stability of the proposed numerical procedure are thoroughly presented and discussed.
提出了一种基于迭代共轭梯度法的正则化方法,用于求解一维波动方程的柯西问题。这个线性但不适定的柯西问题包括从柯西数据测量的剩余友好和可达部分上的相同量的介质边界的敌对和不可达部分上的位移和通量。将该反边值问题转化为最小二乘最小化问题,采用共轭梯度法求解,并根据差异原理停止迭代以获得稳定的重构。证明了目标函数的可微性,并推导了目标函数的梯度公式。用有限差分法解决了共轭梯度法中存在的适定的直接、伴随和灵敏度问题。文中还详细讨论了两个数值算例,以说明所提出的数值计算方法的准确性和稳定性。
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引用次数: 4
A polarization tensor approximation for the Hessian in iterative solvers for non-linear inverse problems 非线性逆问题迭代求解中Hessian的偏振张量近似
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-12-23 DOI: 10.1080/17415977.2021.1951722
F. Watson, M. G. Crabb, W. Lionheart
For many inverse parameter problems for partial differential equations in which the domain contains only well-separated objects, an asymptotic solution to the forward problem involving ‘polarization tensors’ exists. These are functions of the size and material contrast of inclusions, thereby describing the saturation component of the non-linearity. In this paper, we show how such an asymptotic series can be applied to non-linear least-squares reconstruction problems, by deriving an approximate diagonal Hessian matrix for the data misfit term. Often, the Hessian matrix can play a vital role in dealing with the non-linearity, generating good update directions which accelerate the solution towards a global minimum, but the computational cost can make direct calculation infeasible. Since the polarization tensor approximation assumes sufficient separation between inclusions, our approximate Hessian does not account for non-linearity in the form of lack of superposition in the inverse problem. It does, however, account for the non-linear saturation of the change in the data with increasing material contrast. We, therefore, propose to use it as an initial Hessian for quasi-Newton schemes. We present numerical experimentation into the accuracy and reconstruction performance of the approximate Hessian for the case of electrical impedance tomography, providing a proof of principle of the reconstruction scheme.
对于许多只包含良好分离对象的偏微分方程的反参数问题,存在一个涉及“极化张量”的正问题的渐近解。这些是包裹体的大小和材料对比的函数,从而描述了非线性的饱和成分。在本文中,我们通过导出数据不拟合项的近似对角Hessian矩阵,证明了这种渐近级数如何应用于非线性最小二乘重构问题。通常,Hessian矩阵可以在处理非线性中发挥重要作用,产生良好的更新方向,使解加速到全局最小值,但计算成本使直接计算变得不可行的。由于极化张量近似假设包含物之间有足够的分离,我们的近似Hessian不考虑逆问题中缺乏叠加形式的非线性。然而,它确实解释了随着材料对比度的增加,数据变化的非线性饱和。因此,我们建议使用它作为准牛顿格式的初始Hessian。对电阻抗层析成像中近似Hessian的精度和重建性能进行了数值实验,证明了该重建方案的原理。
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引用次数: 1
Influence of Doppler broadening model accuracy in Compton camera list-mode MLEM reconstruction 多普勒展宽模型对康普顿相机表模MLEM重建精度的影响
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-12-12 DOI: 10.1080/17415977.2021.2011863
Yuemeng Feng, J. Létang, D. Sarrut, Voichia Maxim
The Compton camera is a gamma ray imaging device expected to provide clinically relevant images in the SPECT applications where collimated cameras are sub-optimal. Its imaging performances depend not only on the design of the detection system but also on choices related to tomographic reconstruction. The aim of this work is to show that the accuracy in modelling the acquisition largely influences the quality of the images. For this purpose, we restrict here to Doppler broadening models in conjunction with the list-mode maximum likelihood expectation maximization (LM-MLEM) algorithm. The study was carried out with Monte-Carlo simulation. We show that the reconstructed point spread function is location-dependent when the model is not accurate, and the usual elongation artefacts well-known in Compton camera imaging will appear. The model we propose allows us to reconstruct isolated point sources and more complex non-uniform sources with improved resolution even in the direction orthogonal to the camera.
康普顿相机是一种伽马射线成像设备,有望在SPECT应用中提供临床相关的图像,其中准直相机是次优的。其成像性能不仅取决于检测系统的设计,还取决于与层析重建相关的选择。这项工作的目的是表明,在建模采集的准确性在很大程度上影响图像的质量。为此,我们在此将多普勒展宽模型与列表模式最大似然期望最大化(LM-MLEM)算法结合使用。采用蒙特卡罗模拟方法进行了研究。结果表明,当模型不精确时,重构的点扩散函数是位置依赖的,并且会出现康普顿相机成像中常见的伸长伪影。我们提出的模型使我们能够重建孤立的点源和更复杂的非均匀源,即使在与相机正交的方向上也能提高分辨率。
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引用次数: 10
Data assimilation in 2D viscous Burgers equation using a stabilized explicit finite difference scheme run backward in time 利用稳定的显式有限差分格式对二维粘性Burgers方程进行数据同化
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-12-09 DOI: 10.1080/17415977.2021.2009476
A. Carasso
The 2D viscous Burgers equation is a system of two nonlinear equations in two unknowns, . This paper considers the data assimilation problem of finding initial values that can evolve into a close approximation to a desired target result , at some realistic T>0. Highly nonsmooth target data are considered, that may not correspond to actual solutions at time T. Such an ill-posed 2D viscous Burgers problem has not previously been studied. An effective approach is discussed and demonstrated based on recently developed stabilized explicit finite difference schemes that can be run backward in time. Successful data assimilation experiments are presented involving 8 bit, pixel grey-scale images, defined by nondifferentiable intensity data. An instructive example of failure is also included.
二维粘性Burgers方程是一个由两个未知数的两个非线性方程组成的系统。本文考虑了数据同化问题,即在一些现实的T>0下,寻找可以演变成与期望目标结果接近的初始值。考虑了高度非光滑的目标数据,这些数据可能与时间T的实际解不一致。这种不适定的2D粘性Burgers问题以前没有被研究过。基于最近开发的可在时间上向后运行的稳定显式有限差分格式,讨论并证明了一种有效的方法。成功的数据同化实验涉及由不可微分强度数据定义的8位像素灰度图像。还包括一个具有指导意义的失败例子。
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引用次数: 1
Identification of deformable droplets from boundary measurements: the case of non-stationary Stokes problem 从边界测量识别可变形液滴:非平稳Stokes问题
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-12-09 DOI: 10.1080/17415977.2021.2009475
C. Daveau, S. Bornhofen, A. Khelifi, Brice Naisseline
In this paper, we use asymptotic expansion of the velocity field to reconstruct small deformable droplets (i.e. their forms and locations) immersed in an incompressible Newtonian fluid. Here the fluid motion is assumed to be governed by the non-stationary linear Stokes system. Taking advantage of the smallness of the droplets, our asymptotic formula and identification methods extend those already derived for rigid inhomogeneity and for stationary Stokes system. Our derivations, based on dynamical boundary measurements, are rigorous and proved by involving the notion of viscous moment tensor VMT. The viability of our reconstruction approach is documented by numerical results.
在本文中,我们使用速度场的渐近展开来重建浸入不可压缩牛顿流体中的可变形小液滴(即它们的形式和位置)。这里假设流体运动由非平稳线性斯托克斯系统控制。利用液滴的小性,我们的渐近公式和识别方法扩展了已经导出的刚性不均匀性和稳态斯托克斯系统的渐近公式。基于动力学边界测量,我们的推导是严格的,并通过涉及粘性矩张量VMT的概念得到了证明。数值结果证明了我们重建方法的可行性。
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引用次数: 0
Identification of stationary source in the anomalous diffusion equation 异常扩散方程中平稳源的识别
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-11-21 DOI: 10.1080/17415977.2021.2000609
L. Su, V. Vasil'ev, T. Jiang, G. Wang
In this paper, we consider the initial-boundary value problem of determining the stationary right-hand side function in the anomalous diffusion equation with a Caputo fractional derivative with respect to time. The value of the solution of the problem at the final time moment is set as the overdetermination condition. In order to carry out the numerical solution, the iterative conjugate gradient method is used, while at each iteration a direct problem is solved by the finite-difference method using a purely implicit difference scheme. The computational experiment results for the model problem are presented to confirm the efficiency of this new method.
本文研究了具有Caputo分数阶导数的不规则扩散方程中确定平稳右侧函数的初边值问题。将问题在最终时刻的解的值设为超定条件。为了进行数值求解,采用迭代共轭梯度法,而在每次迭代中采用纯隐式差分格式的有限差分法求解一个直接问题。最后给出了模型问题的计算实验结果,验证了该方法的有效性。
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引用次数: 5
Inverse problems for a multi-term time fractional evolution equation with an involution 具有对合的多项时间分数演化方程的反问题
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-11-18 DOI: 10.1080/17415977.2021.2000606
Asim Ilyas, S. Malik, Summaya Saif
This paper focuses on considering two inverse source problems (ISPs) for a multi-term time-fractional evolution equation with an involution term, interpolating the heat and wave equations. The fractional derivatives are defined in Caputo's sense. The ISPs are proved to be ill-posed in the sense of Hadamard. Recovering a space dependent source term from over-specified data given at some time constitute the first ISP, while in the second ISP determination of a time dependent component of the source term is considered when over-specified condition of integral type is given. The solution of ISPs are constructed by using Fourier's method. The time-dependent components of the solutions are presented in terms of the multinomial Mittag-Leffler function. Under certain conditions, the solutions of ISPs for the multi-term time-fractional evolution equation are shown to be classical solutions. In addition, some particular examples are formulated to illustrate the obtained results for the ISPs.
本文主要考虑具有对合项的多项时间分数演化方程的两个逆源问题,插值热和波方程。分数阶导数是卡普托意义上的定义。在Hadamard的意义上,isp被证明是病态的。在第一个ISP中,从给定的某一时刻的过指定数据中恢复空间相关的源项,而在第二个ISP中,当给定整数型的过指定条件时,考虑源项的时间相关分量的确定。利用傅里叶方法构造了isp的解。解的时变分量用多项Mittag-Leffler函数表示。在一定条件下,证明了多项时间分数进化方程的ISPs解是经典解。此外,还制定了一些具体的例子来说明isp的所得结果。
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引用次数: 7
Call For Papers 征稿
IF 1.3 4区 工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2021-11-16 DOI: 10.1080/17415977.2021.2000666
G. Dulikravich
Inverse problems, design theories and multi-objective constrained optimization strategies are three areas of advanced research of great interest for practicing engineers and designers. These three major areas of research have a number of things in common. For example, manymethodologies for solving inverse problems employ optimization algorithms.On the other hand, optimization techniques generally do not employ methods of inverse design, although they could potentially reduce the number of time-consuming analysis required by the typical evolutionary optimization algorithms. Similarly, design theory is commonly not used by the optimization community, where formulation of the appropriate multiple objectives and system-of-systems design formulations are often performed using intuition and personal experience. The solution of inverse, design and optimization problems needs to cope with uncertainties in the mathematical model of the forward problem, in the numerical method of solution,metamodeling,measured data, boundary conditions, properties of themedia, and others. As a result, statistical techniques play a fundamental role in practical applications. The objective of this minisymposium is to offer a forum on inverse, design and optimization problems in heat transfer. Contributions are particularly welcome on novel applications, such as in biomedicine, small scale processes, high temperatures and high pressures, materials design, as well as on statistical solution techniques, like those within the Bayesian framework. DEADLINE FOR ABSTRACT SUBMISSION: December 10, 2021 George S. Dulikravich dulikrav@fiu.edu © 2021 Informa UK Limited, trading as Taylor & Francis Group
反问题、设计理论和多目标约束优化策略是实践工程师和设计师非常感兴趣的三个高级研究领域。这三个主要研究领域有许多共同点。例如,许多求解逆问题的方法都使用优化算法。另一方面,优化技术通常不采用逆设计方法,尽管它们可以潜在地减少典型进化优化算法所需的耗时分析的数量。类似地,设计理论通常不被优化社区使用,在优化社区中,适当的多目标和系统体系设计公式的制定通常使用直觉和个人经验来执行。逆问题、设计问题和优化问题的求解需要处理正向问题的数学模型、求解的数值方法、元模型、测量数据、边界条件、介质性质等方面的不确定性。因此,统计技术在实际应用中发挥着基础性作用。这个小型研讨会的目的是提供一个关于传热中的逆问题、设计问题和优化问题的论坛。在生物医学、小规模工艺、高温高压、材料设计以及统计求解技术(如贝叶斯框架内的技术)等新应用方面的贡献尤其受欢迎。摘要提交截止日期:2021年12月10日George S.Dulikravichdulikrav@fiu.edu©2021 Informa UK Limited,交易名称为Taylor&Francis Group
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引用次数: 0
期刊
Inverse Problems in Science and Engineering
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