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7,163 results on '"Guo, Xu"'

182. A short-memory operator splitting scheme for constant-Q viscoelastic wave equation

Author

Xiong, Yunfeng and Guo, Xu

Subjects
Mathematics - Numerical Analysis, Physics - Geophysics
Abstract

We propose a short-memory operator splitting scheme for solving the constant-Q wave equation, where the fractional stress-strain relation contains multiple Caputo fractional derivatives with order much smaller than 1. The key is to exploit its extension problem by converting the flat singular kernels into strongly localized ones, so that the major contribution of weakly singular integrals over a semi-infinite interval can be captured by a few Laguerre functions with proper asymptotic behavior. Despite its success in reducing both memory requirement and arithmetic complexity, we show that numerical accuracy under prescribed memory variables may deteriorate in time due to the dynamical increments of projection errors. Fortunately, it can be considerably alleviated by introducing a suitable scaling factor $\beta > 1$ and pushing the collocation points closer to origin. An operator splitting scheme is introduced to solve the resulting set of equations, where the auxiliary dynamics can be solved exactly, so that it gets rid of the numerical stiffness and discretization errors. Numerical experiments on both 1-D diffusive wave equation and 2-D constant-Q $P$- and $S$-wave equations are presented to validate the accuracy and efficiency of the proposed scheme.

Published
2021
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183. A mechanistic-based data-driven approach to accelerate structural topology optimization through finite element convolutional neural network (FE-CNN)

Author

Yue, Tianle, Yang, Hang, Du, Zongliang, Liu, Chang, Elkhodary, Khalil I., Tang, Shan, and Guo, Xu

Subjects
Computer Science - Machine Learning
Abstract

In this paper, a mechanistic data-driven approach is proposed to accelerate structural topology optimization, employing an in-house developed finite element convolutional neural network (FE-CNN). Our approach can be divided into two stages: offline training, and online optimization. During offline training, a mapping function is built between high and low resolution representations of a given design domain. The mapping is expressed by a FE-CNN, which targets a common objective function value (e.g., structural compliance) across design domains of differing resolutions. During online optimization, an arbitrary design domain of high resolution is reduced to low resolution through the trained mapping function. The original high-resolution domain is thus designed by computations performed on only the low-resolution version, followed by an inverse mapping back to the high-resolution domain. Numerical examples demonstrate that this approach can accelerate optimization by up to an order of magnitude in computational time. Our proposed approach therefore shows great potential to overcome the curse-of-dimensionality incurred by density-based structural topology optimization. The limitation of our present approach is also discussed.

Published
2021

184. Optimisation of spatially varying orthotropic porous structures based on conformal mapping

Author

Li, Shaoshuai, Zhu, Yichao, and Guo, Xu

Subjects
Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science
Abstract

In this article, a compliance minimisation scheme for designing spatially varying orthotropic porous structures is proposed. With the utilisation of conformal mapping, the porous structures here can be generated by two controlling field variables, the (logarithm of) the local scaling factor and the rotational angle of the matrix cell, and they are interrelated through the Cauchy-Riemann equations. Thus the design variables are simply reduced to the logarithm values of the local scaling factor on selected boundary points. Other attractive features shown by the present method are summarised as follows. Firstly, with the condition of total differential automatically met by the two controlling field variables, the integrability problem which necessitates post-processing treatments in many other similar methods can be resolved naturally. Secondly, according to the maximum principle for harmonic functions, the minimum feature size can be explicitly monitored during optimisation. Thirdly, the rotational symmetry possessed by the matrix cell can be fully exploited in the context of conformal mapping, and the computational cost for solving the cell problems for the homogenised elasticity tensor is maximally abased. In particular, when the design domain takes a rectangle shape, analytical expressions for the controlling fields are available. The homogenised results are shown, both theoretically and numerically, to converge to the corresponding fine-scale results, and the effectiveness of the proposed work is further demonstrated with more numerical examples.

Published
2021
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