Applications and numerical convergence of the partial inverse method

The present paper introduces an accurate numerical procedure to assess the internal thermal energy generation in an annular porous-finned heat sink from the sole assessment of surface temperature profile using the golden section search technique. All possible heat transfer modes and temperature dependence of all thermal parameters are accounted for in the present nonlinear model. At first, the direct problem is numerically solved using the Runge–Kutta method, whereas for predicting the prevailing heat generation within a given generalized fin domain an inverse method is used with the aid of the golden section search technique. After simplifications, the proposed scheme is credibly verified with other methodologies reported in the existing literature. Numerical predictions are performed under different levels of Gaussian noise from which accurate reconstructions are observed for measurement error up to 20%. The sensitivity study deciphers that the surface temperature field in itself is a strong function of the surface porosity, and the same is controlled through a joint trade-off among heat generation and other thermo-geometrical parameters. The present results acquired from the golden section search technique-assisted inverse method are proposed to be suitable for designing effective and robust porous fin heat sinks in order to deliver safe and enhanced heat transfer along with significant weight reduction with respect to the conventionally used systems. The present inverse estimation technique is proposed to be robust as it can be easily tailored to analyse all possible geometries manufactured from any material in a more accurate manner by taking into account all feasible heat transfer modes.

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Phase-to-pattern inverse design paradigm for fast realization of functional metasurfaces via transfer learning

Nature Communications ◽

10.1038/s41467-021-23087-y ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Ruichao Zhu ◽

Tianshuo Qiu ◽

Jiafu Wang ◽

Sai Sui ◽

Chenglong Hao ◽

...

Keyword(s):

Transfer Learning ◽

Electromagnetic Waves ◽

Inverse Method ◽

Inverse Design ◽

Learning Network ◽

Design Paradigm ◽

Simulation And Experiment ◽

Meta Atom ◽

Trained Network ◽

Input Phase

AbstractMetasurfaces have provided unprecedented freedom for manipulating electromagnetic waves. In metasurface design, massive meta-atoms have to be optimized to produce the desired phase profiles, which is time-consuming and sometimes prohibitive. In this paper, we propose a fast accurate inverse method of designing functional metasurfaces based on transfer learning, which can generate metasurface patterns monolithically from input phase profiles for specific functions. A transfer learning network based on GoogLeNet-Inception-V3 can predict the phases of 28×8 meta-atoms with an accuracy of around 90%. This method is validated via functional metasurface design using the trained network. Metasurface patterns are generated monolithically for achieving two typical functionals, 2D focusing and abnormal reflection. Both simulation and experiment verify the high design accuracy. This method provides an inverse design paradigm for fast functional metasurface design, and can be readily used to establish a meta-atom library with full phase span.

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Quadrature Integration Techniques for Random Hyperbolic PDE Problems

Mathematics ◽

10.3390/math9020160 ◽

2021 ◽

Vol 9 (2) ◽

pp. 160

Author(s):

Rafael Company ◽

Vera N. Egorova ◽

Lucas Jódar

Keyword(s):

Numerical Methods ◽

Laplace Transform ◽

Quadrature Rule ◽

Inverse Laplace Transform ◽

Process Time ◽

Efficient Computation ◽

Hyperbolic Pde ◽

Numerical Convergence ◽

Laplace Transform Technique ◽

Integration Techniques

In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also its statistical moments. Hence, appropriate numerical methods should allow for the efficient computation of the expectation and variance. Here, we analyse different numerical methods around the inverse Laplace transform and its evaluation by using several integration techniques, including midpoint quadrature rule, Gauss–Laguerre quadrature and its extensions, and the Talbot algorithm. Simulations, numerical convergence, and computational process time with experiments are shown.

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