Solving Nonlinear Elliptic Inverse Source, Coefficient and Conductivity Problems by the Methods with Bases Satisfying the Boundary Conditions Automatically

Liu, Chein‐Shan; Qiu, Lin

doi:10.1007/s10915-023-02167-9

J Sci Comput

2023

DOI: 10.1007/s10915-023-02167-9

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Solving Nonlinear Elliptic Inverse Source, Coefficient and Conductivity Problems by the Methods with Bases Satisfying the Boundary Conditions Automatically

Chein‐Shan Liu

Lin Qiu

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2023

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Cited by 3 publications

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References 32 publications

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“…Balancing accuracy and computational cost is crucial for practical applications, large-scale and long-time simulations. To overcome some of these difficulties, various meshless methods 18,[23][24][25][26][27][28][29] are conceived and developed rapidly, and proved to be advantageous for addressing many engineering problems. Similar to the FDM, FEM, and BEM, meshless methods defined in space domain need to resort to temporal discretization schemes for simulating dynamic problems.…”

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confidence: 99%

Modified space‐time radial basis function collocation method for long‐time simulation of transient heat conduction in3Danisotropic composite materials

Qiu

Wang

et al. 2023

Numerical Meth Engineering

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In this paper, the standard and the localized space‐time radial basis function (RBF) collocation methods are modified and combined with the time‐marching scheme and space‐time domain decomposition technique for simulating the long‐time transient heat conduction in 3D anisotropic composite materials. In the proposed approaches, we set the source points outside the whole space‐time domain in the standard space‐time RBF collocation method or outside the established subdomain in the localized approach by introducing the space and time magnification factors, instead of distributing them inside the original domain. In addition, the space‐time regulating factor is defined and added to the conventional schemes to improve the stability of numerical methods. The modified approaches are resulted in a simple and effective time‐marching process which can achieve long‐time simulation, resting on the property that the coefficient matrices generated by these two methods are only related to the space‐time distance between the collocation points and source points. Our ultimate aim is to develop a computing system for resolving dynamic problems in composite materials by designing a space‐time domain decomposition technique. Numerical experiments are conducted to demonstrate the accuracy, efficiency and stability of the presented methodologies.

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mentioning

confidence: 99%

Modified space‐time radial basis function collocation method for long‐time simulation of transient heat conduction in3Danisotropic composite materials

Qiu

Wang

et al. 2023

Numerical Meth Engineering

Self Cite

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Nonlinear Cauchy/Robin inverse problems solved by an optimal splitting-linearizing method

Liu

Chang

2023

International Journal of Heat and Mass Transfer

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Multi-domain physics-informed neural networks for solving transient heat conduction problems in multilayer materials

Zhang

Wang

Qiu

2023

Journal of Applied Physics

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In this paper, we aim to numerically resolve linear and nonlinear transient heat conduction problems in multilayer composite materials using a deep learning method called multi-domain physics-informed neural networks (MDPINNs). For this purpose, the multilayer media are first divided into independent sub-domains based on domain decomposition technique. The single-layer deep neural networks are first established, and each sub-domain has its corresponding sub-network. Then, each two sub-networks are connected by continuity conditions on the interface to form a MDPINNs’ framework that can directly solve the transient heat conduction problem in multilayer media. The temperature distribution in the computational domain can be obtained by training the MDPINNs, including the temperature values on the interface. A series of numerical experiments are carried out to verify that the proposed framework can achieve satisfactory accuracy, including in micrometer or even nanometer structures. Compared with conventional methods, the MDPINNs have the advantage of directly solving both linear and nonlinear heat conduction problems in multilayer materials in a unified and concise form.

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Solving Nonlinear Elliptic Inverse Source, Coefficient and Conductivity Problems by the Methods with Bases Satisfying the Boundary Conditions Automatically

Cited by 3 publications

References 32 publications

Modified space‐time radial basis function collocation method for long‐time simulation of transient heat conduction in3Danisotropic composite materials

Modified space‐time radial basis function collocation method for long‐time simulation of transient heat conduction in3Danisotropic composite materials

Nonlinear Cauchy/Robin inverse problems solved by an optimal splitting-linearizing method

Multi-domain physics-informed neural networks for solving transient heat conduction problems in multilayer materials

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