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Yuriy Povstenko, Tamara Kyrylych, Bozena Wozna-Szczesniak and Andrzej Yatsko
The central-symmetric time-fractional heat conduction equation with heat absorption is investigated in a solid with a spherical hole under time-harmonic heat flux at the boundary. The problem is solved using the auxiliary function, for which the Robin-ty...
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Tatiana Lazovskaya, Dmitriy Tarkhov, Maria Chistyakova, Egor Razumov, Anna Sergeeva and Tatiana Shemyakina
The article presents the development of new physics-informed evolutionary neural network learning algorithms. These algorithms aim to address the challenges of ill-posed problems by constructing a population close to the Pareto front. The study focuses o...
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Kwang-Leol Jeong, Sunho Park and Se-Min Jeong
When performing simulations using computational fluid dynamics, the grid systems in the viscous boundary layer regions are important because the velocity and pressure change very rapidly in these regions. Especially for the turbulent flows, thin grids sh...
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Ferenc Izsák and Taki Eddine Djebbar
We propose neural-network-based algorithms for the numerical solution of boundary-value problems for the Laplace equation. Such a numerical solution is inherently mesh-free, and in the approximation process, stochastic algorithms are employed. The chief ...
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Chengyan Wang, Yuanting Zou, Ji Huang and Chia-Ming Fan
The moving pseudo-boundary method of fundamental solutions (MFS) was employed to solve the Laplace equation, which describes the potential flow in a two-dimensional (2D) numerical wave tank. The MFS is known for its ease of programming and the advantage ...
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Nikolay Nefedov, Bogdan Tishchenko and Natalia Levashova
An algorithm is presented for the construction of an asymptotic approximation of a stable stationary solution to a diffusion equation system in a two-dimensional domain with a smooth boundary and a source function that is discontinuous along some smooth ...
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Alexander Köhler and Michael Breuß
The computation of correspondences between shapes is a principal task in shape analysis. In this work, we consider correspondences constructed by a numerical solution of partial differential equations (PDEs). The underlying model of interest is thereby t...
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Indranil Ghosh, Muhammad Mahbubur Rashid, Shukranul Mawa, Rupal Roy, Md Manjurul Ahsan, Muhammad Ramiz Uddin, Kishor Datta Gupta and Pallabi Ghosh
The human immunodeficiency virus (HIV) mainly attacks CD4+ T cells in the host. Chronic HIV infection gradually depletes the CD4+ T cell pool, compromising the host?s immunological reaction to invasive infections and ultimately leading to acquired immuno...
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Zhimin Zhou, Yawei Sun, Lifen Chen, Dezhi Ning and Sulisz Wojciech
In this paper, a two-dimensional time-domain numerical flume has been established to model and investigate nonlinear interactions between nonlinear surface waves and a submerged inclined thin plate. The model solves the Laplace equation and the fully non...
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Yuhao Guo, Yan Wang, Qiqi Hao and Tongguang Wang
An interface-corrected diffuse interface method is presented in this work for the simulation of incompressible multiphase flows with large density ratios. In this method, an interface correction term together with a mass correction term is introduced int...
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