Search Results - domain decomposition for initial value and initial-boundary value problems involving pre

Review of Physics-Informed Neural Networks: Challenges in Loss Function Design and Geometric Integration.

Authors: Plankovskyy, Sergiy Tsegelnyk, Yevgen Shyshko, Nataliia et al.

Source: Mathematics (2227-7390); Oct2025, Vol. 13 Issue 20, p3289, 51p

Subject Terms: PARTIAL differential equations, BOUNDARY value problems, INTEGRALS, SIMULATION software, ENGINEERING models, COST functions, MACHINE learning

A pretraining domain decomposition method using artificial neural networks to solve elliptic PDE boundary value problems.

Authors: Seo, Jeong-Kweon

Source: Scientific Reports; 10/14/2022, Vol. 12 Issue 1, p1-16, 16p

Subject Terms: DOMAIN decomposition methods, BOUNDARY value problems, PARTIAL differential equations, ARTIFICIAL neural networks, DECOMPOSITION method, MACHINE learning

FER/SubDomain: An Integrated Environment for Finite Element Analysis using Object-Oriented Approach: FER/SubDomain: An integrated environment for finite element analysis using object-oriented approach.

Authors: Feng, Zhi-Qiang Cros, Jean-Michel Davesne, Frédéric

Contributors: Feng, Zhi-Qiang Cros, Jean-Michel Davesne, Frédéric

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 36:773-781

Subject Terms: Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.), domain decomposition, Finite element methods applied to problems in solid mechanics, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, graphical interface, Computer graphics, computational geometry (digital and algorithmic aspects), 0211 other engineering and technologies, object-oriented programming, Object-oriented programming, 02 engineering and technology, 0101 mathematics, [SPI.MECA] Engineering Sciences [physics]/Mechanics [physics.med-ph], 01 natural sciences

File Description: application/xml

Access URL: https://www.esaim-m2an.org/articles/m2an/pdf/2002/05/m2anns7.pdf
https://www.esaim-m2an.org/articles/m2an/pdf/2002/05/m2anns7.pdf
https://www.esaim-m2an.org/articles/m2an/abs/2002/05/m2anns7/m2anns7.html
http://www.esaim-m2an.org/articles/m2an/pdf/2002/05/m2anns7.pdf
http://archive.numdam.org/ARCHIVE/M2AN/M2AN_2002__36_5/M2AN_2002__36_5_773_0/M2AN_2002__36_5_773_0.pdf
https://eudml.org/doc/194125
http://archive.numdam.org/article/M2AN_2002__36_5_773_0.pdf
https://hal.science/hal-01179969v1
https://doi.org/10.1051/m2an:2002044

Spectral methods for hyperbolic initial boundary value problems on parallel computers

Authors: Pravir Dutt Smita Bedekar

Source: Journal of Computational and Applied Mathematics. 134:165-190

Subject Terms: Iterative numerical methods for linear systems, Parallel pre-conditioners, Error estimates for the analytic case, Applied Mathematics, Exponential accuracy, Numerical computation of matrix norms, conditioning, scaling, initial boundary value problems, Galerkin-Collocation method, p and h–p versions of FEM, Energy estimates on multidomains, Parallel numerical computation, 01 natural sciences, Domain decomposition methods, Computational Mathematics, preconditioning, linear hyperbolic systems, spectral methods, conjugate gradient method, Symmetric formulation, Initial value problems for first-order hyperbolic systems, 0101 mathematics, Well posedness of continuity boundary conditions, parallel computation, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: https://zbmath.org/1659480
https://doi.org/10.1016/s0377-0427(00)00535-5
https://www.sciencedirect.com/science/article/abs/pii/S0377042700005355
https://www.sciencedirect.com/science/article/pii/S0377042700005355
https://dialnet.unirioja.es/servlet/articulo?codigo=725356
https://ui.adsabs.harvard.edu/abs/2001JCoAM.134..165D/abstract

Model order reduction based on Laguerre orthogonal polynomials for parabolic equation constrained optimal control problems.

Authors: Miao, Zhen Wang, Li Cheng, Gao-yuan et al.

Source: International Journal of Computer Mathematics; Mar2024, Vol. 101 Issue 3, p237-254, 18p

Subject Terms: LAGUERRE polynomials, PONTRYAGIN'S minimum principle, INITIAL value problems, COST functions, ORDINARY differential equations, ORTHOGONAL polynomials

Physics-informed neural networks with domain decomposition for the incompressible Navier–Stokes equations.

Authors: Gu, Linyan Qin, Shanlin Xu, Lei et al.

Source: Physics of Fluids; Feb2024, Vol. 36 Issue 2, p1-21, 21p

Subject Terms: NAVIER-Stokes equations, DOMAIN decomposition methods, FLOW simulations, INCOMPRESSIBLE flow, INVERSE problems, DIFFERENTIAL equations

A Numerical Simulation Study of Complex Multi-Source Groundwater Based on PKAN.

Authors: Feng, Lei Wang, Jun

Source: Water (20734441); Apr2025, Vol. 17 Issue 7, p1075, 15p

Subject Terms: NUMERICAL functions, GROUNDWATER flow, SIMULATION methods & models, COMPUTER simulation, SENSITIVITY analysis

Further N -Frame networking dynamics of conscious observer-self agents via a functional contextual interface: predictive coding, double-slit quantum mechanical experiment, and decision-making fallacy modeling as applied to the measurement problem in humans and AI

Authors: Edwards, Darren J.

Source: Frontiers in Computational Neuroscience; 2025, p1-53, 53p

Subject Terms: LANGUAGE models, ARTIFICIAL intelligence, COGNITIVE bias, QUANTUM operators, COGNITIVE maps (Psychology)

A critical assessment of the parabolized stability equations.

Authors: Towne, Aaron Rigas, Georgios Colonius, Tim

Source: Theoretical & Computational Fluid Dynamics; Aug2019, Vol. 33 Issue 3/4, p359-382, 24p

Subject Terms: INITIAL value problems, BOUNDARY value problems, EQUATIONS, NAVIER-Stokes equations, MATHEMATICAL regularization

COMPARISON BETWEEN GLOBAL, CLASSICAL DOMAIN DECOMPOSITION AND LOCAL, SINGLE AND DOUBLE COLLOCATION METHODS BASED ON RBF INTERPOLATION FOR SOLVING CONVECTION-DIFFUSION EQUATION.

Authors: GUTIERREZ, GAIL FLOREZ, WHADY

Source: International Journal of Modern Physics C: Computational Physics & Physical Computation; Nov2008, Vol. 19 Issue 11, p1737-1751, 15p, 5 Graphs

Subject Terms: COLLOCATION methods, INTERPOLATION, DECOMPOSITION method, BOUNDARY value problems, APPROXIMATION theory

A Fast Sine Transform Accelerated High-Order Finite Difference Method for Parabolic Problems over Irregular Domains.

Authors: Li, Chuan Ren, Yiming Long, Guangqing et al.

Source: Journal of Scientific Computing; May2023, Vol. 95 Issue 2, p1-38, 38p

MT-PINNs: multi-term physics-informed neural networks for solving initial boundary value problems of 2D and 3D nonlinear telegraph equations.

Authors: Tamirie Deresse, Alemayehu Senbeta Bekela, Alemu Temesgen Dufera, Tamirat

Source: Boundary Value Problems; 9/30/2025, Vol. 2025 Issue 1, p1-29, 29p

Subject Terms: BOUNDARY value problems, PARTIAL differential equations, SIMULATION methods & models, STATISTICAL accuracy, PARAMETERIZATION, DEEP learning, NONLINEAR wave equations, ARTIFICIAL neural networks

Neural network-based numerical analysis of some convection-diffusion-based initial boundary-value problems.

Authors: Khan, Muhammad Sabeel Abualnaja, Khadijah M. Sagheer, Ayesha et al.

Source: AIP Advances; Dec2024, Vol. 14 Issue 12, p1-14, 14p

Subject Terms: NUMERICAL solutions to boundary value problems, PARTIAL differential equations, NONLINEAR differential equations, BOUNDARY value problems, NUMERICAL analysis, TRANSPORT equation

Meta-Learning-Based Physics-Informed Neural Network: Numerical Simulations of Initial Value Problems of Nonlinear Dynamical Systems Without Labeled Data and Correlation Analyses.

Authors: Duanyai, Worrawat Weon Keun Song Chitthamlerd, Thanadol et al.

Source: Journal of Nonlinear Modeling & Analysis; 2024, Vol. 6 Issue 2, p485-513, 29p

Subject Terms: ARTIFICIAL neural networks, INITIAL value problems, NONLINEAR dynamical systems, STOCHASTIC convergence, DATA analysis

Fractional regularisation of the Cauchy problem for Laplace's equation and application in some free boundary value problems.

Authors: Kaltenbacher, Barbara Rundell, William

Source: Mathematics of Computation; Mar2025, Vol. 94 Issue 352, p647-679, 33p

Subject Terms: LAPLACE'S equation, BOUNDARY value problems, PARTIAL differential equations, NEWTON-Raphson method, HARMONIC functions

Learning image derived PDE-phenotypes from fMRI data.

Authors: Bica, Ion Trang, Ryan Hu, Rui et al.

Source: Brain Informatics; 12/8/2025, Vol. 12 Issue 1, p1-16, 16p

Physics-informed machine learning for advancing computational medical imaging: integrating data-driven approaches with fundamental physical principles.

Authors: Ahmadi, Mohsen Biswas, Debojit Lin, Maohua et al.

Source: Artificial Intelligence Review; Oct2025, Vol. 58 Issue 10, p1-49, 49p

Subject Terms: COMPUTER-assisted image analysis (Medicine), MACHINE learning, PHYSICAL laws, BOUNDARY value problems, ARTIFICIAL intelligence

The initial boundary value problem and quasi-local Hamiltonians in general relativity.

Authors: An, Zhongshan Anderson, Michael T

Source: Classical & Quantum Gravity; 8/5/2021, Vol. 38 Issue 15, p1-28, 28p

Subject Terms: INITIAL value problems, BOUNDARY value problems, GENERAL relativity (Physics), PHASE space

Geographic Terms: GREECE

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

Authors: Zhang, Benrong Wang, Fajie Qiu, Lin

Source: Journal of Applied Physics; 6/28/2023, Vol. 133 Issue 24, p1-17, 17p

Subject Terms: HEAT conduction, ARTIFICIAL neural networks, DEEP learning, TEMPERATURE distribution

A domain decomposition approach for wave propagation into a layered domain: A domain decomposition approach for wave propagation...: A. Ricciardello.

Authors: Ricciardello, Angela

Source: Ricerche di Matematica; Feb2025, Vol. 74 Issue 1, p79-89, 11p