Search Results - domain decomposition for initial value AND initial-boundary value problems involving PDEs

New Time Domain Decomposition Methods for Parabolic Optimal Control Problems II: Neumann–Neumann Algorithms: New time domain decomposition methods for parabolic optimal control problems. II: Neumann-Neumann algorithms

Authors: Martin J. Gander Liu-Di Lu

Source: SIAM Journal on Numerical Analysis. 62:2588-2610

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Controllability, parallel in time, time domain decomposition, 65M12, 65M55, 65Y05, Parallel numerical computation, parabolic optimal control problems, Numerical Analysis (math.NA), PDE constrained optimization (numerical aspects), 01 natural sciences, convergence analysis, Neumann-Neumann algorithm, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Optimization and Control (math.OC), Approximation by arbitrary linear expressions, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Optimization and Control

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.15522
https://zbmath.org/7957568
https://doi.org/10.1137/24m1634424

A rapidly converging domain decomposition algorithm for a time delayed parabolic problem with mixed type boundary conditions exhibiting boundary layers

Authors: null Aakansha Sunil Kumar Higinio Ramos

Source: GREDOS. Repositorio Institucional de la Universidad de Salamanca
Universidad de Salamanca (USAL)

Subject Terms: Delay differential equations, delay differential equations, Domain decomposition methods, domain decomposition methods, uniformly convergent methods, Error bounds for initial value and initial-boundary value problems involving PDEs, Uniformly convergent methods, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Parabolic problems, singularly perturbed problems, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Singularly perturbed problems, parabolic problems

File Description: application/xml

Access URL: http://hdl.handle.net/10366/156113

A Lagrange Multiplier Method for Fluid-Structure Interaction: Well-Posedness and Domain Decomposition: A Lagrange multiplier method for fluid-structure interaction: well-posedness and domain decomposition

Authors: Amy de Castro Hyesuk Lee Margaret M. Wiecek

Source: Computers & Mathematics with Applications. 181:193-215

Subject Terms: Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, inf-sup condition, Schur complement, interface problem, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, non-iterative partitioned scheme

File Description: application/xml

Access URL: https://zbmath.org/8010407
https://doi.org/10.1016/j.camwa.2024.12.020

A parameter uniform numerical method on a Bakhvalov type mesh for singularly perturbed degenerate parabolic convection–diffusion problems: A parameter uniform numerical method on a Bakhvalov type mesh for singularly perturbed degenerate parabolic convection-diffusion problems

Authors: Shashikant Kumar Sunil Kumar Higinio Ramos et al.

Source: GREDOS. Repositorio Institucional de la Universidad de Salamanca
Universidad de Salamanca (USAL)

Subject Terms: 12 Matemáticas, uniform convergence, 01 natural sciences, Bakhvalov mesh, Error bounds for initial value and initial-boundary value problems involving PDEs, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, upwind scheme, Upwind scheme, Finite difference methods for initial value and initial-boundary value problems involving PDEs, degenerate parabolic problem, Degenerate parabolic problem, Uniform convergence, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Singular perturbation, singular perturbation

File Description: application/xml

Access URL: http://hdl.handle.net/10366/166738

DeepONet Based Preconditioning Strategies for Solving Parametric Linear Systems of Equations: DeepONet based preconditioning strategies for solving parametric linear systems of equations

Authors: Alena Kopaničáková George Em Karniadakis

Source: SIAM Journal on Scientific Computing. 47:C151-C181

Subject Terms: Large-scale problems in mathematical programming, Iterative numerical methods for linear systems, operator learning, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, preconditioning, Learning and adaptive systems in artificial intelligence, FOS: Mathematics, Krylov methods, Preconditioners for iterative methods, spectral bias, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), hybridization

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.02016

A reduced-order two-grid method based on POD technique for the semilinear parabolic equation

Authors: Junpeng Song Hongxing Rui

Source: Applied Numerical Mathematics. 205:240-254

Subject Terms: reduced-order two-grid, error estimate, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, proper orthogonal decomposition, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, degrees of freedom, Finite difference methods for initial value and initial-boundary value problems involving PDEs, semilinear parabolic equation, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Semilinear parabolic equations

File Description: application/xml

Access URL: https://zbmath.org/7901906
https://doi.org/10.1016/j.apnum.2024.07.012

A Multi-domain Spectral Method with Mapping Techniques for the Fokker-Planck Equation in Irregular Domains: A multi-domain spectral method with mapping techniques for the Fokker-Planck equation in irregular domains

Authors: Wang, Chuan Wang, Zicheng Wang, Zhongqing

Source: Journal of Scientific Computing. 102

Subject Terms: Approximation by polynomials, Error bounds for initial value and initial-boundary value problems involving PDEs, convergence, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, multi-domain spectral method, coordinate transformations, Fokker-Planck equation, irregular domains, Fokker-Planck equations, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

A non-overlapping domain decomposition method for parabolic initial-boundary value problems

Authors: H. Müller Gert Lube F. C. Otto

Source: Applied Numerical Mathematics. 28:359-369

Subject Terms: numerical examples, 0209 industrial biotechnology, convergence, parabolic initial boundary value problems, 02 engineering and technology, 01 natural sciences, Reaction-diffusion equations, non-overlapping domain decomposition method, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, advection-reaction-diffusion model, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Galerkin method

File Description: application/xml

Access URL: https://zbmath.org/1311281
https://doi.org/10.1016/s0168-9274(98)00053-1
https://www.sciencedirect.com/science/article/pii/S0168927498000531

An augmented fourth order domain-decomposed method with fast algebraic solvers for three-dimensional Helmholtz interface problems

Authors: Yang, Huanfeng Long, Guangqing Ren, Yiming et al.

Source: Journal of Computational Physics. 524:113742

Subject Terms: Helmholtz interface problems, domain decomposition, matched interface and boundary (MIB) method, fast Fourier transform (FFT), Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, mixed boundary conditions, high order finite difference methods, Numerical methods for discrete and fast Fourier transforms

File Description: application/xml

Access URL: https://zbmath.org/7996154
https://doi.org/10.1016/j.jcp.2025.113742

A type of efficient multigrid method for semilinear parabolic interface problems

Authors: Fan Chen Ming Cui Chenguang Zhou

Source: Communications in Nonlinear Science and Numerical Simulation. 143:108632

Subject Terms: Error bounds for initial value and initial-boundary value problems involving PDEs, nonnested multilevel correction method, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, finite element method, semilinear parabolic interface problem, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, nested multilevel correction method

File Description: application/xml

Access URL: https://zbmath.org/8014706
https://doi.org/10.1016/j.cnsns.2025.108632

GDSW preconditioners for composite Discontinuous Galerkin discretizations of multicompartment reaction–diffusion problems: GDSW preconditioners for composite discontinuous Galerkin discretizations of multicompartment reaction-diffusion problems

Authors: Huynh, Ngoc Mai Monica Pavarino, Luca F. Scacchi, Simone

Source: Computer Methods in Applied Mechanics and Engineering. 433:117501

Subject Terms: Multigrid methods, domain decomposition for boundary value problems involving PDEs, Physiology (general), BDDC preconditioners, Cardiac cell-by-cell models, Composite Discontinuous Galerkin methods, Scalable Domain Decomposition methods, composite discontinuous Galerkin methods, Numerical Analysis (math.NA), domain decomposition for initial value and initial-boundary value problems involving PDEs, scalable domain decomposition methods, FOS: Mathematics, cardiac cell-by-cell models, Preconditioners for iterative methods, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, 65N55, 65M55, 65F10, 92C30

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2405.17601
https://zbmath.org/7967165
https://doi.org/10.1016/j.cma.2024.117501

A non-overlapping optimization-based domain decomposition approach to component-based model reduction of incompressible flows

Authors: Taddei T Xu X Zhang L et al.

Contributors: Taddei T Xu X Zhang L et al.

Source: Journal of Computational Physics. 509:113038

Subject Terms: optimization-based domain decomposition, [SPI] Engineering Sciences [physics], 0211 other engineering and technologies, [MATH] Mathematics [math], 02 engineering and technology, Numerical Analysis (math.NA), 01 natural sciences, 65N30, 41A45, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, component-based model order reduction, FOS: Mathematics, navier-stokes equations, non-overlapping methods, Mathematics - Numerical Analysis, Navier-Stokes equations, 0101 mathematics, Finite element methods applied to problems in fluid mechanics, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, Flow control and optimization for incompressible viscous fluids

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2310.20267
https://zbmath.org/8021004
https://doi.org/10.1016/j.jcp.2024.113038
https://inria.hal.science/hal-04382123v1
https://inria.hal.science/hal-04382123v1/document
https://doi.org/10.1016/j.jcp.2024.113038
https://hdl.handle.net/11573/1745039
https://doi.org/10.1016/j.jcp.2024.113038

A domain decomposition and mixed method for a linear parabolic boundary value problem

Authors: Girault, Vivette Glowinski, Roland Lopez, H. et al.

Contributors: Girault, Vivette Glowinski, Roland Lopez, H. et al.

Source: IMA Journal of Numerical Analysis. 24:491-520

Subject Terms: convergence, mixed methods, non-matching grids, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], quadrilateral finite elements, 01 natural sciences, linear parabolic boundary value problem, Error bounds for initial value and initial-boundary value problems involving PDEs, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, error estimates, Initial-boundary value problems for second-order parabolic equations, inf-sup condition, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Initial value problems for second-order parabolic equations, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: https://hal.science/hal-00020218v1
https://zbmath.org/2124456
https://doi.org/10.1093/imanum/24.3.491
https://academic.oup.com/imajna/article/24/3/491/702197

Two-grid reduced-order method based on POD for a nonlinear poroelasticity model

Authors: Li, Hongpeng Rui, Hongxing Gao, Mengqi

Source: Journal of Computational and Applied Mathematics. 460:116413

Subject Terms: reduced-order finite element method, Linear elasticity with initial stresses, Finite element methods applied to problems in solid mechanics, nonlinear poroelasticity, Flows in porous media, filtration, seepage, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDEs in connection with fluid mechanics, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), Finite difference methods applied to problems in fluid mechanics, Finite difference methods applied to problems in solid mechanics, Error bounds for initial value and initial-boundary value problems involving PDEs, proper orthogonal decomposition, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Soil and rock mechanics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, two-grid method, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, PDEs in connection with mechanics of deformable solids, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Highly efficient, decoupled and unconditionally stable numerical schemes for a modified phase-field crystal model with a strong nonlinear vacancy potential

Authors: Zhang, Xin Wu, Jingwen Tan, Zhijun

Source: Computers & Mathematics with Applications. 132:119-134

Subject Terms: unconditional energy stability, exponential SAV, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, modified phase-field crystal, 0103 physical sciences, vacancy, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, 01 natural sciences, Statistical mechanics of crystals, Stefan problems, phase changes, etc

File Description: application/xml

Access URL: https://zbmath.org/7648419
https://doi.org/10.1016/j.camwa.2022.12.011

A domain decomposition method for the non-intrusive reduced order modelling of fluid flow

Authors: Claire Heaney Christopher C. Pain Ionel Michael Navon et al.

Contributors: Claire Heaney Christopher C. Pain Ionel Michael Navon et al.

Source: Computer Methods in Applied Mechanics and Engineering. 354:307-330

Subject Terms: Mathematics, Interdisciplinary Applications, NAVIER-STOKES, DYNAMICS, Technology, Navier-Stokes equations for incompressible viscous fluids, 0211 other engineering and technologies, Engineering, Multidisciplinary, TRANSIENT, 02 engineering and technology, Mechanics, Reduced order modelling, 01 natural sciences, 09 Engineering, Engineering, proper orthogonal decomposition, POLLUTION, 0103 physical sciences, Interdisciplinary Applications, PETROV-GALERKIN METHODS, Domain decomposition, non-intrusive, OPTIMIZATION, Non-intrusive, EQUATIONS, 01 Mathematical Sciences, Multidisciplinary, Science & Technology, reduced order modelling, Applied Mathematics, Proper orthogonal decomposition, SIMULATIONS, STATE, REDUCTION, domain decomposition, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Physical Sciences, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0045782519303093
https://cronfa.swan.ac.uk/Record/cronfa51800
https://ui.adsabs.harvard.edu/abs/2019CMAME.354..307X/abstract
http://hdl.handle.net/10044/1/70185
https://cronfa.swan.ac.uk/Record/cronfa51800

Time Domain Decomposition in Final Value Optimal Control of the Maxwell System: Time domain decomposition in final value optimal control of the Maxwell system.

Authors: Günter Leugering John E. Lagnese

Source: ESAIM: Control, Optimisation and Calculus of Variations. 8:775-799

Subject Terms: optimal control, domain decomposition, Discrete approximations in optimal control, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Optimality conditions for problems involving partial differential equations, Maxwell system, 0101 mathematics, Optimization problems in optics and electromagnetic theory, PDEs in connection with optics and electromagnetic theory, 01 natural sciences

File Description: application/xml

Access URL: https://www.esaim-cocv.org/articles/cocv/pdf/2002/02/Lagnese.pdf
https://www.esaim-cocv.org/articles/cocv/pdf/2002/02/Lagnese.pdf
http://archive.numdam.org/ARCHIVE/COCV/COCV_2002__8_/COCV_2002__8__775_0/COCV_2002__8__775_0.pdf
https://eudml.org/doc/244606
http://www.numdam.org/item/10.1051/cocv:2002042.pdf
http://archive.numdam.org/article/COCV_2002__8__775_0.pdf
http://www.esaim-cocv.org/articles/cocv/abs/2002/02/Lagnese/Lagnese.html

A Posteriori Error Estimates in Time-Domain Decomposition of Final Value Optimal Control of the Acoustic Wave Equation: A posteriori error estimates in time-domain decomposition of final value optimal control of the acoustic wave equation

Authors: Lagnese Leugering

Source: Applied Mathematics and Optimization. 46:263-290

Subject Terms: a posteriori error estimates, optimal control, domain decomposition, 0209 industrial biotechnology, Error bounds for initial value and initial-boundary value problems involving PDEs, Discrete approximations in optimal control, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, 0211 other engineering and technologies, 02 engineering and technology, acoustic wave equation

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007%2Fs00245-002-0750-6
https://link.springer.com/content/pdf/10.1007/s00245-002-0750-6.pdf

Multi-level adaptive solutions to initial-value problems

Authors: A. B. Shamardan Y. M. Abo Essa

Source: Korean Journal of Computational & Applied Mathematics. 7:215-222

Subject Terms: KdV equations (Korteweg-de Vries equations), Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, finite difference, Finite difference methods for initial value and initial-boundary value problems involving PDEs, nonlinear Burgers' equations, multigrid algorithm, stability, numerical results, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1419903
https://link.springer.com/article/10.1007/BF03009939

A fractional splitting algorithm for nonoverlapping domain decomposition for parabolic problem

Authors: Daoud S. Daoud D. S. Subasi

Source: Numerical Methods for Partial Differential Equations. 18:609-624

Subject Terms: fractional splitting, convergence, parabolic equation, heat equation, Heat equation, error bound, stability, 01 natural sciences, domain decomposition, Error bounds for initial value and initial-boundary value problems involving PDEs, nonoverlapping domains, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, numerical experiments

File Description: application/xml

Access URL: https://zbmath.org/1872722
https://doi.org/10.1002/num.10019
http://onlinelibrary.wiley.com/doi/10.1002/num.10019/abstract