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

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

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

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

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

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

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, null Kuldeep

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

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

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

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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

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

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

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

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

Authors: Yang, Huanfeng, Long, Guangqing, Ren, Yiming, Zhao, Shan

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

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

Fully nonlinear investigation of focused wave slamming on a freely rotating flap

Authors: Yong Cheng, Gen Li, Chunyan Ji, Gangjun Zhai

Source: Engineering Analysis with Boundary Elements. 110:24-41

Subject Terms: Boundary element methods for initial value and initial-boundary value problems involving PDEs, wave slamming, oscillating wave surge converter, HOBEM, Boundary element methods applied to problems in fluid mechanics, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, splash jet, fully nonlinear, focused wave, 0103 physical sciences, Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/7153239
https://doi.org/10.1016/j.enganabound.2019.10.005
https://www.sciencedirect.com/science/article/pii/S0955799719306113

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

Authors: Taddei T, Xu X, Zhang L

Contributors: taddei, tommaso

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

Authors: Claire Heaney, Christopher C. Pain, Ionel Michael Navon, Fangxin Fang, D. Xiao

Contributors: Engineering & Physical Science Research Council (E

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

A modular framework for implicit 3D–0D coupling in cardiac mechanics: A modular framework for implicit 3D-0D coupling in cardiac mechanics

Authors: Aaron L. Brown, Matteo Salvador, Lei Shi, Martin R. Pfaller, Zinan Hu, Kaitlin E. Harold, Tzung Hsiai, Vijay Vedula, Alison L. Marsden

Source: Computer Methods in Applied Mechanics and Engineering. 421:116764

Subject Terms: cardiovascular modeling, Finite element methods applied to problems in solid mechanics, approximate Newton method, FOS: Physical sciences, Numerical Analysis (math.NA), Physiological flows, cardiac mechanics, 3D-0D coupling, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Biological Physics (physics.bio-ph), FOS: Mathematics, Biomechanics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Physics - Biological Physics, Biomechanical solid mechanics, multi-domain modeling

File Description: application/xml

Access URL: https://pubmed.ncbi.nlm.nih.gov/38523716
http://arxiv.org/abs/2310.13780
https://zbmath.org/7824865
https://doi.org/10.1016/j.cma.2024.116764

A novel steepness-adjustable harmonic volume-of-fluid method for interface capturing

Authors: Ni, Weidan, Zeng, Qinghong, Ruan, Yucang, He, Zhiwei

Source: Journal of Computational Physics. 501:112765

Subject Terms: interface capturing scheme, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, steepness-adjustable harmonic scheme, Finite volume methods applied to problems in fluid mechanics, volume-of-fluid method

File Description: application/xml

Analysis and design of a local time stepping scheme for LES acceleration in reactive and non-reactive flow simulations

Authors: N. A., Sreejith, Riber, Eleonore, Cuenot, Bénédicte

Source: Journal of Computational Physics. 470:111580

Subject Terms: Mathematical modeling or simulation for problems pertaining to fluid mechanics, domain-decomposition, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, local time stepping, LES, 0103 physical sciences, explicit time integration, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, 01 natural sciences, spectral analysis, Finite element methods applied to problems in fluid mechanics

File Description: application/xml

Access URL: https://zbmath.org/7599613
https://doi.org/10.1016/j.jcp.2022.111580

Multiresolution schemes for conservation laws

Authors: Siegfried Müller, Wolfgang Dahmen, Birgit Gottschlich-Müller

Source: Multiscale, Nonlinear and Adaptive Approximation ISBN: 9783642034121

Subject Terms: numerical examples, hypersonic flow, multiresolution schemes, hyperbolic conservation laws, Euler equations, wavelets, 01 natural sciences, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Hyperbolic conservation laws, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Numerical methods for wavelets, 0101 mathematics, Hypersonic flows, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, finite volumes

File Description: application/xml

Access URL: https://rd.springer.com/chapter/10.1007/978-3-642-03413-8_11
https://doi.org/10.1007/s211-001-8009-3
https://link.springer.com/chapter/10.1007/978-3-642-03413-8_11
https://core.ac.uk/display/36464172
https://dblp.uni-trier.de/db/journals/nm/nm88.html#DahmenGM01
https://publications.rwth-aachen.de/record/47114

Efficient preconditioning of the linearized Navier—Stokes equations for incompressible flow: Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow

Authors: Silvester, David, Elman, Howard, Kay, David, Wathen, Andrew

Source: Partial Differential Equations ISBN: 9780444506160
Silvester, D, Elman, H, Kay, D & Wathen, A 2001, 'Efficient proconditioning of the linearized Navier-Stokes equations for incompressible flow', Journal of Computational and Applied Mathematics, vol. 128, no. 1-2, pp. 261-279. https://doi.org/10.1016/S0377-0427(00)00515-X

Subject Terms: multigrid iteration, linearized Navier-Stokes equations, Applied Mathematics, Navier-Stokes equations for incompressible viscous fluids, Incompressible flow, Preconditioning, 01 natural sciences, Navier–Stokes equations, convergence rate, Computational Mathematics, Multigrid iteration, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, preconditioning, pressure Poisson operator, scalar convection-diffusion operator, Navier-Stokes equations, 0101 mathematics, incompressible flow, operator splitting, Finite element methods applied to problems in fluid mechanics, multigrid V-cycle

File Description: application/xml

Access URL: http://eprints.maths.manchester.ac.uk/632/1/sdarticle.pdf
https://research.manchester.ac.uk/en/publications/83ee3d98-c00a-472c-855c-8b54bccdcdfd
https://doi.org/10.1016/S0377-0427(00)00515-X
https://www.sciencedirect.com/science/article/pii/S037704270000515X
http://eprints.ma.man.ac.uk/632/
https://dialnet.unirioja.es/servlet/articulo?codigo=725185
http://eprints.maths.manchester.ac.uk/632/
https://www.cs.ox.ac.uk/publications/publication5893-abstract.html
https://drum.lib.umd.edu/handle/1903/1040