1. A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers
   2025/11/11 by Lee, Youngkyu, Liu, Shanqing, Darbon, Jerome +1 · 1 citation
   #65F08 #65F10 #65M55 #68T07 #90C06 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
2. Leveraging Operator Learning to Accelerate Convergence of the Preconditioned Conjugate Gradient Method
   2025/07/31 by Kopaničáková, Alena, Lee, Youngkyu, Karniadakis, George Em · 4 citations
   #49K20 #65M55 #68T05 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
3. Time parallelization for hyperbolic and parabolic problems
   2025/03/15 by Gander, Martin J., Wu, Shu-Lin, Zhou, Tao · 2 citations
   #65M12 #65M15 #65M55 #65Y05 #FOS: Mathematics #Numerical Analysis (math.NA)
4. An hp Multigrid Approach for Tensor-Product Space-Time Finite Element Discretizations of the Stokes Equations
   2025/02/13 by Nils Margenberg, Markus Bause, Margenberg, Nils +3 · 1 citation
   Engineering · #65F10 #65M55 #65M60 #65Y05 #Advanced Numerical Methods in Computational Mathematics #Computational Physics (physics.comp-ph) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Structural Analysis and Optimization
5. RandNet-Parareal: a time-parallel PDE solver using Random Neural Networks
   2024/11/09 by Gattiglio, Guglielmo, Grigoryeva, Lyudmila, Tamborrino, Massimiliano · 1 citation
   #65L05 #65M22 #65M55 #65Y05 #68T07 #68T09 #Computation (stat.CO) #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Parallel #and Cluster Computing (cs.DC)
6. Frequency inversion method and device for malignant melanoma detection using RF/microwaves
   2024/10/04 by Beilina, Larisa, Eriksson, Anders, Neittaanmäki, Noora · 2 citations
   #65J22 #65K10 #65M32 #65M55 #65M60 #65M70 #FOS: Electrical engineering #FOS: Physical sciences #Medical Physics (physics.med-ph) #Signal Processing (eess.SP) #electronic engineering #information engineering
7. U-WNO: U-Net Enhanced Wavelet Neural Operator for Solving Parametric Partial Differential Equations
   2024/08/15 by Lei, Wei-Min, Li, Hou-Biao · 6 citations
   #65M22 #65M55 #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA)
8. MgFNO: Multi-grid Architecture Fourier Neural Operator for Parametric Partial Differential Equations
   2024/07/11 by Guo, Zi-Hao, Li, Hou-Biao · 1 citation
   #65M22 #65M55 #FOS: Mathematics #G.1.3 #G.1.8 #Numerical Analysis (math.NA)
9. Non-diffusive neural network method for hyperbolic conservation laws
   2024/05/23 by Lorin, Emmanuel, Novruzi, Arian · 1 citation
   #35A35 #35D30 #35L02 #35L65 #65M55 #FOS: Mathematics #Numerical Analysis (math.NA)
10. A splitting, discontinuous Galerkin solver for the cell-by-cell electroneutral Nernst-Planck framework
    2024/04/12 by Ada J. Ellingsrud, Ellingsrud, Ada J., Benedusi, Pietro +1 · 1 citation
    Engineering · Materials Science · Physics and Astronomy · #65F10 #65M55 #65M60 #68U20 #92-08 #92C37 #Advancements in Semiconductor Devices and Circuit Design #Anodic Oxide Films and Nanostructures #Computational Engineering #FOS: Computer and information sciences #Finance #and Science (cs.CE) #stochastic dynamics and bifurcation
11. Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems
    2024/01/15 by Heinlein, Alexander, Howard, Amanda A., Beecroft, Damien +1 · 1 citation
    #65M22 #65M55 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
12. A domain decomposition method for stochastic evolution equations
    2024/01/14 by Buckwar, Evelyn, Djurdjevac, Ana, Eisenmann, Monika · 1 citation
    #65C30 #65M55 #90C15 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)
13. Benchmark computations of dynamic poroelasticity
    2023/07/05 by Anselmann, Mathias, Bause, Markus, Margenberg, Nils +1 · 1 citation
    #65M55 #65M60 #76S05 #FOS: Mathematics #Numerical Analysis (math.NA)
14. Rounding-Error Analysis of Multigrid V-Cycles
    2023/07/01 by McCormick, Stephen F., Tamstorf, Rasmus · 1 citation
    #65F10 #65G50 #65M55 #FOS: Mathematics #Numerical Analysis (math.NA)
15. Multigrid Methods using Block Floating Point Arithmetic
    2023/06/30 by Kohl, Nils, McCormick, Stephen F., Tamstorf, Rasmus · 2 citations
    #65F10 #65G50 #65M55 #FOS: Mathematics #Numerical Analysis (math.NA)
16. The Random Feature Method for Time-dependent Problems
    2023/04/14 by Jingrun Chen, Chen, Jingrun, E Weinan +3 · 4 citations
    Decision Sciences · Environmental Science · #65M20 #65M55 #65M70 #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Soil Geostatistics and Mapping
17. Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training
    2023/02/14 by S. Gratton, Gratton, S., A. Kopanicakova +3 · 2 citations
    Computer Science · Engineering · Physics and Astronomy · #49K20 #65M55 #65Y20 #68Q25 #68T05 #90C26 #90C30 #Artificial Intelligence (cs.AI) #Computational Complexity (cs.CC) #F.2.1 #FOS: Computer and information sciences #FOS: Mathematics #G.1.8 #I.2.5 #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Optical Systems and Laser Technology #Optimization and Control (math.OC)
18. Stage-parallel fully implicit Runge-Kutta implementations with optimal multilevel preconditioners at the scaling limit
    2022/09/14 by Peter Münch, Munch, Peter, Ivo Dravins +5 · 2 citations
    Chemistry · Computer Science · Mathematics · #65M55 #65Y05 #68W10 #Advanced NMR Techniques and Applications #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
19. Matrix-free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems
    2022/05/31 by Jodlbauer, Daniel, Langer, Ulrich, Wick, Thomas +1 · 2 citations
    #65M55 #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA)
20. MGM: A meshfree geometric multilevel method for systems arising from elliptic equations on point cloud surfaces
    2022/04/13 by Grady B. Wright, Wright, Grady B., Andrew Jones +3 · 1 citation
    Engineering · Physics and Astronomy · #65F08 #65F10 #65M22 #65M55 #65N22 #65N55 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
21. Randomized quasi-optimal local approximation spaces in time
    2022/03/11 by Schleuß, Julia, Smetana, Kathrin, ter Maat, Lukas · 1 citation
    #65C20 #65M12 #65M15 #65M55 #65M60 #65M75 #FOS: Mathematics #Numerical Analysis (math.NA)
22. Asymptotic spectra of large (grid) graphs with a uniform local structure (part II): numerical applications
    2021/11/27 by Andrea Adriani, Adriani, Andrea, Davide Bianchi +5 · 1 citation
    Computer Science · Mathematics · #05C22 #05C50 #15A06 #65J10 #65M55 #65N22 #Analysis of PDEs (math.AP) #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Spectral Theory in Mathematical Physics
23. Weighted Relaxation for Multigrid Reduction in Time
    2021/07/05 by Masumi Sugiyama, Sugiyama, Masumi, Jacob B. Schroder +5 · 1 citation
    Computer Science · Engineering · Mathematics · #65F10 #65M55 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
24. Multigrid Reduction in Time for non-linear hyperbolic equations
    2021/04/19 by Danieli, Federico, MacLachlan, Scott · 1 citation
    #35L65 #65M08 #65M55 #65Y05 #65Y20 #FOS: Mathematics #Numerical Analysis (math.NA)
25. Optimal local approximation spaces for parabolic problems
    2020/12/04 by Schleuß, Julia, Smetana, Kathrin · 2 citations
    #65M12 #65M15 #65M55 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA)
26. Algebraic error analysis for mixed-precision multigrid solvers
    2020/07/13 by McCormick, Stephen F., Benzaken, Joseph, Tamstorf, Rasmus · 3 citations
    #65F10 #65G50 #65M55 #FOS: Mathematics #Numerical Analysis (math.NA)
27. Discretization-error-accurate mixed-precision multigrid solvers
    2020/07/13 by Tamstorf, Rasmus, Benzaken, Joseph, McCormick, Stephen F. · 2 citations
    #65F10 #65G50 #65M55 #FOS: Mathematics #Numerical Analysis (math.NA)
28. An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids
    2019/03/27 by Paola F. Antonietti, Antonietti, P. F., Paul Houston +5 · 2 citations
    Computer Science · Engineering · Mathematics · #65M50 #65M55 #65Y05 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
29. A monolithic ALE Newton-Krylov solver with Multigrid-Richardson-Schwarz preconditioning for incompressible Fluid Structure Interaction
    2017/09/17 by Aulisa, Eugenio, Bna, Simone, Bornia, Giorgio · 1 citation
    #65M55 #65M60 #65N30 #65N55 #74F10 #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)
30. Weakly imposed symmetry and robust preconditioners for Biot's consolidation model
    2017/03/22 by Baerland, Trygve, Lee, Jeonghun J., Mardal, Kent-Andre +1 · 2 citations
    #65M55 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA)

more