Search Results

• The Geometry Behind Numerical Solvers of the Poisson-Boltzmann Equation

  Xinwei Shi, Patrice Koehl

  2008-03-01

  40436 4211 Pages:1032-1050

• Multigrid Method for the Chan-Vese Model in Variational Segmentation

  Noor Badshah, Ke Chen

  2018-03-24

  38142 3903 Pages:294-316

• Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Lévy Equations

  Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, Kenji Kawaguchi

  2026-04-10

  170 55 Pages:1-26

• Construction of the Local Structure-Preserving Algorithms for the General Multi-Symplectic Hamiltonian System

  Jialing Wang, Yushun Wang, Dong Liang

  2020-07-30

  44852 3769 Pages:828-860

• Long-Time Integration of Nonlinear Wave Equations with Neural Operators

  Guanhang Lei, Zhen Lei, Lei Shi

  2026-01-18

  792 146 Pages:1137-1163

• A Highly Efficient CN-Like Scheme for the Transient Wigner Equation

  Yidan Wang, Haiyan Jiang, Tiao Lu, Wenqi Yao

  2026-01-03

  1924 104 Pages:775-798

• A Coupled High-Order Continuous and Discontinuous Galerkin Finite Element Scheme for the Davey-Stewartson System

  Jinyang Lu, Qi Tao, Yan Xu

  2025-04-27

  9635 584 Pages:975-1007

• A Numerical Methodology for Enforcing Maximum Principles and the Non-Negative Constraint for Transient Diffusion Equations

  K. B. Nakshatrala, H. Nagarajan, M. Shabouei

  2018-04-03

  40479 4767 Pages:53-93

• Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks (PINNs)

  Shamsulhaq Basir

  2023-06-06

  41861 3031 Pages:1240-1269

• Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations

  Lei Li, Jian-Guo Liu, Yijia Tang

  2022-07-06

  43777 3758 Pages:41-82

• Solving Allen-Cahn and Cahn-Hilliard Equations Using the Adaptive Physics Informed Neural Networks

  Colby L. Wight, Jia Zhao

  2021-01-13

  59575 3990 Pages:930-954

• Conservative Finite-Difference Scheme and Two-Stage Iteration Process of Its Realization for the 2D Problem of Semiconductor Plasma Generation by Femtosecond Pulse

  Vyacheslav A. Trofimov, Maria M. Loginova, Vladimir A. Egorenkov

  2018-08-21

  45943 3537 Pages:1512-1533

• Mesh Density Functions Based on Local Bandwidth Applied to Moving Mesh Methods

  Elliott S. Wise, Ben T. Cox, Bradley E. Treeby

  2017-11-02

  42861 3562 Pages:1286-1308

• A Time-Space Adaptive Method for the Schrödinger Equation

  Katharina Kormann

  2018-04-04

  43573 4830 Pages:60-85

• Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations

  F. Chinesta, E. Abisset-Chavanne, A. Ammar, E. Cueto

  2018-04-02

  38833 3012 Pages:975-1006

• Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation

  Rongpei Zhang, Xijun Yu, Jiang Zhu, Abimael F. D. Loula, Xia Cui

  2013-11-05

  40771 3998 Pages:1287-1303

• A Novel Dynamic Quadrature Scheme for Solving Boltzmann Equation with Discrete Ordinate and Lattice Boltzmann Methods

  C. T. Hsu, S. W. Chiang, K. F. Sin

  2020-07-31

  39170 4063 Pages:1397-1414

• Efficient Algorithms for Approximating Particular Solutions of Elliptic Equations Using Chebyshev Polynomials

  Andreas Karageorghis, Irene Kyza

  2007-02-01

  38613 4134 Pages:501-521

• Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics

  Bofeng Liu, Lixing Zhu, Zixuan Yang, Guowei He

  2023-03-13

  41322 3496 Pages:425-451

• Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

  M. J. Baines, M. E. Hubbard, P. K. Jimack

  2011-10-01

  40073 5040 Pages:509-576 Open-access

• Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential Equations

  Sebastian Becker, Ramon Braunwarth, Martin Hutzenthaler, Arnulf Jentzen, Philippe von Wurstemberger

  2020-11-18

  64587 3389 Pages:2109-2138

• Generalization Error in the Deep Ritz Method with Smooth Activation Functions

  Janne Siipola

  2024-04-10

  24367 2450 Pages:761-815 Open-access

• A Normalizing Field Flow Induced Two-Stage Stochastic Homogenization Method for Random Composite Materials

  Zihao Yang, Xintong Wang, Xiaofei Guan, Jizu Huang, Xixin Wu

  2023-10-07

  34829 2871 Pages:787-812

• General Synthetic Iterative Scheme for Unsteady Rarefied Gas Flows

  Jianan Zeng, Wei Su, Lei Wu

  2023-08-14

  33864 3447 Pages:173-207

• A Coupled FEM-BEM Approach for the Solution of the Free-Boundary Axi-Symmetric Plasma Equilibrium Problem

  M. Bonotto, D. Abate, P. Bettini, F. Villone

  2021-12-06

  47453 4121 Pages:27-59

• Layer-Splitting Methods for Time-Dependent Schrödinger Equations of Incommensurate Systems

  Ting Wang, Huajie Chen, Aihui Zhou, Yuzhi Zhou

  2021-10-26

  49890 3330 Pages:1474-1498

• Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study

  Adam Larios, Collin Victor

  2021-02-25

  43797 3207 Pages:1273-1298