Search Results

• The Unified Coordinate System in Computational Fluid Dynamics

  W. H. Hui

  2007-02-01

  39231 4190 pp. 577-610

• High Order Deep Neural Network for Solving High Frequency Partial Differential Equations

  Zhipeng Chang, Ke Li, Xiufen Zou, Xueshuang Xiang

  2022-01-27

  DOI:10.4208/cicp.OA-2021-0092

  46274 3540 pp. 370-397

• DL-PDE: Deep-Learning Based Data-Driven Discovery of Partial Differential Equations from Discrete and Noisy Data

  Hao Xu, Haibin Chang, Dongxiao Zhang

  2021-01-13

  DOI:10.4208/cicp.OA-2020-0142

  55435 3561 pp. 698-728

• Relaxation Exponential Runge-Kutta Methods and Their Applications to Semilinear Dissipative/Conservative Systems

  Dongfang Li, Xiaoxi Li, Jiang Yang

  2024-10-29

  DOI:10.4208/cicp.OA-2023-0241

  23015 1396 pp. 908-942

• High Order Finite Difference Discretization for Composite Grid Hierarchy and Its Applications

  Qun Gu, Weiguo Gao, Carlos J. García-Cervera

  2020-07-30

  DOI:10.4208/cicp.260514.101214a

  41895 3469 pp. 1211-1233

• GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations

  Rajesh Gandham, David Medina, Timothy Warburton

  2018-04-03

  DOI:10.4208/cicp.070114.271114a

  42678 4694 pp. 37-64

• Numerical Methods for Solving the Hartree-Fock Equations of Diatomic Molecules I

  John C. Morrison, Scott Boyd, Luis Marsano, Bernard Bialecki, Thomas Ericsson, Jose Paulo Santos

  2009-05-01

  38879 4052 pp. 959-985

• A Kernel Based Unconditionally Stable Scheme for Nonlinear Parabolic Partial Differential Equations

  Kaipeng Wang, Andrew Christlieb, Yan Jiang, Mengping Zhang

  2020-11-26

  DOI:10.4208/cicp.OA-2019-0197

  46446 4465 pp. 237-264

• Weak Minimization-Sampling Network for Solving PDEs

  Zhenqian E, Weiguo Gao

  2026-01-03

  DOI:10.4208/cicp.OA-2024-0153

  1940 120 pp. 696-712

• Data Generation-Based Operator Learning for Solving Partial Differential Equations on Unbounded Domains

  Jihong Wang, Xin Wang, Jing Li, Bin Liu

  2025-05-29

  DOI:10.4208/cicp.OA-2023-0327

  9043 520 pp. 1383-1416

• Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations

  Yan Xu, Chi-Wang Shu

  2010-07-01

  DOI:10.4208/cicp.2009.09.023

  42255 4906 pp. 1-46 Open Access

• A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions

  Yaqin Zhang, Ke Li, Zhipeng Chang, Xuejiao Liu, Yunqing Huang, Xueshuang Xiang

  2025-07-11

  DOI:10.4208/cicp.OA-2024-0095

  5374 896 pp. 181-222

• Frame Invariance and Scalability of Neural Operators for Partial Differential Equations

  Muhammad I. Zafar, Jiequn Han, Xu-Hui Zhou, Heng Xiao

  2022-08-11

  DOI:10.4208/cicp.OA-2021-0256

  303899 3517 pp. 336-363

• Eulerian Algorithms for Computing the Forward Finite Time Lyapunov Exponent Without Finite Difference upon the Flow Map

  Guoqiao You, Changfeng Xue, Shaozhong Deng

  2022-05-06

  DOI:10.4208/cicp.OA-2021-0193

  44154 3324 pp. 1467-1488

• Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

  Ameya D. Jagtap, George Em Karniadakis

  2020-11-18

  DOI:10.4208/cicp.OA-2020-0164

  151550 6990 pp. 2002-2041

• Nonstandard Fourier Pseudospectral Time Domain (PSTD) Schemes for Partial Differential Equations

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

  2018-09-17

  DOI:10.4208/cicp.OA-2017-0192

  46850 3342 pp. 623-634

• A Robust and Efficient Adaptive Multigrid Solver for the Optimal Control of Phase Field Formulations of Geometric Evolution Laws

  Feng Wei Yang, Chandrasekhar Venkataraman, Vanessa Styles, Anotida Madzvamuse

  2018-04-08

  DOI:10.4208/cicp.240715.080716a

  41672 4638 pp. 65-92

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

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

  2011-10-01

  DOI:10.4208/cicp.201010.040511a

  40073 5040 pp. 509-576 Open Access

• A Complete Error Analysis of PINNs for Elliptic Equations Using Projected Stochastic Gradient Descent

  Yuling Jiao, Ruoxuan Li, Defeng Sun, Peiying Wu, Jerry Zhijian Yang

  2026-04-10

  DOI:10.4208/cicp.OA-2025-0102

  243 68 pp. 27-60

• A Splitting Method for Nonlinear Filtering Problems with Diffusive and Point Process Observations

  Fengshan Zhang, Yongkui Zou, Shimin Chai, Yanzhao Cao

  2024-10-29

  DOI:10.4208/cicp.OA-2024-0074

  17992 1206 pp. 996-1020

• Laplacian Preconditioning for the Inverse Arnoldi Method

  Laurette S. Tuckerman

  2020-07-30

  DOI:10.4208/cicp.281114.290615a

  40635 3422 pp. 1336-1351

• A Simple, Fast and Stabilized Flowing Finite Volume Method for Solving General Curve Evolution Equations

  Karol Mikula, Daniel Ševčovič, Martin Balažovjech

  2010-07-01

  DOI:10.4208/cicp.2009.08.169

  41221 4354 pp. 195-211

• Finite Difference Approximation with ADI Scheme for Two-Dimensional Keller-Segel Equations

  Yubin Lu, Chi-An Chen, Xiaofan Li, Chun Liu

  2024-06-14

  DOI:10.4208/cicp.OA-2023-0284

  28005 1893 pp. 1352-1386

• Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition

  Mingze Qin, Ruishu Wang, Qilong Zhai, Ran Zhang

  2023-03-13

  DOI:10.4208/cicp.OA-2022-0138

  39193 3387 pp. 568-595

• Continuous Finite Element Subgrid Basis Functions for Discontinuous Galerkin Schemes on Unstructured Polygonal Voronoi Meshes

  Walter Boscheri, Michael Dumbser, Elena Gaburro

  2022-07-06

  DOI:10.4208/cicp.OA-2021-0235

  42379 3776 pp. 259-298

• The Hyperbolic Schrödinger Equation and the Quantum Lattice Boltzmann Approximation

  Renato Spigler

  2022-05-06

  DOI:10.4208/cicp.OA-2022-0001

  44645 3325 pp. 1341-1361

• Discrete Duality Finite Volume Discretization of the Thermal-$P_N$ Radiative Transfer Equations on General Meshes

  Francois Hermeline

  2022-01-27

  DOI:10.4208/cicp.OA-2021-0084

  42943 3364 pp. 398-448