| Publication | Date of Publication | Type |
|---|
| Solving diffusive equations by proper generalized decomposition with preconditioner | 2024-04-16 | Paper |
| Isogeometric convolution hierarchical deep-learning neural network: isogeometric analysis with versatile adaptivity | 2024-01-15 | Paper |
| Clustering analysis for elastodynamic homogenization | 2023-12-02 | Paper |
| Convolution hierarchical deep-learning neural networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond | 2023-07-27 | Paper |
| Discovery of PDEs driven by data with sharp gradient or discontinuity | 2023-06-05 | Paper |
| Long-time simulations of rogue wave solutions in the nonlinear Schrödinger equation | 2023-03-07 | Paper |
| A variational fracture method based on Eshelby transformation | 2022-11-29 | Paper |
| Numerical boundary treatment for shock propagation in the fractional KdV-Burgers equation | 2022-03-17 | Paper |
| Finite difference approach for multiscale computations of atomic chain at finite temperature | 2022-03-02 | Paper |
| HiDeNN-TD: reduced-order hierarchical deep learning neural networks | 2022-01-26 | Paper |
| Accurate Boundary Conditions for Twin Boundary | 2021-11-03 | Paper |
| Accurate boundary treatment for Riesz space fractional diffusion equations | 2021-10-25 | Paper |
| Stability and convergence analysis of artificial boundary conditions for the Schrödinger equation on a rectangular domain | 2021-09-02 | Paper |
| Hierarchical deep-learning neural networks: finite elements and beyond | 2021-06-17 | Paper |
| HiDeNN-PGD: reduced-order hierarchical deep learning neural networks | 2021-05-13 | Paper |
| Adaptive selection of reference stiffness in virtual clustering analysis | 2021-04-27 | Paper |
| Analytical expression of RKPM shape functions | 2021-02-18 | Paper |
| Accurate boundary treatment for transient Schrödinger equation under polar coordinates | 2020-10-11 | Paper |
| Nonlocal matching boundary conditions for non-ordinary peridynamics with correspondence material model | 2020-04-08 | Paper |
| High-order central difference scheme for Caputo fractional derivative | 2020-04-06 | Paper |
| A Petrov-Galerkin finite element method for the fractional advection-diffusion equation | 2020-04-03 | Paper |
| Clustering discretization methods for generation of material performance databases in machine learning and design optimization | 2019-08-19 | Paper |
| Fast calculation of interaction tensors in clustering-based homogenization | 2019-08-19 | Paper |
| Enriched reproducing kernel particle method for fractional advection-diffusion equation | 2018-12-19 | Paper |
| From virtual clustering analysis to self-consistent clustering analysis: a mathematical study | 2018-12-05 | Paper |
| Eliminating corner effects in square lattice simulation | 2018-10-25 | Paper |
| Artificial boundary conditions for out-of-plane motion in penta-graphene | 2018-06-12 | Paper |
| Approximate linear relations for Bessel functions | 2018-04-06 | Paper |
| An enriched finite element method to fractional advection-diffusion equation | 2018-02-28 | Paper |
| Exact boundary condition for semi-discretized Schrödinger equation and heat equation in a rectangular domain | 2017-08-22 | Paper |
| Matching boundary conditions for lattice dynamics | 2016-12-30 | Paper |
| Almost exact boundary conditions for transient Schrödinger-Poisson system | 2016-12-05 | Paper |
| Differential operator multiplication method for fractional differential equations | 2016-11-16 | Paper |
| Artificial boundary conditions for Euler-Bernoulli beam equation | 2016-10-05 | Paper |
| Artificial boundary conditions for atomic simulations of face-centered-cubic lattice | 2013-01-29 | Paper |
| Time history kernel functions for square lattice | 2012-04-04 | Paper |
| Matching boundary conditions for diatomic chains | 2010-10-08 | Paper |
| Time history interfacial conditions in multiscale computations of lattice oscillations | 2009-06-08 | Paper |
| Mathematical foundations of the immersed finite element method | 2009-05-08 | Paper |
| Wave interactions in Suliciu model for dynamic phase transitions | 2008-09-17 | Paper |
| Liquid-gas coexistence equilibrium in a relaxation model | 2008-09-01 | Paper |
| Numerical study of dynamic phase transitions in shock tube | 2008-09-01 | Paper |
| A finite difference approach with velocity interfacial conditions for multiscale computations of crystalline solids | 2008-05-09 | Paper |
| A mathematical framework of the bridging scale method | 2007-05-21 | Paper |
| Asymptotics in nonlinear evolution system with dissipation and ellipticity on quadrant | 2006-12-07 | Paper |
| Numerical approximation of the viscous quantum hydrodynamic model for semiconductors | 2006-06-30 | Paper |
| A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations | 2006-04-28 | Paper |
| Numerical Study of Dynamic Phase Transitions in 2-D with a Relaxed Scheme | 2005-03-14 | Paper |
| Stability of Suliciu model for phase transitions | 2005-03-10 | Paper |
| On hybrid quantum–classical transport models | 2004-08-20 | Paper |
| Positive entropic schemes for a nonlinear fourth-order parabolic equation | 2003-11-16 | Paper |
| Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems | 2003-10-29 | Paper |
| A relaxation scheme for the hydrodynamic equations for semiconductors | 2003-03-10 | Paper |
| https://portal.mardi4nfdi.de/entity/Q2782885 | 2002-04-08 | Paper |
| Nonlinear stability and optimal decay rate for a multidimensional generalized Kuramoto-Sivashinsky system | 2001-03-22 | Paper |
| Nonlinear stability for dissipative nonlinear evolution equations with ellipticity | 2000-02-28 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3836326 | 2000-02-20 | Paper |
| Steady states of some models for van der Waals fluids | 1999-11-11 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4358377 | 1998-11-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4868757 | 1997-01-27 | Paper |
