| Publication | Date of Publication | Type |
|---|
| Exponential Convergence Theory of the Multipole and Local Expansions for the 3-D Laplace Equation in Layered Media | 2024-03-11 | Paper |
| Linearized Learning with Multiscale Deep Neural Networks for Stationary Navier-Stokes Equations with Oscillatory Solutions | 2023-12-16 | Paper |
| A Correction and Comments on “Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains CiCP, 28(5):1970–2001,2020” | 2023-07-06 | Paper |
| Fast multipole method for 3-D Laplace equation in layered media | 2023-05-26 | Paper |
| A path integral Monte Carlo (PIMC) method based on Feynman-Kac formula for electrical impedance tomography | 2023-02-10 | Paper |
| On Spectral Bias Reduction of Multi-scale Neural Networks for Regression Problems | 2022-12-06 | Paper |
| A Parallel Iterative Probabilistic Method for Mixed Problems of Laplace Equations with the Feynman--Kac Formula of Killed Brownian Motions | 2022-11-16 | Paper |
| A Matrix Basis Formulation for the Dyadic Green’s Functions of Maxwell’s Equations in Layered Media | 2022-11-01 | Paper |
| FBSDE based neural network algorithms for high-dimensional quasilinear parabolic PDEs | 2022-10-11 | Paper |
| A Causality-DeepONet for Causal Responses of Linear Dynamical Systems | 2022-09-17 | Paper |
| Fast multipole method for 3-D Poisson-Boltzmann equation in layered electrolyte-dielectric media | 2022-04-22 | Paper |
| A NONLINEAR STRAIN-DEPENDENT VARIABLE-ORDER FRACTIONAL MODEL WITH APPLICATIONS TO ALUMINUM FOAMS | 2022-03-15 | Paper |
| DeepPropNet -- A Recursive Deep Propagator Neural Network for Learning Evolution PDE Operators | 2022-02-27 | Paper |
| Properties of the Eshelby tensor and existence of the equivalent ellipsoidal inclusion solution | 2022-02-15 | Paper |
| Multiscale DeepONet for Nonlinear Operators in Oscillatory Function Spaces for Building Seismic Wave Responses | 2021-11-08 | Paper |
| A Highly Scalable Boundary Integral Equation and Walk-On-Spheres (BIE-WOS) Method for the Laplace Equation with Dirichlet Data | 2021-11-03 | Paper |
| Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains | 2021-11-02 | Paper |
| Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains | 2021-11-02 | Paper |
| The temperature-dependent fractional evolutional model for sintered nanoscale silver films | 2021-09-08 | Paper |
| Derivation and numerical validation of the fundamental solutions for constant and variable-order structural derivative advection-dispersion models | 2021-05-03 | Paper |
| What is the fractional Laplacian? A comparative review with new results | 2021-01-28 | Paper |
| A high order efficient numerical method for 4-D Wigner equation of quantum double-slit interferences | 2021-01-27 | Paper |
| An \(O(N \log N)\) hierarchical random compression method for kernel matrices by sampling partial matrix entries | 2021-01-27 | Paper |
| Taylor expansion based fast multipole method for 3-d Helmholtz equations in layered media | 2021-01-27 | Paper |
| FBSDE based Neural Network Algorithms for High-Dimensional Quasilinear Parabolic PDEs | 2020-12-14 | Paper |
| On the existence of Eshelby’s equivalent ellipsoidal inclusion solution | 2020-11-27 | Paper |
| A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems | 2020-11-09 | Paper |
| https://portal.mardi4nfdi.de/entity/Q5128365 | 2020-10-27 | Paper |
| A Matrix Basis Formulation For The Green's Functions Of Maxwell's Equations And The Elastic Wave Equations In Layered Media | 2020-08-03 | Paper |
| Exponential Convergence for Multipole and Local Expansions and Their Translations for Sources in Layered Media: Two-Dimensional Acoustic Wave | 2020-05-20 | Paper |
| Vertical impedance of a tapered pile in inhomogeneous saturated soil described by fractional viscoelastic model | 2020-04-07 | Paper |
| Adaptive finite element method for fractional differential equations using hierarchical matrices | 2020-04-06 | Paper |
| Fast Multipole Method for 3-D Linearized Poisson-Boltzmann Equation in Layered Media | 2020-02-03 | Paper |
| Taylor expansion based fast multipole method for 3-d Helmholtz equations in layered media | 2020-01-10 | Paper |
| Accurate and efficient calculation of singular electrostatic potentials in charge-dielectric sphere systems | 2019-08-05 | Paper |
| A Path Integral Monte Carlo Method based on Feynman-Kac Formula for Electrical Impedance Tomography | 2019-07-29 | Paper |
| Efficient two-dimensional simulations of the fractional Szabo equation with different time-stepping schemes | 2019-03-12 | Paper |
| Taylor expansion based fast Multipole Methods for 3-D Helmholtz equations in Layered Media | 2019-02-15 | Paper |
| Hausdorff Calculus | 2019-02-06 | Paper |
| Network linear discriminant analysis | 2018-08-17 | Paper |
| Non-Euclidean distance fundamental solution of Hausdorff derivative partial differential equations | 2018-08-10 | Paper |
| A heterogeneous FMM for layered media Helmholtz equation. I: Two layers in \(\mathbb{R}^2\) | 2018-08-01 | Paper |
| A Computational Stochastic Methodology for the Design of Random Meta-materials under Geometric Constraints | 2018-03-14 | Paper |
| A hierarchical random compression method for kernel matrices | 2018-03-13 | Paper |
| Accurate and Efficient Nyström Volume Integral Equation Method for Electromagnetic Scattering of 3-D Metamaterials in Layered Media | 2018-02-21 | Paper |
| Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization | 2018-02-06 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3132535 | 2018-01-29 | Paper |
| High Order Hierarchical Divergence-Free Constrained Transport H(div) Finite Element Method for Magnetic Induction Equation | 2018-01-29 | Paper |
| Linear Scaling Discontinuous Galerkin Density Matrix Minimization Method with Local Orbital Enriched Finite Element Basis: 1-D Lattice Model System | 2017-10-27 | Paper |
| On the Construction of Well-Conditioned Hierarchical Bases for (div)-Conforming ℝn Simplicial Elements | 2017-10-27 | Paper |
| Investigating the Selectivity of KcsA Channel by an Image Charge Solvation Method (ICSM) in Molecular Dynamics Simulations | 2017-10-27 | Paper |
| A Well-Conditioned Hypersingular Boundary Element Method for Electrostatic Potentials in the Presence of Inhomogeneities within Layered Media | 2017-10-27 | Paper |
| Quadrature Weights on Tensor-Product Nodes for Accurate Integration of Hypersingular Functions over Some Simple 3-D Geometric Shapes | 2017-10-27 | Paper |
| A High-Order Time Domain Discontinuous Galerkin Method with Orthogonal Tetrahedral Basis for Electromagnetic Simulations in 3-D Heterogeneous Conductive Media | 2017-10-27 | Paper |
| Efficient and accurate computation of electric field dyadic Green's function in layered media | 2017-08-11 | Paper |
| https://portal.mardi4nfdi.de/entity/Q5268648 | 2017-06-20 | Paper |
| https://portal.mardi4nfdi.de/entity/Q5268663 | 2017-06-20 | Paper |
| Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport | 2017-06-07 | Paper |
| A Well-Conditioned Hierarchical Basis for Triangular H(curl)-Conforming Elements | 2017-06-07 | Paper |
| Image Charge Method for Reaction Fields in a Hybrid Ion-Channel Model | 2017-06-07 | Paper |
| Computation of the local time of reflecting Brownian motion and the probabilistic representation of the Neumann problem | 2017-02-17 | Paper |
| A device adaptive inflow boundary condition for Wigner equations of quantum transport | 2016-12-05 | Paper |
| Accuracy and efficiency in computing electrostatic potential for an ion channel model in layered dielectric/electrolyte media | 2016-12-05 | Paper |
| Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers | 2016-12-05 | Paper |
| Numerical solution of the Robin problem of Laplace equations with a Feynman-Kac formula and reflecting Brownian motions | 2016-11-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q2824633 | 2016-10-06 | Paper |
| Interactions of delta shock waves for zero-pressure gas dynamics with energy conservation law | 2016-09-08 | Paper |
| https://portal.mardi4nfdi.de/entity/Q2804788 | 2016-05-04 | Paper |
| Modeling a distribution of point defects as misfitting inclusions in stressed solids | 2015-10-30 | Paper |
| Highly Accurate Nystr\"{o}m Volume Integral Equation Method for the Maxwell equations for 3-D Scatters | 2015-06-15 | Paper |
| Fast integral equation solver for Maxwell's equations in layered media with FMM for Bessel functions | 2014-12-02 | Paper |
| A parallel fast algorithm for computing the Helmholtz integral operator in 3-D layered media | 2013-12-12 | Paper |
| Divergence-free \(\mathbf{\mathcal{H}}(\mathbf{div})\)-conforming hierarchical bases for magnetohydrodynamics (MHD) | 2013-10-31 | Paper |
| A Parallel Method for Solving Laplace Equations with Dirichlet Data Using Local Boundary Integral Equations and Random Walks | 2013-10-28 | Paper |
| Random Processes in Physics and Finance | 2013-08-28 | Paper |
| Image approximations to electrostatic potentials in layered electrolytes/dielectrics and an ion-channel model | 2013-08-13 | Paper |
| https://portal.mardi4nfdi.de/entity/Q2839916 | 2013-07-16 | Paper |
| Energy of a Prismatic Dislocation Loop in an Elastic Cylinder | 2013-02-18 | Paper |
| Preface | 2013-02-15 | Paper |
| On the Construction of Well-Conditioned Hierarchical Bases for Tetrahedral H(curl)-Conforming Nedelec Elements | 2012-06-01 | Paper |
| Well-conditioned orthonormal hierarchical \(\mathcal{L}_{2}\) bases on \(\mathbb R^{n }\) simplicial elements | 2012-05-23 | Paper |
| Fast Analytical Methods for Macroscopic Electrostatic Models in Biomolecular Simulations | 2012-01-09 | Paper |
| A wideband fast multipole method for the two-dimensional complex Helmholtz equation | 2011-06-30 | Paper |
| Improved rigorous coupled-wave analysis for polar magnetic gratings | 2011-05-31 | Paper |
| NHAR: A non-homogeneous Arnoldi method for fast simulation of RCL circuits with a large number of ports | 2011-05-20 | Paper |
| Accurate simulations of 2-D phase shift masks with a generalized discontinuous Galerkin (GDG) method | 2011-04-05 | Paper |
| Accuracy of the Frensley inflow boundary condition for Wigner equations in simulating resonant tunneling diodes | 2011-03-17 | Paper |
| A sixth-order image approximation to the ionic solvent induced reaction field | 2011-01-16 | Paper |
| A comparable study of image approximations to the reaction field | 2010-10-18 | Paper |
| High-order DGTD methods for dispersive Maxwell's equations and modelling of silver nanowire coupling | 2010-09-10 | Paper |
| Effect of boundary treatments on quantum transport current in the Green's function and Wigner distribution methods for a nano-scale DG-MOSFET | 2010-06-08 | Paper |
| Torsion and bending periodic boundary conditions for modeling the intrinsic strength of nanowires | 2009-10-09 | Paper |
| Computing image stress in an elastic cylinder | 2009-06-30 | Paper |
| Image charge approximations of reaction fields in solvents with arbitrary ionic strength | 2009-04-03 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3609582 | 2009-03-06 | Paper |
| A new FFT-based algorithm to compute Born radii in the generalized Born theory of biomolecule solvation | 2009-01-06 | Paper |
| A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D high frequency electromagnetic scattering in dispersive inhomogeneous media | 2008-11-25 | Paper |
| A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger-Poisson equations with discontinuous potentials | 2008-08-22 | Paper |
| A full vectorial generalized discontinuous Galerkin beam propagation method (GDG-BPM) for nonsmooth electromagnetic fields in waveguides | 2008-07-29 | Paper |
| Boundary treatments in non-equilibrium Green's function (NEGF) methods for quantum transport in nano-MOSFETs | 2008-07-21 | Paper |
| https://portal.mardi4nfdi.de/entity/Q5456005 | 2008-04-04 | Paper |
| A generalized discontinuous Galerkin (GDG) method for Schrödinger equations with nonsmooth solutions | 2008-03-28 | Paper |
| Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: high-order image approximations for reaction fields | 2007-12-18 | Paper |
| Electronic structure calculations in a uniform magnetic field using periodic supercells | 2007-11-01 | Paper |
| A non-singular continuum theory of dislocations | 2007-10-29 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3593762 | 2007-08-06 | Paper |
| Extending the fast multipole method to charges inside or outside a dielectric sphere | 2007-05-23 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3433837 | 2007-04-19 | Paper |
| Accurate calculation of Green's function of the Schrödinger equation in a block layered potential | 2006-12-14 | Paper |
| Random Processes in Physics and Finance | 2006-11-15 | Paper |
| A boundary integral equation method for photonic crystal fibers | 2006-10-31 | Paper |
| https://portal.mardi4nfdi.de/entity/Q5469658 | 2006-05-26 | Paper |
| Analysis and Application of an Orthogonal Nodal Basis on Triangles for Discontinuous Spectral Element Methods | 2006-01-10 | Paper |
| Advances in Neural Networks – ISNN 2005 | 2005-11-23 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4680704 | 2005-06-07 | Paper |
| Discontinuous Galerkin methods for dispersive and lossy Maxwell's equations and PML boundary conditions | 2004-11-22 | Paper |
| An inversion method for parabolic equations based on quasireversibility | 2004-08-20 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4463081 | 2004-05-27 | Paper |
| An upwinding embedded boundary method for Maxwell's equations in media with material interfaces: 2D case | 2003-09-15 | Paper |
| https://portal.mardi4nfdi.de/entity/Q2724538 | 2003-03-12 | Paper |
| Algorithmic issues for electromagnetic scattering in layered media: Green's functions, current basis, and fast solver | 2002-04-23 | Paper |
| Inverse matrix evaluation for linear systems | 2002-01-27 | Paper |
| A fast wavelet collocation method for high-speed circuit simulation | 2001-07-08 | Paper |
| An adaptive wavelet method for nonlinear circuit simulation | 2001-07-05 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4952260 | 2001-04-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4499756 | 2001-01-29 | Paper |
| High-order mixed current basis functions for electromagnetic scattering of curved surfaces | 2000-09-19 | Paper |
| Fast calculations of dyadic Green's functions for electromagnetic scattering in a multilayered medium. | 2000-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4392023 | 1999-06-07 | Paper |
| An adaptive spline wavelet ADI(SW-ADI) method for two-dimensional reaction-diffusion equations | 1998-08-04 | Paper |
| Adaptive Multiresolution Collocation Methods for Initial-Boundary Value Problems of Nonlinear PDE<scp>s</scp> | 1997-02-24 | Paper |
| Direct Numerical Calculations of a Neutral Stability Curve for One-Dimensional Detonations | 1997-02-16 | Paper |
| High-order hybrid numerical simulations of two-dimensional detonation waves | 1996-05-05 | Paper |
| Perfect Parallel Parking Via Pontryagin’s Principle | 1995-11-26 | Paper |
| https://portal.mardi4nfdi.de/entity/Q4326708 | 1995-08-15 | Paper |
| Uniform high-order spectral methods for one- and two-dimensional Euler equations | 1993-05-16 | Paper |
| Cell averaging Chebyshev methods for hyperbolic problems | 1993-02-11 | Paper |
| On One-Sided Filters for Spectral Fourier Approximations of Discontinuous Functions | 1993-01-16 | Paper |
| Essentially Nonoscillatory Spectral Fourier Method for Shocks Wave Calculations | 1989-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3760057 | 1986-01-01 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3776773 | 1986-01-01 | Paper |
