相关论文: Computational Analysis of Dispersive and Nonlinear…

In this article, we develop a systematic approach of the invariant subspace method combined with variable transformation to find the generalized separable exact solutions of the nonlinear two-component system of time-fractional PDEs…

In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD…

Real-time reconstruction of deformable surgical scenes is vital for advancing robotic surgery, improving surgeon guidance, and enabling automation. Recent methods achieve dense reconstructions from da Vinci robotic surgery videos, with…

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires…

We introduce a rigorous and simple method for analyzing metasurfaces, modeled as zero-thickness electromagnetic sheets, in Finite Difference (FD) techniques. The method consists in describing the spatial discontinuity induced by the…

An alternative way of visualizing electromagnetic waves in matter and of deriving the Finite Difference Time Domain method (FDTD) for simulating Maxwell's equations for one dimensional systems is presented. The method uses d'Alembert's…

This paper describes a model for nonlinear acoustic wave propagation through absorbing and weakly dispersive media, and its numerical solution by means of finite differences in time domain method (FDTD). The attenuation is based on multiple…

A discontinuous Galerkin time-domain (DGTD) method based on dynamically adaptive Cartesian meshes (ACM) is developed for a full-wave analysis of electromagnetic fields in dispersive media. Hierarchical Cartesian grids offer simplicity close…

Advances in deep learning have enabled physics-informed neural networks to solve partial differential equations. Numerical differentiation using the finite-difference (FD) method is efficient in physics-constrained designs, even in…

This paper proposes a novel Generalized Non-Standard Finite Difference (GNSFD) scheme for the numerical solution of a class of fractional partial differential equations (FrPDEs). The formulation of the method is grounded in optimization and…

3D Gaussian splatting (GS) has emerged as a transformative technique in radiance fields. Unlike mainstream implicit neural models, 3D GS uses millions of learnable 3D Gaussians for an explicit scene representation. Paired with a…

Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is…

In this paper, we introduce a 3D Gaussian Splatting (3DGS)-based pipeline for stereo dataset generation, offering an efficient alternative to Neural Radiance Fields (NeRF)-based methods. To obtain useful geometry estimates, we explore…

Predicting the effect of amino acid mutations on enzyme thermodynamic stability (DDG) is fundamental to protein engineering and drug design. While recent deep learning approaches have shown promise, they often process sequence and structure…

Over the past twenty years, the field of plasmonics has been revolutionized with the isolation and utilization of two--dimensional materials, particularly graphene. Consequently there is significant interest in rapid, robust, and highly…

We propose a novel finite-difference time-domain (FDTD) scheme for the solution of the Maxwell's equations in which linear dispersive effects are present. The method uses high-order accurate approximations in space and time for the…

One of the key advantages of 3D rendering is its ability to simulate intricate scenes accurately. One of the most widely used methods for this purpose is Gaussian Splatting, a novel approach that is known for its rapid training and…

The finite-difference time-domain (FDTD) algorithm is a popular numerical method for solving electromagnetic problems. FDTD simulations can suffer from instability due to the explicit nature of the method. Stability enforcement can be…

This paper is concerned with the numerical solution of compressible fluid flow in a fractured porous medium. The fracture represents a fast pathway (i.e., with high permeability) and is modeled as a hypersurface embedded in the porous…

Integrated computational materials engineering (ICME) has significantly enhanced the systemic analysis of the relationship between microstructure and material properties, paving the way for the development of high-performance materials.…