Related papers: NURBS-SEM: a hybrid spectral element method on NUR…
Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process.…
This paper presents transient numerical simulations of hydraulic systems in engineering applications using the spectral element method (SEM). Along with a detailed description of the underlying numerical method, it is shown that the SEM…
The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose…
Current successful approaches for generic (non-semantic) segmentation rely mostly on edge detection and have leveraged the strengths of deep learning mainly by improving the edge detection stage in the algorithmic pipeline. This is in…
Dynamic NURBS, also called D-NURBS, is a known dynamic version of the nonuniform rational B-spline (NURBS) which integrates free-form shape representation and a physically-based model in a unified framework. More recently, computer aided…
G-splines are a generalization of B-splines that deals with extraordinary points by imposing G^1 constraints across their spoke edges, thus obtaining a continuous tangent plane throughout the surface. Using the isoparametric concept and the…
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…
The spectrum of the Laplace-Beltrami (LB) operator is central in geometric deep learning tasks, capturing intrinsic properties of the shape of the object under consideration. The best established method for its estimation, from a…
IR or near-infrared (NIR) spectroscopy is a method used to identify a compound or to analyze the composition of a material. Calibration of NIR spectra refers to the use of the spectra as multivariate descriptors to predict concentrations of…
Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices…
Most existing RGB-D semantic segmentation methods focus on the feature level fusion, including complex cross-modality and cross-scale fusion modules. However, these methods may cause misalignment problem in the feature fusion process and…
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…
This work undertakes to combine the interests of IsoGeometric Analysis (IGA) and standard Finite Element Methods (FEM) for the global/local simulation of structures. The idea is to adopt a hybrid global-IGA/local-FEM modeling, thereby…
We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. We analyze the strong error of convergence for spatially…
Neural network-based solvers for partial differential equations (PDEs) have attracted considerable attention, yet they often face challenges in accuracy and computational efficiency. In this work, we focus on time-dependent PDEs and observe…
In order to simulate elastic wave propagation in a complex structure with inhomogeneous media, we often need to obtain the propagating eigenmodes of an elastic waveguide. As the waveguide is assumed uniform in one direction, the original…
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…