Gauss Newton Method for Solving Variational Problems of PDEs with Neural Network Discretizaitons [0.03%]
基于神经网络离散化的PDE变分问题的高斯牛顿法
Wenrui Hao,Qingguo Hong,Xianlin Jin
Wenrui Hao
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a powerful tool for solving differential equations by parameteriz...
Calibration-Based ALE Model Order Reduction for Hyperbolic Problems with Self-Similar Travelling Discontinuities [0.03%]
基于校准的ALE模型降阶方法及其在自相似间断问题中的应用
Monica Nonino,Davide Torlo
Monica Nonino
We propose a novel Model Order Reduction framework that is able to handle solutions of hyperbolic problems characterized by multiple travelling discontinuities. By means of an optimization based approach, we introduce suitable calibration m...
Riemannian Newton Methods for Energy Minimization Problems of Kohn-Sham Type [0.03%]
Kohn-Sham型能量极小化问题的黎曼牛顿法
R Altmann,D Peterseim,T Stykel
R Altmann
This paper is devoted to the numerical solution of constrained energy minimization problems arising in computational physics and chemistry such as the Gross-Pitaevskii and Kohn-Sham models. In particular, we introduce Riemannian Newton meth...
Error Estimates and Adaptivity of the Space-Time Discontinuous Galerkin Method for Solving the Richards Equation [0.03%]
求解Richards方程的时空间断Galerkin方法的误差估计及自适应算法研究
Vít Dolejší,Hyun-Geun Shin,Miloslav Vlasák
Vít Dolejší
We present a higher-order space-time adaptive method for the numerical solution of the Richards equation that describes a flow motion through variably saturated media. The discretization is based on the space-time discontinuous Galerkin met...
Implicit Low-Rank Riemannian Schemes for the Time Integration of Stiff Partial Differential Equations [0.03%]
隐式低秩黎曼方案在刚性偏微分方程的时间积分中的应用
Marco Sutti,Bart Vandereycken
Marco Sutti
We propose two implicit numerical schemes for the low-rank time integration of stiff nonlinear partial differential equations. Our approach uses the preconditioned Riemannian trust-region method of Absil, Baker, and Gallivan, 2007. We demon...
Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations [0.03%]
压缩Navier-Stokes方程的梯度稳健杂交DG离散方法
P L Lederer,C Merdon
P L Lederer
This paper studies two hybrid discontinuous Galerkin (HDG) discretizations for the velocity-density formulation of the compressible Stokes equations with respect to several desired structural properties, namely provable convergence, the pre...
Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport [0.03%]
高效高阶空间-角-能量多面体间断有限元方法求解线性玻尔兹曼输运方程
Paul Houston,Matthew E Hubbard,Thomas J Radley et al.
Paul Houston et al.
We introduce an hp-version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented in...
Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis [0.03%]
非均匀有理B样条(NURBS)模型的离散化用于无网格等几何分析方法
Urban Duh,Varun Shankar,Gregor Kosec
Urban Duh
We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new al...
Visualizing Fluid Flows via Regularized Optimal Mass Transport with Applications to Neuroscience [0.03%]
基于正则化最优传输的流体流动可视化及其在神经科学中的应用
Xinan Chen,Anh Phong Tran,Rena Elkin et al.
Xinan Chen et al.
The regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the optimal mass transport (OMT) problem proposed by Benamou and Brenier. We show that the rOMT mo...
Multilevel Monte Carlo Methods for Stochastic Convection-Diffusion Eigenvalue Problems [0.03%]
随机对流扩散特征值问题的多水平蒙特卡洛方法
Tiangang Cui,Hans De Sterck,Alexander D Gilbert et al.
Tiangang Cui et al.
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element (FE...