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Machine learning has been successfully applied to various fields in computational science and engineering. In this paper, we propose interfaced neural networks (INNs) to solve interface problems with ...
Machine learning has been successfully applied to various fields in computational science and engineering. In this paper, we propose interfaced neural networks (INNs) to solve interface problems with ...
基于周期理论和COMSOL PDE的排桩减振特性研究
周期排桩 COMSOL PDE 衰减域 环境减振
2018/11/29
基于周期理论和COMSOL PDE有限元法，研究了排桩的衰减域（attenuation zone，简称AZ），讨论了相关参数对衰减域的影响；针对实测环境振动设计了具体的排桩结构，并对该排桩的减振特性在频域和时域内分别进行了数值模拟。研究结果表明：周期理论可以用于揭示排桩的动力特性，为排桩结构在环境减振中的应用提供新思路；基于控制方程建模的COMSOL PDE有限元法，不仅能够用于周期结构的衰减域计...
Liszt: A Domain Specific Language for Building Portable Mesh-based PDE Solvers
compiler analysis and program transformations, programming and runtime environments for high performance and high throughput computing
2016/5/24
Heterogeneous computers with processors and accelerators are becoming widespread in scientific computing. However,it is difficult to program hybrid architectures and there is no commonly accepted prog...
Nonlinear Stochastic Perturbations of Dynamical Systems and Quasi-linear Parabolic PDE’s with a Small Parameter
Quasi linear parabolic equations parameters quasi linear initial boundary value
2015/9/28
In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time beh...
Averaging principle for quasi-linear parabolic PDE’s and related diffusion processes
Quasi linear disturbance two dimensional flow parabola and small parameter
2015/9/28
Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDE’s with a small parameter at the second order derivatives are considered in th...
红外云图的台风内核风速建模的RBFNN和PDE方法
建模 偏微分方程 径向基函数神经网络 台风云图
2016/8/4
目前反演台风内核风场时多采用线性回归方法进行建模,针对基于线性回归法的台风内核风速拟合效果较差的缺点,提出一种基于径向基函数神经网络(RBFNN)和偏微分方程(PDE)结合的红外卫星云图有眼台风内核风速和云图灰度建模方法。首先采用基于测地活动轮廓模型的PDE提取有眼台风的眼壁,获得台风眼壁空间位置和亮度数据;然后结合台风年鉴给出的台风近中心最大风速数据基于RBFNN进行有眼台风内核风速和云图灰度建...
On a fully non-linear elliptic PDE in conformal geometry
Fully nonlinear PDE generalized Yamabe problem
2014/4/3
We give an expository survey on the subject of the Yamabe-type problem and applications. With a recent technique in hand, we also present a simplified proof of the result by Chang-Gursky-Yang on...
MATLAB/PDE在弹性力学可视化教学中的应用
偏微分方程 弹性力学 边界条件 可视化
2014/8/14
MATLAB 的PDE（partial differential equations）工具箱为平面问题求解结果提供了彩色可视化图形，便于弹性力学的学与教. 工具箱采用椭圆型偏微分方程求解平面问题的结果实质上是弹性力学位移法的数值解，该文推导并整理出PDE 的边界方程参数，用于描述弹性力学中常见的边界条件. 结合弯矩和均布载荷作用下的简支梁、受内外压的圆环板和受拉的带孔矩形板3 个例子，说明PDE ...
Designing Optical Fibers: Fitting the Derivatives of a Nonlinear Pde-Eigenvalue Problem
Symmetric Indefinite Eigenvalue Gradient Optical Fiber Design
2013/1/30
When trying to fit data to functions of the eigensystem of a pde-eigenvalue problem, such as Maxwell’s equation, numerical differentiation is ineffective and analytic gradients must be supplied. In ou...
基于PDE算法的指静脉图像预处理
偏微分方程(PDE) 图像去噪 PM模型 信噪比（SNR）
2012/11/12
为了更好地去除手指静脉图片中的噪声, 提出一种基于偏微分方程算法（PDE）的去噪新模型. 该模型在PM模型的基础上, 采用新的扩散函数, 并结合四阶PDE模型对原模型结构进行变换. 用合成图像和真实指静脉图像分别对新模型进行实验验证, 结果表明, 相对于PM模型, 新模型使信噪比（SNR）值提高了约5 dB, 且能在去除噪声的同时很好地保持指静脉特征。
针对传统光流场配准模型会造成图像模糊和细节丢失的问题，提出了一种基于偏微分方程的自适应各向异性配准模型。新模型将具有自适应性的扩散滤波方法引入图像配准，定义具有图像结构保持能力的各向异性扩散函数作为模型的正则项；数据项采用作用于亮度常量假设的非二次惩罚函数以增加模型的稳健性。实验结果表明，新模型能够有效保持图像特征，实现对大脑等复杂图像的有效配准。
Consistency Analysis of Finite Difference Approximations to PDE Systems
systems of partial differential equations involution Thomas decomposition finite difference approximations consistency
2011/9/16
Abstract: In the given paper we consider finite difference approximations to systems of polynomially-nonlinear partial differential equations whose coefficients are rational functions over rationals i...
On the Quasi-Linear Elliptic PDE $-\nabla\cdot(\nabla{u}/\sqrt{1-|\nabla{u}|^2}) = 4π\sum_k a_k δ_{s_k}$ in Physics and Geometry
Lorentz manifolds maximal foliations lightcone singularities
2011/9/15
Abstract: It is shown that for each finite number of Dirac measures supported at points $s_n$ in three-dimensional Euclidean space, with given amplitudes $a_n$, there exists a unique real-valued Lipsc...
Algebra properties for Sobolev spaces- Applications to semilinear PDE's on manifolds
Sobolev spaces Riemannian manifold algebra rule paraproducts heat semigroup
2011/9/15
Abstract: In this work, we aim to prove algebra properties for generalized Sobolev spaces $W^{s,p} \cap L^\infty$ on a Riemannian manifold, where $W^{s,p}$ is of Bessel-type $W^{s,p}:=(1+L)^{-s/m}(L^p...