FlexPDE V 7——偏微分方程有限元软件

偏微分有限元素软件,有二维及三维FlexPDE 是一个有弹性的,易学,一般的目的用途的有限元素软件,FlexPDE可获得偏微分方程的数值解,偏微分方程在工程上常见于,物理、电机、电子、通讯、土木、机械、化工、化学、生物学、地质学、数学和其它科学领域FlexPDE使用这超强有限元素方法获得数值解。然而,使用FlexPDE并不需要了解复杂的有限元素方法。



FlexPDE 7新功能


分层基础-新的分层FEM基础函数可改善矩阵条件。

优化-内置参数优化器。

CAD网格导入-导入以CAD程序(OBJ格式)创建的边界网格。

常规边界形状-使用隐式代数方程式创建边界路径。

交互式绘图缩放-无需请求特殊绘图即可放大图形。

材料集-用户定义的材料属性组简化了脚本编写。

边界条件集-用户定义的边界条件组简化了脚本编写。

多向周期性-支持角点处多个方向的周期性边界。

扩展首选项面板-所有主要设置都位于方便的首选项面板中。

自动网格输出-更容易后处理与自动网格传输输出。

自动网格输入-尽可能通过导入以前的网格,以更快地重新启动。

简化StopRestart-从网格传输文件重新启动的简化命令。

新的加密狗供应商-Wibu-Systems加密狗提供了更大的灵活性和成本效益。


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V7版本CAD导入截图

Here are some of the new features in version 7 :


CAD Mesh Import - Import a bounding mesh created in a CAD program (OBJ format).

Optimization - Built-in parameter optimizer.

General boundary shapes - Create boundary paths using implicit algebraic equations.

Interactive Plot Zoom - Zoom in on plots without the need to request a special plot.

Material Sets - User-defined groups of material properties simplify script writing.

Boundary Condition Sets - User-defined groups of boundary conditions simplify script writing.

Multidirectional Periodicity - Support for periodic boundaries in more than one direction at corners.

Extended Preferences Panel - All major settings located in a convenient preference panel.

Automatic Mesh Output - Easier post-processing with automatic mesh transfer output.

Automatic Mesh Input - Faster restarts by importing previous mesh when possible.

Simplified Stop & Restart - Simplified commands for restarting from mesh transfer files.

Heirarchical Basis - New heirarchical FEM basis functions improve matrix conditioning.

New Dongle Vendor - Wibu-Systems dongles provide more flexibility and cost effectiveness.FlexPDE does not merely pass a translation on to some other package for processing. In fact, FlexPDE is designed to be the package other applications call for processing.

FlexPDE does not merely pass a translation on to some other package for processing. In fact, FlexPDE is designed to be the package other applications call for processing.
One, two or three space dimensions
Automatic mesh construction
Time dependent, steady-state or eigenvalues.
Flexible integrated graphical output
Dynamic adaptive mesh refinement
Dynamic timestep control
Nonlinear equation solver
Unlimited equation complexity
Unlimited number of simultaneous equations
Multiple Equation Sets*
Complex, Vector and Array Variables and Equations*
Regionally Inactive Variables*
Arbitrary Lagrange/Eulerian moving mesh
Export capability for 3rd-party visualizations
Multithreading support for dual and quad core processors*

Well, you don’t have to just imagine. Because that’s what FlexPDE will do for you.

Join hundreds of the world’s most sophisticated scientists, and take advantage of the most versatile problem-solving environment in existence.

FlexPDE continually monitors the accuracy of the solution, and adapts the finite element mesh to resolve those areas of high error.
You don’t need a dense mesh throughout the domain, because FlexPDE will find the areas that need it, and put it there!

The problem shown here is a two-phase flow calculation, modeling the extraction of oil by water injection. FlexPDE adapts the mesh to the front of the wave.
By locking the mesh to the fluid velocity, you can create a fully Lagrangian model.
Or, you can define a relaxive mesh within moving boundaries to maintain mesh integrity.

Or, by omitting the mesh moving equations, you can perform a fully Eulerian computation.
In any case, FlexPDE automatically corrects the PDE system to represent the motion of the mesh.
The problem shown here computes the motion of a gas in a compressor cylinder

Example: Viscous Flow in a 2D channel:
This problem examines viscous fluid flow in a 2D channel. FlexPDE solves for the X- and Y- velocities of a fluid, with fixed pressures applied at the ends of the channel. The reynolds number in this problem is approximately 20.

The Navier-Stokes equation for steady incompressible flow in two cartesian dimensions is

rho*(dt(U) + U*dx(U) + V*dy(U)) = mu*div(grad(U)) - dx(P)
rho*(dt(V) + U*dx(V) + V*dy(V)) = mu*div(grad(V)) - dy(P)

together with the continuity equation,

dx(U) + dy(V) = 0.

Here U and V are the X- and Y-velocities, P is the pressure (introduced as a surrogate for the continuity equation), rho is density, and mu is viscosity.

Example: Permanent Magnet
This problem considers the magnetic field in a core containing a permanent magnet.

The system obeys the PDE
curl(curl(A)-P)/mu) + J = 0,
where A is the magnetic vector potential, P is the magnetization, J is the current density, and mu is the permeability.

Example: Stress Analysis
This problem shows the deformation of a tension bar with a hole. FlexPDE solves two simultaneous Partial Differential Equations for the X- and Y- displacements within the bar.

dx(Sx) + dy(Txy) + Fx = 0
dx(Txy) + dy(Sy) + Fy = 0

where Sx and Sy are the stresses in the X- and Y- directions, Txy is the shear stress, and Fx and Fy are the body forces in the X- and Y- directions.

Sx = C11*dx(U) + C12*dy(V) + C13*[dy(U) + dx(V)]
Sy = C12*dx(U) + C22*dy(V) + C23*(dy(U) + dx(V))
Txy = C13*dx(U) + C23*dy(V) + C33*(dy(U) + dx(V))

Here the Cnn are the constitutive relations of the material.

Example : Chemical Reactions
This problem follows a cross section of the gas in an open tube chemical reactor as the gas flows down the tube. The chemical reaction has a reaction rate which is exponential in tempreature, and shows an explosive reaction completion once the ’ignition’ temperature is reached. There is a heated band on each side of the tube, to help induce ignition. We model one quarter of the circular cross section. There are two simultaneous PDE’s, one for the temperature and one for the chemical concentration:

dt(T) = div(grad(T)) + a*(1-C)*exp(G-G/T)
dt(C) = div(grad(C)) + b*(1-C)*exp(G-G/T)

Here T is the temperature, C is the concentration. a, b, and G are constants.

Example : Diffusion
This problem considers the thermally driven diffusion of a dopant into a solid from a constant masked source. Parameters have been chosen to be those typically encountered in semiconductor diffusion. The PDE is just the diffusion equation:

dt(C) = div(D*grad(C)) ,

where C is the concentration and D is the diffusivity. At early times, the solution near the source can be compared to the analytic solution for 1D diffusion.

License Methods:
Internet Key -The standard method of licensing FlexPDE Professional is by internet activation. This mode of licensing generates a text key that locks the execution of FlexPDE to a specific computer CPU. Access to the internet is required on a periodic basis to validate the key. The key can be released from one machine and reactivated on another without difficulty.

Dongle - FlexPDE Professional can be configured to use a portable hardware key (dongle) for USB (or parallel port by request). FlexPDE can be run on any machine that has the dongle installed in an appropriate I/O port. There is a $50 surcharge for the dongle.

Network - FlexPDE Professional can be configured to run in a networked mode. A single network accessible computer is configured with a network dongle and a license manager application. Any other computer with network access can then run FlexPDE, up to a specified maximum number of simultaneous users. There is a $150 surcharge for the dongle.

Software Key -On request, Professional configurations can be licensed in the form of a text key that locks the execution of FlexPDE to a specific computer CPU. If you prefer a software license key, you must first download and install the software and record the computer ID from the "Help | Register FlexPDE" screen. Include the computer ID on the license application form. Your software key will be sent to you by Email. Copy this key to the FlexPDE installation directory (you may need administrator privileges to do this).