matlab有限元網(wǎng)格劃分程序
DistMesh is a simple MATLAB code for generation of unstructured triangular and tetrahedral meshes. It was developed by Per-Olof Persson (now at UC Berkeley) and Gilbert Strang in the Department of Mathematics at MIT. A detailed description of the program is provided in our SIAM Review paper, see documentation below.
One reason that the code is short and simple is that the geometries are specified by Signed Distance Functions. These give the shortest distance from any point in space to the boundary of the domain. The sign is negative inside the region and positive outside. A simple example is the unit circle in 2-D, which has the distance function d=r-1, where r is the distance from the origin. For more complicated geometries the distance function can be computed by interpolation between values on a grid, a common representation for level set methods.
For the actual mesh generation, DistMesh uses the Delaunay triangulation routine in MATLAB and tries to optimize the node locations by a force-based smoothing procedure. The topology is regularly updated by Delaunay. The boundary points are only allowed to move tangentially to the boundary by projections using the distance function. This iterative procedure typically results in very well-shaped meshes.
Our aim with this code is simplicity, so that everyone can understand the code and modify it according to their needs. The code is not entirely robust (that is, it might not terminate and return a well-shaped mesh), and it is relatively slow. However, our current research shows that these issues can be resolved in an optimized C++ code, and we believe our simple MATLAB code is important for demonstration of the underlying principles.
To use the code, simply download it from below and run it from MATLAB. For a quick demonstration, type "meshdemo2d" or "meshdemond". For more details see the documentation.
標簽：
matlab有限元網(wǎng)格劃分程序
上傳時間：
2015-08-12
上傳用戶：凜風拂衣袖
Computational models are commonly used in engineering design and scientific discovery activities for simulating
complex physical systems in disciplines such as fluid mechanics, structural dynamics, heat transfer, nonlinear
structural mechanics, shock physics, and many others. These simulators can be an enormous aid to engineers who
want to develop an understanding and/or predictive capability for complex behaviors typically observed in the
corresponding physical systems. Simulators often serve as virtual prototypes, where a set of predefined system
parameters, such as size or location dimensions and material properties, are adjusted to improve the performance
of a system, as defined by one or more system performance objectives. Such optimization or tuning of the
virtual prototype requires executing the simulator, evaluating performance objective(s), and adjusting the system
parameters in an iterative, automated, and directed way. System performance objectives can be formulated, for
example, to minimize weight, cost, or defects; to limit a critical temperature, stress, or vibration response; or
to maximize performance, reliability, throughput, agility, or design robustness. In addition, one would often
like to design computer experiments, run parameter studies, or perform uncertainty quantification (UQ). These
approaches reveal how system performance changes as a design or uncertain input variable changes. Sampling
methods are often used in uncertainty quantification to calculate a distribution on system performance measures,
and to understand which uncertain inputs contribute most to the variance of the outputs.
A primary goal for Dakota development is to provide engineers and other disciplinary scientists with a systematic
and rapid means to obtain improved or optimal designs or understand sensitivity or uncertainty using simulationbased
models. These capabilities generally lead to improved designs and system performance in earlier design
stages, alleviating dependence on physical prototypes and testing, shortening design cycles, and reducing product
development costs. In addition to providing this practical environment for answering system performance questions,
the Dakota toolkit provides an extensible platform for the research and rapid prototyping of customized
methods and meta-algorithms
標簽：
Optimization and Uncertainty Quantification
上傳時間：
2016-04-08
上傳用戶：huhu123456
