Locally Adaptive Greedy Approximations for Anisotropic Parameter Reduced Basis Spaces
Locally Adaptive Greedy Approximations for Anisotropic Parameter Reduced Basis Spaces
复制标题
各向异性参数缩减基空间的局部自适应贪婪逼近
DOI：
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发表时间：
2012
影响因子：
3.1
通讯作者：
B. Stamm
中科院分区：
文献类型：
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作者：
Y. Maday;B. Stamm
降阶模型，特别是缩减基方法，依赖于在离线阶段构建的经验构建的和问题相关的基函数。在在线阶段，预先计算的问题相关的解决方案的空间，这是跨越的基础功能，然后可以使用，以减少计算问题的大小。对于复杂的问题，为了从模型简化中获得计算上的好处，保证一定误差容限所需的基函数的数量可能会变得太大。为了克服这一点，目前的工作介绍了一个框架，局部近似空间（在参数空间）被用来定义的降阶近似，以便有明确的控制在线成本。这种方法还使局部近似空间适应参数空间中的局部各向异性行为。我们提出的算法和大量的数值试验。
Reduced order models, in particular the reduced basis method, rely on empirically built and problem dependent basis functions that are constructed during an off-line stage. In the on-line stage, the precomputed problem-dependent solution space, that is spanned by the basis functions, can then be used in order to reduce the size of the computational problem. For complex problems, the number of basis functions required to guarantee a certain error tolerance can become too large in order to benefit computationally from the model reduction. To overcome this, the present work introduces a framework where local approximation spaces (in parameter space) are used to define the reduced order approximation in order to have explicit control over the on-line cost. This approach also adapts the local approximation spaces to local anisotropic behavior in the parameter space. We present the algorithm and numerous numerical tests.
影响因子：
2.8
作者：
Cantwell, C. D.;Sherwin, S. J.;Kelly, P. H. J.
通讯作者：
Kelly, P. H. J.