Adaptive Reduced Basis Methods for Nonlinear Convection–Diffusion Equations
Adaptive Reduced Basis Methods for Nonlinear Convection–Diffusion Equations
复制标题
非线性对流扩散方程的自适应降基方法
DOI：
10.1007/978-3-642-20671-9_39
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Ohlberger M.
中科院分区：
文献类型：
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作者：
Drohmann M;Haasdonk B;Ohlberger M.
许多科学和工程应用都是基于参数化的演化方程，并且依赖于耗时的参数研究或需要确保对仿真时间的关键约束。对于这两种设置，通过缩减基方法的模型降阶是减少计算时间的合适手段。在本程序中，我们展示了减少的基础框架的适用性，一个参数化和高度非线性对流扩散问题的不连续的解决方案的有限体积计划。问题设置的复杂性，需要使用几个新的技术，如参数化的经验算子插值，有效的后验误差估计和自适应生成的减少数据。后者通常是通过自适应搜索参数空间中的基函数来实现的。常见的方法和效果在本演示文稿中进行了简短的修改，并补充了一个新的策略，自适应搜索经验插值数据的时域分析。
Many applications from science and engineering are based on parametrized evolution equations and depend on time-consuming parameter studies or need to ensure critical constraints on the simulation time. For both settings, model order reduction by the reduced basis methods is a suitable means to reduce computational time. In this proceedings, we show the applicability of the reduced basis framework to a finite volume scheme of a parametrized and highly nonlinear convection-diffusion problem with discontinuous solutions. The complexity of the problem setting requires the use of several new techniques like parametrized empirical operator interpolation, efficient a posteriori error estimation and adaptive generation of reduced data. The latter is usually realized by an adaptive search for base functions in the parameter space. Common methods and effects are shortly revised in this presentation and supplemented by the analysis of a new strategy to adaptively search in the time domain for empirical interpolation data.
参数化演化方程有限体积逼近的减基法
DOI：
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发表时间：
2006
期刊：
影响因子：
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作者：
B. Haasdonk;Mario Ohlberger
通讯作者：
Mario Ohlberger