Localized Reduced Basis Methods for PDE-constrained Parameter Optimization
偏微分方程约束参数优化的局部化简基方法
基本信息
- 批准号:415818537
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Research Grants
- 财政年份:2018
- 资助国家:德国
- 起止时间:2017-12-31 至 2022-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This projects is concerned with model reduction for parameter optimization of nonlinear elliptic partial differential equations (PDEs). The goal is to develop a new paradigm for PDE-constrained optimization based on adaptive online enrichment. The essential idea is to design a localized version of the reduced basis (RB) method which is called Localized Reduced Basis Method (LRBM). This allows us to tighten the quality of the reduced order approximation online within each iteration of the applied optimization algorithms. A localized a posteriori error analysis ensures convergence of the reduced basis solution to the solution of the underlying infinite dimensional parameter optimization problem. In the case of a locally inaccurate approximation quality the RB discretization is improved only locally in a very efficient way. The approach is designed for numerical multiscale methods, trust region based optimization methods and for iteratively regularized Gauß-Newton algorithms.
该项目涉及非线性椭圆型偏微分方程(偏微分方程)参数优化的模型降阶。我们的目标是开发一个新的模式,基于自适应在线富集偏微分方程约束优化。其基本思想是设计一种局部化的缩减基方法,称为局部化缩减基方法(LRBM)。这使我们能够在所应用的优化算法的每次迭代内在线收紧降阶近似的质量。一个局部的后验误差分析,确保收敛的减少基础解决方案的解决方案的基础无穷维参数优化问题。在局部不准确的近似质量的情况下,RB离散化仅以非常有效的方式局部地改进。该方法是专为数值多尺度方法,信赖域为基础的优化方法和迭代正则化高斯-牛顿算法。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Professor Dr. Mario Ohlberger其他文献
Professor Dr. Mario Ohlberger的其他文献
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{{ truncateString('Professor Dr. Mario Ohlberger', 18)}}的其他基金
Wave propagation in periodic structures and negative refraction mechanisms
周期性结构中的波传播和负折射机制
- 批准号:
258039653 - 财政年份:2014
- 资助金额:
-- - 项目类别:
Research Grants
Reduzierte Basis Methoden zur Modellreduktion für nichtlineare parametrisierte Evolutionsgleichungen
非线性参数化演化方程模型简化的简化基方法
- 批准号:
104795624 - 财政年份:2009
- 资助金额:
-- - 项目类别:
Research Grants
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2C型蛋白磷酸酶REDUCED DORMANCY 5通过激酶-磷酸酶蛋白复合体调控种子休眠的分子机制
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- 批准年份:2020
- 资助金额:24.0 万元
- 项目类别:青年科学基金项目
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