REDUCED-BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR MANY-PARAMETER HEAT CONDUCTION PROBLEMS

Sen S

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REDUCED-BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR MANY-PARAMETER HEAT CONDUCTION PROBLEMS

机译：多参数传热问题的降基逼近和后误差估计

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Reduced-basis (RB) methods enable repeated and rapid evaluation of parametrized partial differential equation (PDE)-constrained input-output relationships required in the context of parameter estimation, design, optimization, and control. These methods have been successfully applied to problems with few parameters [O(3)]. Here we introduce efficient sampling algorithms that enable the efficient exploration of many parameters. We apply the RB methods to an illustrative heat conduction problem with P = 25 parameters, obtaining accurate and certified results in real time with significant computational savings relative to standard finite-element techniques.

机译：减少基数（RB）方法可以在参数估计，设计，优化和控制的情况下，重复快速评估参数化偏微分方程（PDE）约束的输入输出关系。这些方法已成功应用于参数较少的问题[O（3）]。在这里，我们介绍了有效的采样算法，可以有效地探索许多参数。我们将RB方法应用于P = 25参数的说明性导热问题，与标准的有限元技术相比，可以实时获得准确且经过认证的结果，并且可以节省大量计算量。

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《Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology》 |2008年第6期|共21页
作者
Sen S;
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正文语种 eng
中图分类热力工程、热机;
关键词
PARTIAL-DIFFERENTIAL-EQUATIONS;

机译：偏微分方程;

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1. REDUCED-BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR MANY-PARAMETER HEAT CONDUCTION PROBLEMS [J] . Sen S Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology . 2008,第5a6期

机译：多参数传热问题的降基逼近和后误差估计
2. A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations [J] . Martin A. Grepl, Anthony T. Patera RAIRO. Mathematical Modelling and Numerical Analysis. = Modelisation Mathematique et Analyse Numerique . 2005,第1期

机译：参数化抛物型偏微分方程的减基近似的后验误差界
3. Rapid inverse parameter estimation using reduced-basis approximation with asymptotic error estimation [J] . G.R. Liu, Khin Zaw, Y.Y. Wang Computer Methods in Applied Mechanics and Engineering . 2008,第45a48期

机译：使用减少基近似与渐近误差估计的快速逆参数估计
4. Transient Non-linear Heat Conduction Solution by a Dual Reciprocity Boundary Element Method with an Effective Posteriori Error Estimator [C] . Eduardo Divo, Alain J. Kassab HTD-vol.375-1; American Society of Mechanical Engineers(ASME) International Mechanical Engineering Congress and Exposition vol.1; 20041113-19; Anaheim,CA(US) . 2004

机译：具有有效后验误差估计器的双互易边界元方法求解瞬态非线性导热问题
5. Adaptive finite element approximation of the Black-Scholes equation based on residual-type a posteriori error estimators. [D] . Li, Huifang. 2009

机译：基于残差型后验误差估计量的Black-Scholes方程的自适应有限元逼近。
6. Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations [O] . Michael Feischl, Gregor Gantner, Dirk Praetorius -1

机译：弱奇异积分方程的自适应IGA边界元方法的可靠高效后验误差估计
7. Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations [O] . Grepl Martin A. (Martin Alexander) 1974- 2005

机译：基于简约逼近的抛物型偏微分方程的后验误差估计

REDUCED-BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR MANY-PARAMETER HEAT CONDUCTION PROBLEMS

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