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 计算数学  2017, Vol. 39 Issue (4): 431-444    DOI:
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FAST SOLUTION OF PARAMETRIZED PARTIAL DIFFERENTIAL EQUATIONS BY USING REDUCED BASIS FINITE ELEMENT METHOD
Zhang Chunyu, Chen Gong, Wang Yizheng, Wang Ye
Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen Univeristy, Zhuhai 519082, China
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Abstract： High-fidelity simulation based on numerical solution of governing partial differential equations has been widely applied in scientific research and engineering design. However, even by exploiting the modern high-performance computation, fast solution is still a challenging task when the simulations have to be run many times such as in optimization problems or in nonlinear coupling problems. For the class of problems which can be described by parametrized partial differential equations, the reduced basis finite element constructs the basis functions on top of typical high-fidelity solutions and thus greatly reduces the number of unknowns. The principles of the method is introduced in the present study and the favorable features are demonstrated through solving the heat conduction problem and the neutron diffusion problem. It is shown a speedup of three orders of magnitude is achieved during the online stage.

NSFC-广东联合基金超级计算科学应用专项项目（20144500031650003）

 引用本文: . 快速求解参数化偏微分方程的缩减基有限元方法及其在核工程中的应用[J]. 计算数学, 2017, 39(4): 431-444. . FAST SOLUTION OF PARAMETRIZED PARTIAL DIFFERENTIAL EQUATIONS BY USING REDUCED BASIS FINITE ELEMENT METHOD[J]. Mathematica Numerica Sinica, 2017, 39(4): 431-444.

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