The temperature field distribution directly reflects the combustion condition in a furnace.In this paper,acoustic thermometry to reconstruct temperature distribution is investigated.A method based on radial basis func...The temperature field distribution directly reflects the combustion condition in a furnace.In this paper,acoustic thermometry to reconstruct temperature distribution is investigated.A method based on radial basis function approximation with polynomial reproduction(RBF-PR)is proposed in order to improve the accuracy and stability of the method based on RBF approximation.In addition,the refraction effect of sound wave paths is considered in the process of reconstruction.The curved lines with refraction effect are numerically calculated by solving differential equations,which show that sonic waves curve towards the zones of higher temperature.The reconstructed performance is validated via numerical simulation using four temperature distribution models.Results and analysis show that the proposed method has much greater accuracy than the method based on RBF approximation,and when considering the effect of refraction,our method can reconstruct more excellent reconstruction performance than others,which do not take into account the refraction effect of sound wave paths.展开更多
Given a multivariate quasi-interpolation operator with the partition of unity property,we propose a method to raise the accuracy with simple knots.The resulting operators possess higher accuracy while not requiring an...Given a multivariate quasi-interpolation operator with the partition of unity property,we propose a method to raise the accuracy with simple knots.The resulting operators possess higher accuracy while not requiring any derivative information of the underlying function.On that basis,we improve the multivariate spline quasi-interpolants with higher accuracy over type-2triangulations.Moreover,we apply the improved quasi-interpolants to simulate time developing partial differential equations(PDEs).The numerical experiments verify the efficiency of the proposed methods.展开更多
In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can ...In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of lo- cation points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly im- proved which is consistent with the theoretical results.展开更多
基金This research is supported by the National Science Foundation of China(No.11674093 and No.11474091)the Fundamental Research Funds for the Central Universities of China(No.2018 MS131)the State Key Laboratory of Acoustics,Institute of Acoustics,Chinese Academy of Science,China(SKLA201808).
文摘The temperature field distribution directly reflects the combustion condition in a furnace.In this paper,acoustic thermometry to reconstruct temperature distribution is investigated.A method based on radial basis function approximation with polynomial reproduction(RBF-PR)is proposed in order to improve the accuracy and stability of the method based on RBF approximation.In addition,the refraction effect of sound wave paths is considered in the process of reconstruction.The curved lines with refraction effect are numerically calculated by solving differential equations,which show that sonic waves curve towards the zones of higher temperature.The reconstructed performance is validated via numerical simulation using four temperature distribution models.Results and analysis show that the proposed method has much greater accuracy than the method based on RBF approximation,and when considering the effect of refraction,our method can reconstruct more excellent reconstruction performance than others,which do not take into account the refraction effect of sound wave paths.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1207105711671068+1 种基金12001487)the Characteristic&Preponderant Discipline of Key Construction Universities in Zhejiang Province(Zhejiang Gongshang University-Statistics)。
文摘Given a multivariate quasi-interpolation operator with the partition of unity property,we propose a method to raise the accuracy with simple knots.The resulting operators possess higher accuracy while not requiring any derivative information of the underlying function.On that basis,we improve the multivariate spline quasi-interpolants with higher accuracy over type-2triangulations.Moreover,we apply the improved quasi-interpolants to simulate time developing partial differential equations(PDEs).The numerical experiments verify the efficiency of the proposed methods.
文摘In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of lo- cation points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly im- proved which is consistent with the theoretical results.
