In this paper,Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation.First of all,the interpolation basis function is appli...In this paper,Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation.First of all,the interpolation basis function is applied to treat the spatial variables and their partial derivatives,and the collocation method for solving the second order differential equations is established.Secondly,the differential matrix is used to simplify the given differential equations on a given test node.Finally,based on three kinds of test nodes,numerical experiments show that the present scheme can not only calculate the high wave numbers problems,but also calculate the variable wave numbers problems.In addition,the algorithm has the advantages of high calculation accuracy,good numerical stability and less time consuming.展开更多
A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving time-dependent wave equations.Acoustic propagation problems in1＋1,2＋1,3＋1 dimensions with the Dirichlet boundary ...A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving time-dependent wave equations.Acoustic propagation problems in1＋1,2＋1,3＋1 dimensions with the Dirichlet boundary conditions are simulated via space-time coupled spectral element method using quadrilateral,hexahedral and tesseractic elements respectively.Space-time coupled spectral element method can obtain high-order precision over time.With the same total number of nodes,higher numerical precision is obtained if the higher-order Chebyshev polynomials in space directions and lower-order Chebyshev polynomials in time direction are adopted.Numerical illustrations have indicated that the space-time algorithm provides higher precision than the semi-discretization.When space-time coupled spectral element method is used,time subdomain-by-subdomain approach is more economical than time domain approach.展开更多
基金partially supported by National Natural Science Foundation of China(11772165,11961054,11902170)Key Research and Development Program of Ningxia(2018BEE03007)+1 种基金National Natural Science Foundation of Ningxia(2018AAC02003,2020AAC03059)Major Innovation Projects for Building First-class Universities in China’s Western Region(Grant No.ZKZD2017009).
文摘In this paper,Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation.First of all,the interpolation basis function is applied to treat the spatial variables and their partial derivatives,and the collocation method for solving the second order differential equations is established.Secondly,the differential matrix is used to simplify the given differential equations on a given test node.Finally,based on three kinds of test nodes,numerical experiments show that the present scheme can not only calculate the high wave numbers problems,but also calculate the variable wave numbers problems.In addition,the algorithm has the advantages of high calculation accuracy,good numerical stability and less time consuming.
基金supported by the the State Plan for Development of Basic Research in Key Area(973Project)(2012CB026004)
文摘A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving time-dependent wave equations.Acoustic propagation problems in1＋1,2＋1,3＋1 dimensions with the Dirichlet boundary conditions are simulated via space-time coupled spectral element method using quadrilateral,hexahedral and tesseractic elements respectively.Space-time coupled spectral element method can obtain high-order precision over time.With the same total number of nodes,higher numerical precision is obtained if the higher-order Chebyshev polynomials in space directions and lower-order Chebyshev polynomials in time direction are adopted.Numerical illustrations have indicated that the space-time algorithm provides higher precision than the semi-discretization.When space-time coupled spectral element method is used,time subdomain-by-subdomain approach is more economical than time domain approach.
