Spectral element methods on simplicial meshes,say TSEM,show both the advantages of spectral and finite element methods,i.e.,spectral accuracy and geometrical flexibility.We present a TSEM solver of the two-dimensional...Spectral element methods on simplicial meshes,say TSEM,show both the advantages of spectral and finite element methods,i.e.,spectral accuracy and geometrical flexibility.We present a TSEM solver of the two-dimensional(2D)incompressible Navier-Stokes equations,with possible extension to the 3D case.It uses a projection method in time and piecewise polynomial basis functions of arbitrary degree in space.The so-called Fekete-Gauss TSEM is employed,i.e.,Fekete(resp.Gauss)points of the triangle are used as interpolation(resp.quadrature)points.For the sake of consistency,isoparametric elements are used to approximate curved geometries.The resolution algorithm is based on an efficient Schur complement method,so that one only solves for the element boundary nodes.Moreover,the algebraic system is never assembled,therefore the number of degrees of freedom is not limiting.An accuracy study is carried out and results are provided for classical benchmarks:the driven cavity flow,the flow between eccentric cylinders and the flow past a cylinder.展开更多
An efficient p-multigrid method is developed to solve the algebraic systems which result from the approximation of elliptic problems with the so-called FeketeGauss Spectral Element Method,which makes use of the Fekete...An efficient p-multigrid method is developed to solve the algebraic systems which result from the approximation of elliptic problems with the so-called FeketeGauss Spectral Element Method,which makes use of the Fekete points of the triangle as interpolation points and of the Gauss points as quadrature points.A multigrid strategy is defined by comparison of different prolongation/restriction operators and coarse grid algebraic systems.The efficiency and robustness of the approach,with respect to the type of boundary condition and to the structured/unstructured nature of the mesh,are highlighted through numerical examples.展开更多
文摘Spectral element methods on simplicial meshes,say TSEM,show both the advantages of spectral and finite element methods,i.e.,spectral accuracy and geometrical flexibility.We present a TSEM solver of the two-dimensional(2D)incompressible Navier-Stokes equations,with possible extension to the 3D case.It uses a projection method in time and piecewise polynomial basis functions of arbitrary degree in space.The so-called Fekete-Gauss TSEM is employed,i.e.,Fekete(resp.Gauss)points of the triangle are used as interpolation(resp.quadrature)points.For the sake of consistency,isoparametric elements are used to approximate curved geometries.The resolution algorithm is based on an efficient Schur complement method,so that one only solves for the element boundary nodes.Moreover,the algebraic system is never assembled,therefore the number of degrees of freedom is not limiting.An accuracy study is carried out and results are provided for classical benchmarks:the driven cavity flow,the flow between eccentric cylinders and the flow past a cylinder.
文摘An efficient p-multigrid method is developed to solve the algebraic systems which result from the approximation of elliptic problems with the so-called FeketeGauss Spectral Element Method,which makes use of the Fekete points of the triangle as interpolation points and of the Gauss points as quadrature points.A multigrid strategy is defined by comparison of different prolongation/restriction operators and coarse grid algebraic systems.The efficiency and robustness of the approach,with respect to the type of boundary condition and to the structured/unstructured nature of the mesh,are highlighted through numerical examples.
