Spectral Methods on Arbitrary Grids
نویسندگان
چکیده
Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial di erential equations. These new methods are equivalent to conventional spectral methods but do not rely on speci c grid distributions. Speci cally, we show how to implement Legendre Galerkin, Legendre collocation, and Laguerre Galerkin methodology on arbitrary grids. Research supported by AFOSR grant no. 93-0090, ARPA grant no. N00014-91-J-4016, and NSF grant no. DMS-9211820. The research was also partially supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the second author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001. i
منابع مشابه
Figure 1. Convergence of the Arbitrary Grid Legendre Galerkin Method on Various Grids
FIGURE 2. Divergence of the arbitrary grid Legendre Galerkin method for improperly imposed initial conditions. Time-stable boundary conditions for nite-diierence schemes solving hyperbolic systems: methodology and application to high-order compact schemes, JCP 111, 220, (1994). 25 To initialize the problem, we must construct an approximation to the initial condition f(x), based on the grid poin...
متن کاملA Clifford Fourier Transform for Vector Field Analysis and Visualization
Vector fields arise in many areas of computational science and engineering. For effective visualization of vector fields it is necessary to identify and extract important features inherent in the data, defined by filters that characterize certain patterns. Our prior approach for vector field analysis used the Clifford Fourier transform for efficient pattern recognition for vector field data def...
متن کاملA New Implicit Dissipation Term for Solving 3D Euler Equations on Unstructured Grids by GMRES+LU-SGS Scheme
Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in t...
متن کاملA New Implicit Dissipation Term for Solving 3D Euler Equations on Unstructured Grids by GMRES+LU-SGS Scheme
Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in t...
متن کاملSpectral/hp Methods For Elliptic Problems on Hybrid Grids
We review the basic algorithms of spectral/hp element methods on tetrahedral grids and present newer developments on hybrid grids consisting of tetrahedra, hexahedra, prisms, and pyramids. A unified tensor-product trial basis is developed for all elements in terms of non-symmetric Jacobi polynomials. We present in some detail the patching procedure to ensure C continuity and appropriate solutio...
متن کامل