Optimal Multigrid Convergence by Elliptic/Hyperbolic Splitting
نویسندگان
چکیده
We describe a multigrid method for solving the steady Euler equations in O(N) operations, where N is the number of unknowns, based on an elliptic/hyperbolic decomposition achieved by local preconditioning. The splitting allows the embedded advection equations to be treated with streamwise semicoarsening rather than full coarsening, which would not be effective. A simple 2-D numerical computation is presented as proof of concept. A convergence study indicates the split method has complexity N0.97 over a wide range of grid spacings and Mach numbers, while the use of full coarsening for all equations makes the complexity deteriorate to N1.44.
منابع مشابه
Multigrid Methods for PDE Optimization
Research on multigrid methods for optimization problems is reviewed. Optimization problems include shape design, parameter optimization, and optimal control problems governed by partial differential equations of elliptic, parabolic, and hyperbolic type.
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