Least-squares Proper Generalised Decompositions for Elliptic Systems
نویسندگان
چکیده
Proper generalised decompositions (PGDs) are a family of methods for efficiently solving high-dimensional PDEs. Convergence of PGD algorithms can be proven provided that the weak form of the PDE can be recast as the minimisation of some energy functional. A large number of elliptic problems, such as the Stokes problem, cannot be guaranteed to converge when employing a Galerkin PGD. Least-squares methods are derived from the minimisation of the residual of the differential operator under a carefully selected norm. This provides an ‘artificial’ energy functional with which convergence of least-squares PGDs can be proven for all elliptic problems. In this paper robust least-squares PGD algorithms for the Poisson and Stokes problems are contructed and a comparison of the efficiency of different formulations is given.
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