On a construction of fast direct solvers. (English) Zbl 1099.65027

The author constructs fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra. The construction is performed in such a way that the given domain is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped, and a fast direct solver is used there. All extendable domains are found.


65F05 Direct numerical methods for linear systems and matrix inversion
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
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