Poisson equation; boundary value problem; fast direct solver; triangle; tetrahedron
Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given 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. Eigenproblems are also considered.
 Handbook of Convex Geometry
. P. M. Gruber, J. M. Wills (eds.), Elsevier Science Publishers B.V., 1993. Zbl 0777.52002
 P. A. Swarztrauber: The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson’s equation on a rectangle
. SIAM Review 19 (1977), 490–501. DOI 10.1137/1019071
| MR 0438732
| Zbl 0358.65088
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