Previous |  Up |  Next


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.
[1] M.  Práger: Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle. Appl. Math. 43 (1998), 311–320. DOI 10.1023/A:1023269922178 | MR 1627985
[2] M. Práger: Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case. Appl. Math. 46 (2001), 231–239. DOI 10.1023/A:1013744008028 | MR 1828307 | Zbl 1059.65101
[3] Handbook of Convex Geometry. P. M. Gruber, J. M.  Wills (eds.), Elsevier Science Publishers B.V., 1993. Zbl 0777.52002
[4] R. W.  Hockney: A fast direct solution of Poisson’s equation using Fourier analysis. J. Assoc. Comp. Mach. 12 (1965), 95–113. DOI 10.1145/321250.321259 | MR 0213048 | Zbl 0139.10902
[5] J. W.  Cooley J. W.  Tukey: An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19 (1965), 297–301. DOI 10.1090/S0025-5718-1965-0178586-1 | MR 0178586
[6] 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
[7] D. M. Y.  Sommerville: Space-filling tetrahedra in Euclidean space. Proc. Edinburgh Math. Soc. 41 (1923), 49–57.
Partner of
EuDML logo