TY - JOUR
T1 - Spectral Elliptic Solvers in a Finite Cylinder
AU - F. Auteri & L. Quartapelle
JO - Communications in Computational Physics
VL - 2-4
SP - 426
EP - 441
PY - 2009
DA - 2009/02
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7741.html
KW - 
AB - <p style="text-align: justify;">New direct spectral solvers for the 3D Helmholtz equation in a finite cylindrical region are presented. A purely variational (no collocation) formulation of the
problem is adopted, based on Fourier series expansion of the angular dependence and
Legendre polynomials for the axial dependence. A new Jacobi basis is proposed for the
radial direction overcoming the main disadvantages of previously developed bases for
the Dirichlet problem. Nonhomogeneous Dirichlet boundary conditions are enforced
by a discrete lifting and the vector problem is solved by means of a classical uncoupling technique. In the considered formulation, boundary conditions on the axis of
the cylindrical domain are never mentioned, by construction. The solution algorithms
for the scalar equations are based on double diagonalization along the radial and axial
directions. The spectral accuracy of the proposed algorithms is verified by numerical
tests.</p>