Summary: On a Fast Direct Elliptic Solver by a Modified Fourier
A. Averbuch, M. Israeli, L. Vozovoi
appeared in Numerical Algorithms, Vol. 15 (3,4) pp. 287313, 1997.
A fast elliptic solver of high order accuracy is constructed for the solution of the
Poisson and the Helmholtz equations in rectangular domains. The algorithm is based
on the Fourier method in combination with a subtraction procedure. The singularities
at the corner points, arising due to nonsmoothness of the boundaries, are treated
explicitly using properly constructed singular corner functions. The present algorithm
is a generalization of the Fast Poisson Solver developed in our previous paper .
Key words: Helmholtz equation, Fourier method, fast solver, corner singularities.
This paper presents further developments of a fast direct Poisson solver constructed previ
ously in . The present approach is applied, with only slight modifications, to a wider
class of second order elliptic problems in rectangular regions: Poisson, the oscillatory (in
definite) Helmholtz (OH) and the monotonic Helmholtz (MH) equations. The MH equation
frequently appears in Computational Fluid Dynamics as a result of time discretization of
the NavierStokes equations.
Our approach is based on the Fourier method in combination with the subtraction tech