The numerical solution of the biharmonic equation by conformal mapping
- Chinese Univ. of Hong Kong, Shatin (Hong Kong). Dept. of Mathematics
- Wichita State Univ., KS (United States). Dept. of Mathematics and Statistics
The solution to the biharmonic equation in a simply connected region {Omega} in the plane is computed in terms of the Goursat functions. The boundary conditions are conformally transplanted to the disk with a numerical conformal map. A linear system is obtained for the Taylor coefficients of the Goursat functions. The coefficient matrix of the linear system can be put in the form I + K, where K is the discretization of a compact operator. K can be thought of as the composition of a block Hankel matrix with a diagonal matrix. The compactness leads to clustering of eigenvalues, and the Hankel structure yields a matrix-vector multiplication cost of O(N log N). Thus, if the conjugate gradient method is applied to the system, then superlinear convergence will be obtained. Numerical results are given to illustrate the spectrum clustering and superlinear convergence.
- Sponsoring Organization:
- USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
- DOE Contract Number:
- FG02-92ER25124
- OSTI ID:
- 556631
- Journal Information:
- SIAM Journal on Scientific Computing, Vol. 18, Issue 6; Other Information: PBD: Nov 1997
- Country of Publication:
- United States
- Language:
- English
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