The Numerical Solution of the Biharmonic Equation by Conformal Mapping

@article{Chan1997TheNS,
  title={The Numerical Solution of the Biharmonic Equation by Conformal Mapping},
  author={Raymond H. Chan and Thomas K. DeLillo and Mark A. Horn},
  journal={SIAM J. Scientific Computing},
  year={1997},
  volume={18},
  pages={1571-1582}
}
The solution to the biharmonic equation in a simply connected region 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 coeecients of the Goursat functions. The coeecient 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… CONTINUE READING