Ronen Feldman, Martin Charles Golumbic
Ann. Math. Artif. Intell.
The biharmonic equation arises in a variety of problems in applied mathematics, most notably in plane elasticity and in viscous incompressible flow. Integral equation methods are natural candidates for the numerical solution of such problems, since they discritize the boundary alone, are easy to apply in the case of free or moving boundaries, and achieve superalgebraic convergence rates on sufficiently smooth domains, regardless of shape. In this paper, we follow the work of Mayo and Greenbaum and make use of the Sherman-Lauricella integral equation which is a Fredholm equation with bounded kernel. We describe a fast algorithm for the evaluation of the integral operators appearing in that equation. When combined with a conjugate gradient like algorithm, we are able to solve the discretized integral equation in an amount of time proportional to N, where N is the number of nodes in the discretization of the boundary. © 1992.
Ronen Feldman, Martin Charles Golumbic
Ann. Math. Artif. Intell.
W.C. Tang, H. Rosen, et al.
SPIE Optics, Electro-Optics, and Laser Applications in Science and Engineering 1991
Paul J. Steinhardt, P. Chaudhari
Journal of Computational Physics
Michael E. Henderson
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering