Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
The rapid evaluation of volume integrals of potential theory on general regions
Journal of Computational Physics
On the numerical solution of the biharmonic equation in the plane
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A fast Poisson solver for complex geometries
Journal of Computational Physics
Integral equation methods for Stokes flow and isotropic elasticity in the plane
Journal of Computational Physics
A Fast Poisson Solver of Arbitrary Order Accuracy in Rectangular Regions
SIAM Journal on Scientific Computing
Parallel Adaptive Solution of a Poisson Equation with Multiwavelets
SIAM Journal on Scientific Computing
On the efficient solution of sparse systems of linear and nonlinear equations.
On the efficient solution of sparse systems of linear and nonlinear equations.
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We present a fast, new method for evaluating particular solutions of the biharmonic equation on general two dimensional regions. The cost of our method is essentially twice the cost of solving Poisson's equation on a regular rectangular region in which the irregular region is embedded. Thus, the cost is O(n2 log n) where n is the number of mesh points in each direction in the embedding region. Moreover, we can compute derivatives of the particular solution directly, with little loss of accuracy if the boundary and inhomogeneous term are sufficiently accurate. The is especially important in applications, since it is generally derivatives that are needed. Computational results are provided.