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A First Course in the Numerical Analysis of Differential Equations by Arieh Iserles

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15

Fast Poisson solvers

15.1 TST matrices and the Hockney method

This chapter is concerned with yet another approach to the solution of the linear equations that occur when the Poisson equation is discretized by finite differences. This approach is an alternative to the direct methods of Chapter 11 and to the iterative schemes of Chapters 1214. We intend to present two techniques for the very fast approximation of ∇2u = f, one in a rectangle and the other in a disc. These techniques share two features. Firstly, they originate in numerical solution ...

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