Residual cutting method for elliptic boundary value problems: Application to Poisson's equation
The paper is concerned with an iterative solver for elliptic boundary value problems. The main idea of the method is to present the current solutions increments as a linear combination of the approximate solution of the corresponding residual equation obtained as a result of \(M\) internal iterations and increments corresponding to \(L\) previous iterations. The coefficients of the combination (the residual cutting coefficients) are then determined as the least squares solutions of the next residual equation. It is proved that the process converges if some not very restrictive condition is met. Computational examples for the Poisson equation showing fast convergence with relatively small values of \(M\) and \(L\) are presented. The application of the method to ill-posed Neumann problems is discussed and demonstrated.
scientific article; zbMATH DE number 1100736