The technique of iterative reenement for improving the computed solution to a linear system was used on desk calculators and computers in the 1940s and has remained popular. In the 1990s iterative reenement is well supported in software libraries, notably in LAPACK. Although the behaviour of iterative re-nement in oating point arithmetic is reasonably well understood, the existing theory is not...

In this work, sparse linear systems obtained from the streamline diffusion finite element discretization of the convection-diffusion equations are solved by a multigrid method and the generalized minimal residule method. Adaptive mesh refinement process is considered as an integral part of the solution process. We propose some stopping criteria for iterative solvers to ensure the iterative erro...

The technique of iterative refinement for improving the computed solution to a linear system was used on desk calculators and computers in the 1940s and has remained popular. In the 1990s iterative refinement is well,supported in software libraries, notably in LAPACK. Although the behaviour of iterative refinement in floating point arithmetic is reasonably well understood, the existing theory i...

We consider quadrature formulas of high order in time based on Radau–type, L–stable implicit Runge–Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs iterative deferred corrections to compute the solution at the collocation nodes of the quadrature formulas. The numerical stability is guaranteed by a dedic...

Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields many scientists strive to solve them an efficient robust manner. In this paper, we propose interpretable neural solver, the Fourier solver (FNS), address them. FNS is based on deep learning fast transform. Because error between iterative solution ground truth involves wide range frequency modes,...

This paper describes a hybrid direct and iterative solver for two and three dimensional h adaptive grids with point singularities. The point singularities are eliminated by using a sequential linear computational cost solver O(N) on CPU [1]. The remaining Schur complements are submitted to incomplete LU preconditioned conjugated gradient (ILUPCG) iterative solver. The approach is compared to th...

The practical aspect in the parareal algorithm that it consist of using two solvers over different time stepping, the coarse and fine solvers to produce a rapid convergent iterative method for multi processors computations. The coarse solver solve the equation sequentially on the coarse time step while the fine solver use the information from the coarse solution to solve, in parallel, over the ...