An algorithm based error detection scheme for the multigrid algorithm

In this paper an Algorithm Based Error Detection (ABED) scheme is applied to the multigrid algorithm which provides an iterative solution to a system of linear algebraic equations resulting from a finite difference discretization of a Poisson equation. Invariants are created to implement checking in the relaxation, restriction and interpolation operators. Modifications to invariants due to roundoff errors accumulated within the operators which often lead to a situation known as false alarms have been addressed by deriving the expressions for the roundoff errors in the algebraic processes in the operators and correcting the invariants accordingly. ABED encoded multigrid algorithm is shown to be insensitive to the size and the range of the input data, besides providing excellent error coverage at a low latency for floating point integer and memory errors.