a b s t r a c tIn this work, a space-time multigrid method which uses standard coarsening in both temporal and spatial domains and combines the use of different smoothers is proposed for the solution of the heat equation in one and two space dimensions. In particular, an adaptive smoothing strategy, based on the degree of anisotropy of the discrete operator on each grid-level, is the basis of the proposed multigrid algorithm. Local Fourier analysis is used for the selection of the crucial parameter defining such an adaptive smoothing approach. Central differences are used to discretize the spatial derivatives and both implicit Euler and Crank-Nicolson schemes are considered for approximating the time derivative. For the solution of the second-order scheme, we apply a double discretization approach within the space-time multigrid method. The good performance of the method is illustrated through several numerical experiments.
The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.