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• W1629991045 abstract "In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H3-regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems." @default.
• W1629991045 created "2016-06-24" @default.
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• W1629991045 date "2017-09-01" @default.
• W1629991045 modified "2023-10-16" @default.
• W1629991045 title "A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems" @default.
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• W1629991045 doi "https://doi.org/10.1016/j.jcp.2017.04.069" @default.
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