Sparse-grid finite-volume multigrid for 3D-problems
Copyright policy )Sparse-grid finite-volume multigrid for 3D-problems
This paper introduces a multigrid method based on Haar wavelets, and the method is applied to second-order, elliptic partial differential equations. It is shown that the question of which collection of Haar wavelets to use as a basis has significant influence on the computational efficiency. The paper provides a Fourier analysis of the convergence of the algorithm, and it is shown that \(W\)-cycles are more reliable than \(V\)-cycles for strongly anisotropic elliptic operators.
- Dutch Research Council Netherlands
- Centrum Wiskunde & Informatica Netherlands
- University of Amsterdam Netherlands
Multigrid methods; domain decomposition for boundary value problems involving PDEs, computational efficiency, convergence, Haar wavelets, \(W\)-cycles, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Complexity and performance of numerical algorithms, Boundary value problems for second-order elliptic equations, \(V\)-cycles, strongly anisotropic elliptic operators, multigrid method
Multigrid methods; domain decomposition for boundary value problems involving PDEs, computational efficiency, convergence, Haar wavelets, \(W\)-cycles, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Complexity and performance of numerical algorithms, Boundary value problems for second-order elliptic equations, \(V\)-cycles, strongly anisotropic elliptic operators, multigrid method
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