An algebraic multilevel multigraph algorithm. (English) Zbl 1006.65027
Summary: We describe an algebraic multilevel multigraph algorithm. Many of the multilevel components are generalizations of algorithms originally applied to general sparse Gaussian elimination. Indeed, general sparse Gaussian elimination with minimum degree ordering is a limiting case of our algorithm. Our goal is to develop a procedure which has the robustness and simplicity of use of sparse direct methods, yet offers the opportunity to obtain the optimal or near-optimal complexity typical of classical multigrid methods.
MSC:
65F10 | Iterative numerical methods for linear systems |
65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
65F35 | Numerical computation of matrix norms, conditioning, scaling |
65Y20 | Complexity and performance of numerical algorithms |
35J25 | Boundary value problems for second-order elliptic equations |