Abstract:The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exists for the indefinite matrix if the mesh size is reasonably small, and that this factorization can serve as an effici… Show more
“…Algebraic multigrid methods are currently a topic of intense research interest [17,18,20,46,12,48,38,11,44,3,4,1,2,5,16,7,29,28,27,42,41,21]. An excellent recent survey is given in Wagner [49].…”
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.
“…Algebraic multigrid methods are currently a topic of intense research interest [17,18,20,46,12,48,38,11,44,3,4,1,2,5,16,7,29,28,27,42,41,21]. An excellent recent survey is given in Wagner [49].…”
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.
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