Hierarchical Matrices for Convection-Dominated Problems
Hierarchical matrices provide a technique to efficiently compute and store explicit approximations to the inverses of stiffness matrices computed in the discretization of partial differential equations. In a previous paper, Le Borne , it was shown how standard ℌ-matrices must be modified in order to obtain good approximations in the case of a convection dominant equation with a constant convection direction. This paper deals with a generalization to arbitrary (non-constant) convection directions. We will show how these ℌ-matrix approximations to the inverse can be used as preconditioners in iterative methods.
KeywordsDomain Decomposition Method Admissibility Condition Sparse Approximate Inverse Hierarchical Matrice FETI Method
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