Superfast Multifrontal Method for Large Structured Linear Systems of Equations
SIAM Journal on Matrix Analysis and Applications
Preconditioning the bidomain model with almost linear complexity
Journal of Computational Physics
Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices
SIAM Journal on Matrix Analysis and Applications
A fast direct solver for elliptic problems on general meshes in 2D
Journal of Computational Physics
A fast BIE iteration method for an arbitrary body in a flow of incompressible inviscid fluid
Journal of Computational and Applied Mathematics
| Hi-index | 0.01 |
Hierarchical ($$\mathcal {H}$$-) matrices provide a data-sparse way to approximate fully populated matrices. The two basic steps in the construction of an $$\mathcal {H}$$-matrix are (a) the hierarchical construction of a matrix block partition, and (b) the blockwise approximation of matrix data by low rank matrices. In the context of finite element discretisations of elliptic boundary value problems, $$\mathcal {H}$$-matrices can be used for the construction of preconditioners such as approximate $$\mathcal {H}$$-LU factors. In this paper, we develop a new black box approach to construct the necessary partition. This new approach is based on the matrix graph of the sparse stiffness matrix and no longer requires geometric data associated with the indices like the standard clustering algorithms. The black box clustering and a subsequent $$\mathcal {H}$$-LU factorisation have been implemented in parallel, and we provide numerical results in which the resulting black box $$\mathcal {H}$$-LU factorisation is used as a preconditioner in the iterative solution of the discrete (three-dimensional) convection-diffusion equation.