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Item type:Publication, Access status: with files , Coupled clustering in hierarchical matrices for the oseen problemFluid flow problems can be modelled by the Navier-Stokes or, after linearization, by the Oseen equations. Their discretization results in discrete saddle point problems. These systems of equations are typically very large and need to be solved iteratively. Standard (block-) preconditioning techniques for saddle point problems rely on an approximation of the Schur complement. Such an approximation can be obtained by a hierarchical ((Formula presented.) -) matrix LU-decomposition which first approximates the Schur complement explicitly. The computational complexity of this computation depends, among other things, on the hierarchical block structure of the involved hierarchical matrices. However, widely used techniques do not consider the connection between the discretization grids for the velocity field and the pressure, respectively. Here we present a hierarchical block structure for the finite element discretization of the gradient operator which is improved by considering the connection between the two involved grids. We prove a logarithmic depth estimate for cluster trees generated with the coupled clustering. Numerical results will show that the improved block structure allows for a faster computation of the Schur complement which is the bottleneck for the set-up of the (Formula presented.) -matrix LU-decomposition. The presented coupled clustering is also applicable to other types of mixed (finite element) problems.Publicationtype: Journal Article34 39 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Construction of hierarchical matrices for the preconditioning of the three-dimensional Navier-Stokes equations(2025); Solving saddle point problems, e.g. obtained from the discretization of the Navier-Stokes equations, with Krylov subspace methods is a difficult task due to often unfavorable (spectral) properties of the system matrix. A popular preconditioning technique for those kinds of systems are block preconditioners relying on approximations to the upper left system matrix block and the so-called Schur complement. These approximations can be obtained by hierarchical matrix LU factorizations but require the explicit computation of an approximate Schur complement. We present improvements in the construction of the required hierarchical matrices leading to a speed-up for the preconditioner set-up.Publicationtype: Doctoral Thesis98 86 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Coupled clustering strategies for hierarchical matrix preconditioners in saddle point problemsFluid flow problems can be modeled by the Navier–Stokes or, after linearization, by the Oseen equations. Their discretization results in discrete saddle point problems. These systems of equations are typically very large and need to be solved iteratively. Standard (block-) preconditioning techniques for saddle point problems rely on an approximation of the Schur complement. Such an approximation can be obtained by a hierarchical (H-) matrix LU-decomposition, which first approximates the Schur complement explicitly. The computational complexity of this computation depends, among other things, on the hierarchical block structure of the involved matrices. However, widely used techniques do not consider the connection between the discretization grids for the velocity field and the pressure, respectively. Here, we present a hierarchical block structure for the finite element discretization of the gradient operator that is improved by considering the connection between the two involved grids. Numerical results imply that the improved block structure allows for a faster computation of the Schur complement, which is the bottleneck for the set-up of the H-matrix LU-decomposition.Publicationtype: Journal Article44 48