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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 84 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A block householder based algorithm for the QR decomposition of hierarchical matrices(2025); This thesis introduces a new approach to compute QR factorizations of hierarchical matrices using block Householder transformations and a newly developed implicit storage scheme for them. The algorithm and the analysis of its numerical cost track low-rank factorizations in intermediate results. Numerical tests on several types of square matrices like 2D Laplacian boundary element matrices and different RBF kernel matrices show a good performance, although the algorithm struggles with rectangular matrices. A version of the H-LU decomposition is also implemented, demonstrating potential benefits.Publicationtype: Doctoral Thesis51 60