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Item type:Publication, Access status: with files , Adaptive tolerances for staggered solution algorithms in fluid-structure interaction(Springer, 2026); ; ; ; Staggered solution algorithms are a well-known alternative to monolithic approaches for solving strongly coupled multi-field problems. A coupling between the subproblems is achieved by exchanging coupling quantities between the solvers. Implicit coupling schemes are realized by letting the solvers solve each load or time step repeatedly until convergence up to a given coupling tolerance is achieved. In fluid-structure interaction as well as a variety of other problem classes, the equations governing the individual fields are nonlinear. Accordingly, each solver performs an inner iterative solution procedure that terminates once an inner tolerance is reached. The basic idea of this work builds on the possibility to adaptively adjust these inner tolerances based on carefully designed rules while preserving the black-box nature of the solvers. The resulting coupling scheme yields significant improvements in computational efficiency compared to classical schemes where the inner solver tolerances are held fixed. This is demonstrated in several numerical examples. The idea is tested in combination with state-of-the-art convergence acceleration schemes and can be realized within any staggered solution approach by only minor modifications to the participating solvers.Publicationtype: Journal Article56 28 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Stabilization techniques and adaptive conjugate gradient solver tolerances for the finite cell method(2025-03); ; ; Immersed boundary methods such as the finite cell method provide a versatile tool for the analysis of structures, which are difficult to discretize in a boundary conforming manner due to their complex geometries. Using Cartesian grids and a fictitious domain approach, the effort is shifted from meshing toward the quadrature, which needs to be adapted to discontinuous integrands for cut cells, i.e., elements cut by the immersed boundary. Further, the condition number of the stiffness matrix of such discretizations is typically much larger compared to boundary fitted discretizations, making the use of iterative solvers challenging. In order to restore the performance of iterative solvers, i.e., lower the condition number of the stiffness matrix, several stabilization methods are available. In this work, we compare the performance of two stabilization methods. The classical -stabilization method uses a material with low (but non-zero) stiffness in the fictitious domain. The so called eigenvalue- or -stabilization is based on an eigendecomposition of the stiffness matrix and selectively stabilizes modes, which are associated with very low eigenvalues. Generally, both stabilization methods introduce an error, which, however, can be corrected. This work includes an investigation of such correction mechanisms for linear and nonlinear problems.Publicationtype: Journal Article33