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Item type:Publication, Access status: with files , Generalized Eigenvalue stabilization for immersed explicit dynamics(Elsevier, 2026-04-15); ; ; ; Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass matrices of cut elements to cure their adverse impact on the critical time step size of the global system. We use spectral basis functions, specifically C0 continuous Lagrangian interpolation polynomials defined on Gauss-Lobatto-Legendre (GLL) points, which, in combination with its associated GLL quadrature rule, yield high-order convergent diagonal mass matrices for uncut elements. Moreover, considering cut elements, we combine the proposed GEVS approach with the finite cell method to guarantee definiteness of the system matrices. However, the proposed GEVS stabilization can directly be applied to other immersed boundary finite element methods. Numerical experiments demonstrate that the stabilization strategy achieves optimal convergence rates and recovers critical time step sizes of equivalent boundary-conforming discretizations. This also holds in the presence of weakly enforced Dirichlet boundary conditions using either Nitsche's method or penalty formulations.Publicationtype: Journal Article38 25 - Some of the metrics are blocked by yourconsent settings
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 , Application of the Non-Negative Moment Fitting Approach in the Finite Cell Analysis of Brittle Phase-Field Fracture(World Scientific Publishing (WSPC), 2025-04-21); ; ; ; This paper addresses the prediction of fracture processes in complex geometries. In this approach, phase-field modeling is integrated into the finite cell method to have an efficient and robust simulation tool for brittle fracture. The non-negative moment fitting approach is employed as an integration scheme to reduce the number of integration points, which leads to shorter simulation times as well as lower memory requirements for history variables. Two 3D benchmark examples are provided to demonstrate the performance of the implemented approach compared to the standard quadrature based on the space-tree approach. Finally, the proposed method is applied to predict the sequence of strut fractures in brittle foams.Publicationtype: Journal Article131 - 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 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , On the efficiency of explicit and semi-explicit immersed boundary finite element methods for wave propagation problems(American Institute of Mathematical Sciences, 2025-03-01); ; ; ; Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements. Immersed boundary methods provide a simple and fully automatic discretization based on Cartesian grids and tailored quadrature schemes that account for the geometric model. It can thus be described independently of the grid, e.g., by image data obtained from computed tomography scans. The drawback of such a discretization lies in the potentially small overlap between certain elements in the grid and the geometry. These badly cut elements with small physical support pose a particular challenge for nonlinear and/or dynamic simulations. In this work, we focus on problems in structural dynamics and acoustics and concentrate on solving them with explicit time-marching schemes. In this context, badly cut elements can lead to unfeasibly small critical time step sizes. We investigate the performance of implicit-explicit time marching schemes and two stabilization methods developed in previous works as potential remedies. While these have been studied before with regard to their effectiveness in in-creasing the critical time step size, their numerical efficiency has only been considered in terms of accuracy per degree of freedom. In this paper, we eval-uate the computation time required for a given accuracy, which depends not only on the number of degrees of freedom but also on the selected spatial dis-cretization, the sparsity patterns of the system matrices, and the employed time-marching scheme.Publicationtype: Journal Article15 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Using surrogate models to accelerate load step methods for nonlinear finite element problems in hyperelasticityFinite element methods for displacement problems in hyperelasticity lead to systems of nonlinear equations. These equations are usually solved with Newton's method or a related method. The convergence of Newton's method depends heavily on the proximity of the initial guess to the numerical solution. Load step methods overcome problems with divergence by applying the load in increments, leading to a sequence of sub‐problems with initial guesses closer to the numerical solution of each sub‐problem, supporting the convergence. The downside of this approach is the high computational effort needed to solve the load steps. Based on a benchmark problem in high‐order FEM, we extend traditional load step methods to a new approach exploiting the hierarchical basis used for the spatial discretization of the problem and saving up to 50% of computation time (vs. benchmark).Publicationtype: Journal Article38 33 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Experimental characterization of acoustic damping materials(Wiley, 2024-09-30); ; ; ; Due to their ease of use and low cost, passive damping methods are a preferred mean for the reduction of noise in many engineering applications. This applies in particular to foam materials, which exhibit good acoustic and mechanical damping properties. The selection of suitable materials is usually carried out experimentally and can be very labor‐intensive and time‐consuming. For this reason, it is helpful to develop qualified numerical methodsthat can be used for material design and selection. Hence, foam materials must be characterized experimentally in order to enable a later comparison with vibroacoustic simulations. This contribution, therefore, aims at providing suitable parameters for the use in numerical analyses and their validation. Firstly, the microstructure of a foam specimen is captured by means of a CT scan. In addition to providing the geometry for the multi‐physics simulations, this measurement is also used to determine characteristic foam features, for example, strut thickness and pore size distribution. In the second step, the frequency‐dependent stiffness and damping properties of the material are determined by a special experimental setup utilizing an electrodynamic shaker. Here, the dynamic system is approximated as a single‐mass oscillator, which is sufficiently accurate for low frequencies. These properties will later be used in the numerical model to evaluate different parameter identification approaches. In the third and last step of the experimental campaign, measurements with an impedance tube are conducted to obtain the coefficient of absorption. This material parameter is particularly suitable for comparing experiments and simulations. Finally, the correlation between the experimental results is examined to provide a deeper understanding of the foam materials.Publicationtype: Journal Article18 19 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , An automatic simulation pipeline for coupled simulations of acoustic damping materials(Wiley, 2024-09-18); ; ; ; Foamed materials are widely used to reduce noise due to their comparably good acoustic damping behavior. However, out of a large variety of these materials a suitable candidate has to be identified for each application. This is a challenging process that is typically guided by experiments and experience. While numerical simulations could support these experiments and reduce the effort to a great extent, no suitable discretization approach has yet been established that can fully capture the complex geometry of the foam. A fully resolved model is desirable in order to yield reliable predictions that can then be used to establish homogenized models. We established a monolithic coupling approach based on the finite cell method (FCM) that realizes a vibroacoustic simulation in this sense. The fluid and the structure domain are discretized by Cartesian grids and the geometry defined based on computed tomography scans is accounted for during the quadrature of the weak form. Our simulation in the time domain makes use of explicit time marching schemes and is therefore limited by a critical time step size. This is known to be arbitrarily low for discretizations with the FCM containing cells with arbitrarily small support. As a remedy against this we use the classical ‐stabilization technique and investigate its potentials and limitations.Publicationtype: Journal Article33 14 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , An analysis of high order FEM and IGA for explicit dynamics : mass lumping and immersed boundaries(Wiley, 2024-08-30); ; ; Sangalli, GiancarloWe investigate the behavior of different shape functions for the discretization of hyperbolic problems. In particular, we consider classical Lagrange polynomials and B-splines. The studies focus on the performance of the these functions as a spatial discretization approach combined with an explicit time marching scheme. In this regard, a major concern is the maximum eigenvalue that imposes restrictions on the critical time step size and suitable lumping techniques that yield a diagonal mass matrix. The accuracy of the discretization methods is assessed in an asymptotic manner in terms of the convergence of eigenvalues and eigenvectors. Further, the global accuracy is investigated in terms of the full spectrum. The results show that B-spline discretization with a consistent mass matrix are more accurate than those based on Lagrange shape functions, which holds true in the boundary-fitted as well as in the immersed setting. On the other hand, Lagrange shape functions are more robust with respect to standard lumping techniques, which cannot be directly applied for B-splines without loss of accuracy. In general, we observe that none of the standard lumping schemes yields optimal results for B-splines, even in the boundary-fitted setting. For the immersed setting, also Lagrange shape functions show a drop in accuracy which depends on the position of the boundary that cuts the element. Several remedies are considered in order to overcome these issues, including interpolatory B-spline bases as well as eigenvalue stabilization methods. While accuracy and stability can be improved using these remedies, we conclude from our study that it is still an open question, how to design a discretization method that achieves large critical time step sizes in combination with a diagonal mass matrix and high accuracy in the immersed setting. We note that these considerations primarily relate to linear structural dynamics applications, such as for example, structural acoustics. In nonlinear problems, such as automotive crash dynamics, other considerations predominate. An example of a one-dimensional elastic-plastic bar impacting a rigid wall is illustrative.Publicationtype: Journal Article26 16 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , An eigenvalue stabilization technique for immersed boundary finite element methods in explicit dynamics(Elsevier, 2024-07-15); ; ; 23 193