Discretization technologies · Computational Mechanics Weimar

Key works

GPU-accelerated simulation

Graphics cards accelerate highly parallel, repetitive computations, which numerical simulations can exploit for much shorter runtimes. cuwave is a differentiable finite difference code for wave propagation on a single GPU, and mlhp can run parts of its finite element pipeline (matrix-free assembly and iterative solvers) on the GPU.

wave propagation

Wave propagation in the Discobolus: 28 million degrees of freedom over 1500 time steps, simulated in 0.21 s on an NVIDIA RTX 5090. powered by cuwave

topology optimization

Compliance topology optimization: 373 million voxels (quarter MBB beam) at 28.6 s per iteration on an NVIDIA RTX 5090, so 300 iterations took 2 h 23 min. powered by mlhp

Phase-field fracture

Phase-field models describe discrete cracks as a narrow band of damage. mlhp supports the most common phase-field fracture models with adaptive refinement, as well as GPU acceleration to limit computational effort.

refinement

Adaptive refinement: the mesh follows the crack tip and coarsens behind it, so the computation stays small. powered by mlhp

as-built

From CT scan to crack path: a 3D-printed concrete prism simulated on its scanned, as-built geometry with 914 million degrees of freedom, 136 load steps in 21 min on an NVIDIA RTX 5090. powered by mlhp

Publications

Generalized eigenvalue stabilization for immersed explicit dynamics Computer Methods in Applied Mechanics and Engineering, 2026
Restores usable explicit time steps on badly cut cells by stabilizing the governing eigenvalues.
Efficient finite element quadrature on immersed voxel data Engineering with Computers, 2026
Fits a custom quadrature rule per element to CT voxel data, so refined and high-order elements integrate scans exactly with few points.
A CFL condition for the finite cell method Computational Mechanics, 2025
Derives the critical time step that explicit time integration must respect on immersed meshes.
On the efficiency of explicit and semi-explicit immersed boundary finite element methods for wave propagation problems Advances in Computational Science and Engineering, 2025
Compares explicit and semi-explicit immersed schemes for transient wave problems.
A Plastic Damage Model With Mixed Isotropic–Kinematic Hardening for Low‐Cycle Fatigue in 7020 Aluminum Fatigue & Fracture of Engineering Materials & Structures, 2025
A plastic damage model with mixed hardening that captures low-cycle fatigue in high-strength aluminum.
Code
The discontinuous strain method: accurately representing fatigue and failure Computational Mechanics, 2025
Represents localized failure through a strain discontinuity instead of a smeared damage band.
Code
Competition between arbitrarily oriented tunnel cracks and delamination International Journal of Fracture, 2025
Predicts which damage mode wins as tunnel cracks and delamination compete in laminates.
Implicit-explicit time integration for the immersed wave equation Computers & Mathematics with Applications, 2024
Treats only the small cut cells implicitly, keeping the bulk of the mesh explicit and cheap.
Robust numerical integration of embedded solids described in boundary representation Computer Methods in Applied Mechanics and Engineering, 2024
Robust moment-fitting quadrature for cut cells of solids described by boundary meshes.
Code
Wave propagation in a three-dimensional half-space with semi-infinite irregularities Waves in Random and Complex Media, 2024
Simulates seismic waves in half-spaces containing semi-infinite irregularities such as valleys.
From ductile damage to unilateral contact via a point-wise implicit discontinuity Computational Mechanics, 2024
Carries ductile damage through to crack closure and contact within a single formulation.
On the radial discretization in the frequency-domain SBFEM: Recovering inner-subdomain solutions Computer Methods in Applied Mechanics and Engineering, 2024
Recovers interior solution fields in the scaled boundary method without enlarging the global system.
Performance of acceleration techniques for staggered phase-field solutions Computer Methods in Applied Mechanics and Engineering, 2023
Compares techniques that speed up the slow staggered iterations of phase-field fracture.
The scaled boundary finite element method for dispersive wave propagation in higher‐order continua International Journal for Numerical Methods in Engineering, 2023
Extends the scaled boundary method to gradient elasticity, capturing dispersive waves in microstructured media.
A fracture energy–based viscoelastic–viscoplastic–anisotropic damage model for rate-dependent cracking of concrete International Journal of Fracture, 2023
Models rate-dependent cracking of concrete by combining viscoelasticity, viscoplasticity and anisotropic damage.
A three-field phase-field model for mixed-mode fracture in rock based on experimental determination of the mode II fracture toughness Engineering with Computers, 2022
A phase-field model with separate tensile and shear cracks, calibrated against experiments on rock.
Predicting fracture in the proximal humerus using phase field models Journal of the Mechanical Behavior of Biomedical Materials, 2022
Predicts how the proximal humerus fractures using phase-field models.
Efficient multi-level hp-finite elements in arbitrary dimensions Computer Methods in Applied Mechanics and Engineering, 2022
The data structures and algorithms behind multi-level hp-refinement in any dimension.
The finite cell method with least squares stabilized Nitsche boundary conditions Computer Methods in Applied Mechanics and Engineering, 2022
Least-squares stabilized Nitsche boundary conditions for the finite cell method, with error and conditioning bounds.
Fiber bridging in polypropylene‐reinforced high‐strength concrete: An experimental and numerical survey Structural Concrete, 2022
Studies fiber bridging in polypropylene-reinforced concrete through experiments and simulations.
An efficient stiffness degradation model for layered composites with arbitrarily oriented tunneling and delamination cracks Composites Science and Technology, 2022
A cheap model for how cracking degrades laminate stiffness, without resolving every crack.
Code
An accurate strategy for computing reaction forces and fluxes on trimmed locally refined meshes Journal of Mechanics, 2022
Computes accurate reaction forces on trimmed, immersed meshes, where classic nodal methods fail.
A special finite element method applied to off-axis tunnel cracking in laminates Engineering Fracture Mechanics, 2022
A tailored 2D element that captures three-dimensional off-axis tunnel cracks.
Code
Enforcing essential boundary conditions on domains defined by point clouds Computers & Mathematics with Applications, 2022
Imposes boundary conditions directly on geometries that are given only as point clouds.
The influence of the fiber–matrix microstructure on the energy release rate of off-axis tunnel cracks in laminates Composites Part B: Engineering, 2022
Quantifies how fiber arrangement at the microscale changes crack driving forces.
A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics Archives of Computational Methods in Engineering, 2021
Benchmark problems in solid mechanics for comparing discretizations and implementations.
Hierarchically refined isogeometric analysis of trimmed shells Computational Mechanics, 2020
Local hierarchical refinement for isogeometric analysis of trimmed shells.
Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method Computational Mechanics, 2019
Resolves brittle phase-field cracks with multi-level hp-refinement on immersed meshes.
Robust and parallel scalable iterative solutions for large-scale finite cell analyses Finite Elements in Analysis and Design, 2019
Robust iterative solvers that scale in parallel for large finite cell analyses.
Integrating CAD and numerical analysis: ‘Dirty geometry’ handling using the Finite Cell Method Computer Methods in Applied Mechanics and Engineering, 2019
Simulates directly on flawed CAD geometry, tolerating gaps and overlaps, with the finite cell method.
Multi-level Bézier extraction for hierarchical local refinement of Isogeometric Analysis Computer Methods in Applied Mechanics and Engineering, 2018
Multi-level Bézier extraction for hierarchical local refinement in isogeometric analysis.
Multi-level hp-finite cell method for embedded interface problems with application in biomechanics International Journal for Numerical Methods in Biomedical Engineering, 2018
Resolves material interfaces in complex geometry with the multi-level hp finite cell method, applied to biomechanics.
Numerical integration of discontinuous functions: moment fitting and smart octree Computational Mechanics, 2017
Integrates discontinuous functions in cut cells by combining moment fitting with smart octrees.
From geometric design to numerical analysis: A direct approach using the Finite Cell Method on Constructive Solid Geometry Computers & Mathematics with Applications, 2017
Analyzes constructive solid geometry models directly with the finite cell method, without meshing.
Smart octrees: Accurately integrating discontinuous functions in 3D Computer Methods in Applied Mechanics and Engineering, 2016
Integrates discontinuous functions accurately in 3D with octrees that follow the geometry.
The multi-level hp-method for three-dimensional problems: dynamically changing high-order mesh refinement with arbitrary hanging nodes Computer Methods in Applied Mechanics and Engineering, 2016
Multi-level hp-refinement in 3D with arbitrary hanging nodes and dynamically changing meshes.
An easy treatment of hanging nodes in hp-finite elements Finite Elements in Analysis and Design, 2016
A simple treatment of hanging nodes in hp-finite elements.
Multi-level hp-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes Computational Mechanics, 2015
High-order mesh adaptivity by superposing refinement levels, avoiding hanging-node constraints.
Efficient and accurate numerical quadrature for immersed boundary methods Advanced Modeling and Simulation in Engineering Sciences, 2015
Subdivides cut elements robustly and accurately so that high-order immersed methods keep optimal convergence.
XFEM analysis of fiber bridging in mixed-mode crack propagation in composites Composite Structures, 2015
Simulates fiber bridging in mixed-mode crack propagation in composites with the extended finite element method.
Parameter-free, weak imposition of Dirichlet boundary conditions and coupling of trimmed and non-conforming patches International Journal for Numerical Methods in Engineering, 2015
Couples trimmed and non-conforming patches weakly, without penalty parameters or extra unknowns.
Normal contact with high order finite elements and a fictitious contact material Computers & Mathematics with Applications, 2015
Models normal contact with high-order elements through a fictitious contact material.
FCMLab: A finite cell research toolbox for MATLAB Advances in Engineering Software, 2014
FCMLab, an open MATLAB toolbox for finite cell research.
Geometric modeling, isogeometric analysis and the finite cell method Computer Methods in Applied Mechanics and Engineering, 2012
Connects geometric modeling, isogeometric analysis and the finite cell method.
An efficient integration technique for the voxel‐based finite cell method International Journal for Numerical Methods in Engineering, 2012
Precomputes cell matrices so that voxel-based finite cell models are cheap to integrate.
The Finite Cell Method for linear thermoelasticity Computers & Mathematics with Applications, 2012
Extends the finite cell method to linear thermoelasticity.
Shell Finite Cell Method: A high order fictitious domain approach for thin-walled structures Computer Methods in Applied Mechanics and Engineering, 2011
A high-order fictitious domain approach for thin-walled structures.
Non-standard bone simulation: interactive numerical analysis by computational steering Computing and Visualization in Science, 2011
Interactive bone simulation, where results update while the user changes the model.
Fixed-grid fluid–structure interaction in two dimensions based on a partitioned Lattice Boltzmann and p-FEM approach International Journal for Numerical Methods in Engineering, 2009
Couples Lattice Boltzmann flow with p-FEM structures for fluid–structure interaction on fixed grids.