arXiv subjects

Marcus Wagner

Publications and source records attributed to Marcus Wagner.

4 recordsLinked to original sources

arXiv2026

Boundary-Level-Constrained Refinement for Suppressing Trimming-Induced High-Frequency Outliers in Explicit Isogeometric Analysis

In explicit dynamics, the critical time step is governed by the maximum eigenfrequency of the semi-discrete system. In Isogeometric Analysis (IGA), open knot vectors introduce a characteristic spectral boundary effect that can lead to high-frequency outliers and restrict the admissible time step. In the row-sum-lumped setting considered here, extending the computational patch and trimming away the exterior boundary functions mitigates this time-step penalty, but does not necessarily prevent boundary-adjacent basis functions from governing the maximum eigenfrequency. We show that reduced-support basis functions adjacent to the trimming boundary can remain critical spectral contributors even for knot-exact trimming, i.e., in the absence of small cut cells. Hence, small cut cells are not required for trimming-induced time-step penalties. Knot-exact and arbitrary trimming represent different degrees of support reduction within the same underlying mechanism. To control this effect, we propose the Boundary-Level-Constrained Refinement (BLCR) strategy, a local refinement constraint for LR- and THB-splines. BLCR constrains the refinement level of basis functions whose support intersects the trimming boundary relative to that of the refined interior. In all configurations investigated in this work, this constraint ensures that the maximum eigenfrequency is governed by untrimmed interior basis functions rather than by refined trimmed functions. Consequently, the trimming-induced high-frequency outliers governing the critical time step are suppressed, yielding a larger admissible time step than globally refined trimmed B-splines with the same interior resolution.[...]

math.NA↗

arXiv2026

Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variation

Nonlinear finite element crash simulations are accurate but computationally expensive, limiting their use in iterative design optimisation. Machine-learning surrogate models based on graph neural networks (GNNs) offer a faster alternative. Message-passing GNNs are widely used for mesh simulation, and their shared node and edge update functions are relatively generalisable across varying graph structures. By contrast, non-shareable edge-specific aggregation layers can capture nonlinear relationships more accurately but usually require fixed graph connectivity, which limits generalisability. This paper presents Mask-Morph Graph U-Net (MMGUNet), a practical approach to addressing the limitation of hierarchical Graph U-Net architectures that use edge-specific downsampling and upsampling layers. Fixed coarse graph connectivity is required for edge-specific layers. To retain this while improving spatial correspondence, the proposed method morphs the coarsened graph hierarchy to each input mesh using feature-aligned barycentric parameterisation before constructing cross-graph edges. It further applies node masking during supervised pretraining, followed by parameter-efficient fine-tuning in which high-parameter edge-specific layers are frozen. The proposed approach is evaluated in in-distribution, out-of-distribution, and cross-component transfer settings using mean Euclidean distance and maximum intrusion percentage error. Results show that coarse-graph morphing improves test accuracy relative to a fixed-coarse-graph baseline, while masked supervised pretraining reduces the train-test discrepancy and improves data efficiency during transfer. The proposed model also achieves lower prediction error compared with external baselines. These results demonstrate a practical route toward reusable, data-efficient mesh-based surrogate modelling for crashworthiness design exploration.

cs.LG↗

arXiv2025

Local h-, p-, and k-Refinement Strategies for the Isogeometric Shifted Boundary Method Using THB-Splines

The concept of trimming, embedding, or immersing geometries into a computational background mesh has gained considerable attention in recent years, particularly in isogeometric analysis (IGA). In this approach, the physical domain is represented independently from the computational mesh, allowing the latter to be generated more easily compared with body-fitted meshes. While this facilitates the treatment of complex geometries, it also introduces challenges, such as ill-conditioning of the stiffness matrix caused by small cut elements and difficulties in accurately enforcing boundary conditions. A recently proposed technique to address these issues is the Shifted Boundary Method (SBM), which represents the computational domain solely through uncut elements and enforces boundary conditions via a Taylor expansion from a surrogate boundary to the true boundary. Previous studies have shown that, for Neumann boundary conditions, the flux evaluation requires additional derivatives in the Taylor expansion, effectively reducing the order of convergence by one. In this work, we investigate for the first time the performance of SBM combined with Truncated Hierarchical B-splines (THB-splines) under various local refinement strategies. In particular, we propose local p- and k-refinement schemes for THB-splines and compare them with local h-refinement and the unmodified SBM. Furthermore, we propose an enhanced shift operator that incorporates mixed partial derivatives, in contrast to the standard operator. The study assesses accuracy, stability, and computational efficiency for benchmark problems on trimmed domains. The results highlight how different refinement strategies affect convergence behavior in trimmed IGA formulations using SBM and demonstrate that targeted degree elevation can mitigate the Neumann boundary limitations of the standard method.

math.NA↗

arXiv2015

Optimal control of the bidomain system (IV): Corrected proofs of the stability and regularity theorems

In a series of papers on optimal control problems for the monodomain as well as for the bidomain equations of cardiac electrophysiology, the authors studied existence of minimizers and derived first-order necessary optimality conditions. The analysis of these control problems is based on a regularity discussion for weak solutions, resulting in a stability estimate and a uniqueness theorem for the monodomain and bidomain system, respectively. Unfortunately, the authors recognized a serious error within the proof of these theorems. However, the present investigation shows that the assertions from [Kunisch/Wagner 12] and [Kunisch/Wagner 13a] can be maintained (with minor changes only) while the proofs must be subjected to considerable alterations. As a consequence, the optimization theorems from [Kunisch/Wagner 13b] allow for substantial improvements. Therefore, in the present paper we provide a refined regularity discussion of the bidomain system together with corrected proofs.

math.OC↗