arXiv subjects

Maik Punke

Publications and source records attributed to Maik Punke.

7 recordsLinked to original sources

arXiv2026

Multi-GPU fast Fourier transforms in MATLAB (for large-scale phase-field crystal simulations)

We present a MATLAB-based framework for two- and three-dimensional fast Fourier transforms on multiple GPUs for large-scale numerical simulations using the pseudo-spectral Fourier method. The software implements two complementary multi-GPU strategies that overcome single-GPU memory limitations and accelerate spectral solvers. This approach is motivated by and applied to phase-field crystal (PFC) models, which are governed by tenth-order partial differential equations, require fine spatial resolution, and are typically formulated in periodic domains. Our resulting numerical framework achieves significant speedups, approximately sixfold for standard PFC simulations and up to sixtyfold for multiphysics extensions, compared to a purely CPU-based implementation running on hundreds of cores.

cs.MS↗

arXiv2026

Grain-Growth Stagnation from Vacancy-Diffusion-Limited Disconnection Climb

Grain growth in polycrystals typically stagnates at long times. We identify disconnection climb, limited by vacancy diffusion, as a fundamental microscopic mechanism underlying this behavior. Using a phase-field crystal framework extended to model vacancy diffusion, we resolve grain-boundary migration on diffusive time scales and show that disconnection climb rates correlate with the characteristic grain size at which growth arrests. These results link vacancy transport, disconnection dynamics, and microstructural evolution, establishing vacancy diffusion as a key governing factor.

cond-mat.mtrl-sci↗

arXiv2024

A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks

We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The thermal compatibility condition, as well as a positive entropy-production property, is derived analytically and further verified by numerical benchmark simulations. Furthermore, we examine how the different model parameters control density and temperature evolution during dendritic solidification through extensive parameter studies. Finally, we extend our framework to the modeling of open systems considering external mass and heat fluxes. This work sets the ground for a comprehensive mesoscale model of non-isothermal solidification including thermal expansion within a positive entropy-producing framework, and provides a benchmark for further meso- to macroscopic modeling of solidification.

cond-mat.mtrl-sci↗

arXiv2024

Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation

The phase-field crystal (PFC) model describes crystal structures at diffusive timescales through a periodic, microscopic density field. It has been proposed to model elasticity in crystal growth and encodes most of the phenomenology related to the mechanical properties of crystals like dislocation nucleation and motion, grain boundaries, and elastic or interface-energy anisotropies. To overcome limitations to small systems, a coarse-grained formulation focusing on slowly varying complex amplitudes of the microscopic density field has been devised. This amplitude-PFC (APFC) model describes well elasticity and dislocations while approximating microscopic features and being limited in describing large-angle grain boundaries. We present here seminal concepts for a hybrid multiscale PFC-APFC framework that combines the coarse-grained description of the APFC model in bulk-like crystallites while exploiting PFC resolution at dislocations, grain boundaries, and interfaces or surfaces. This is achieved by coupling the two models via an advanced discretization based on the Fourier spectral method and allowing for local solution updates. This discretization also generalizes the description of boundary conditions for PFC models. We showcase the framework capabilities through two-dimensional benchmark simulations. We also show that the proposed formulation allows for overcoming the limitations of the APFC model in describing large-angle grain boundaries.

cond-mat.mtrl-sci↗

arXiv2023

Evaluation of the elastic field in phase-field crystal simulations

The phase-field crystal model (PFC) describes crystal structures at diffusive timescales through a periodic order parameter representing the atomic density. One of its main features is that it naturally incorporates elastic and plastic deformation. To correctly interpret numerical simulation results or devise extensions related to the elasticity description, it is important to have direct access to the elastic field. In this work, we discuss its evaluation in classical PFC models based on the Swift-Hohenberg energy functional. We consider approaches where the stress field can be derived from the microscopic density field (i.e., the order parameter), and a simple novel numerical routine is proposed. By numerical simulations, we demonstrate that it overcomes some limitations of currently used methods. Moreover, we shed light on the elasticity description conveyed by classical PFC models, characterizing a residual stress effect present at equilibrium. We show explicitly and discuss the evaluation of the elastic fields in prototypical representative cases involving an elastic inclusion, a grain boundary, and dislocations.

cond-mat.mtrl-sci↗

arXiv2022

Improved time integration for phase-field crystal models of solidification

We optimize a numerical time-stabilization routine for the phase-field crystal (PFC) models of solidification. By numerical experiments, we showcase that our approach can improve the accuracy of underlying time integration schemes by a few orders of magnitude. We investigate different time integration schemes. Moreover, as a prototypical example for applications, we extend our numerical approach to a PFC model of solidification with an explicit temperature coupling.

cond-mat.mtrl-sci↗

arXiv2022

Explicit temperature coupling in phase-field crystal models of solidification

We present a phase-field crystal (PFC) model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the microscopic density field. We showcase the model capabilities via selected numerical investigations which focus on the prototypical growth of two-dimensional crystals from the melt, resulting in faceted shapes and dendrites. This work sets the grounds for a comprehensive mesoscale model of solidification including thermal expansion.

cond-mat.mtrl-sci↗