arXiv subjects

Erik Faulhaber

Publications and source records attributed to Erik Faulhaber.

3 recordsLinked to original sources

arXiv2026

Adaptive Multiphysics Coupling for Hyperbolic Systems

For the discontinuous Galerkin code Trixi$.$jl we implement capabilities for adaptively coupling arbitrarily many domains with different physics. The coupling of the systems is realized through the exchange of boundary information and user-definable coupling functions. This gives us the ability to couple systems that do not share a single variable or have a very different number of variables. This is particularly useful when we have a hierarchy of systems. Our implementation is such that we can adaptively select the model of the coupled systems in the course of the simulation. This allows for highly dynamical scenarios as can be found e.g. in astrophysics. The criteria for adaptivity can be user defined and tailored to the physical problem. Compared to computing the most complex model in the entire simulation domain, our method of coupled systems of high and low complexity leads to a significant reduction in computational time with very little overhead.

math.NA↗

arXiv2025

Robust and efficient pre-processing techniques for particle-based methods including dynamic boundary generation

Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for smoothed particle hydrodynamics (SPH) and other particle-based methods. Our pipeline begins with the generation of a resolution-adaptive point cloud near the geometry's surface employing a face-based neighborhood search. This point cloud forms the basis for a signed distance field, enabling efficient, localized computations near surface regions. To create an initial particle configuration, we apply a hierarchical winding number method for fast and accurate inside-outside segmentation. Particle positions are then relaxed using an SPH-inspired scheme, which also serves to pack boundary particles. This ensures full kernel support and promotes isotropic distributions while preserving the geometry interface. By leveraging the meshless nature of particle-based methods, our approach does not require connectivity information and is thus straightforward to integrate into existing particle-based frameworks. It is robust to imperfect input geometries and memory-efficient without compromising performance. Moreover, our experiments demonstrate that with increasingly higher resolution, the resulting particle distribution converges to the exact geometry.

math.NA↗

arXiv2022

Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing

We present Trixi.jl, a Julia package for adaptive high-order numerical simulations of hyperbolic partial differential equations. Utilizing Julia's strengths, Trixi.jl is extensible, easy to use, and fast. We describe the main design choices that enable these features and compare Trixi.jl with a mature open source Fortran code that uses the same numerical methods. We conclude with an assessment of Julia for simulation-focused scientific computing, an area that is still dominated by traditional high-performance computing languages such as C, C++, and Fortran.

cs.MS↗