**FULL TITLE** ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION** **NAMES OF EDITORS** Visualization of Scalar Adaptive Mesh Refinement Data

Abstract. Adaptive Mesh Refinement (AMR) is a highly effective computation method for simulations that span a large range of spatiotemporal scales, such as astrophysical simulations, which must accommodate ranges from interstellar to sub-planetary. Most mainstream visualization tools still lack support for AMR grids as a first class data type and AMR code teams use custom built applications for AMR visualization. The Department of Energy's (DOE's) Science Discovery through Advanced Computing (SciDAC) Visualization and Analytics Center for Enabling Technologies (VACET) is currently working on extending VisIt, which is an open source visualization tool that accommodates AMR as a first-class data type. These efforts will bridge the gap between generalpurpose visualization applications and highly specialized AMR visual analysis applications. Here, we give an overview of the state of the art in AMR scalar data visualization research

On the Computation of Integral Curves in Adaptive Mesh Refinement Vector Fields

Integral curves, such as streamlines, streaklines, pathlines, and timelines, are an essential tool in the analysis of vector field structures, offering straightforward and intuitive interpretation of visualization results. While such curves have a long-standing tradition in vector field visualization, their application to Adaptive Mesh Refinement (AMR) simulation results poses unique problems. AMR is a highly effective discretization method for a variety of physical simulation problems and has recently been applied to the study of vector fields in flow and magnetohydrodynamic applications. The cell-centered nature of AMR data and discontinuities in the vector field representation arising from AMR level boundaries complicate the application of numerical integration methods to compute integral curves. In this paper, we propose a novel approach to alleviate these problems and show its application to streamline visualization in an AMR model of the magnetic field of the solar system as well as to a simulation of two incompressible viscous vortex rings merging

Ray Tracing Structured AMR Data Using ExaBricks

Structured Adaptive Mesh Refinement (Structured AMR) enables simulations to adapt the domain resolution to save computation and storage, and has become one of the dominant data representations used by scientific simulations; however, efficiently rendering such data remains a challenge. We present an efficient approach for volume- and iso-surface ray tracing of Structured AMR data on GPU-equipped workstations, using a combination of two different data structures. Together, these data structures allow a ray tracing based renderer to quickly determine which segments along the ray need to be integrated and at what frequency, while also providing quick access to all data values required for a smooth sample reconstruction kernel. Our method makes use of the RTX ray tracing hardware for surface rendering, ray marching, space skipping, and adaptive sampling; and allows for interactive changes to the transfer function and implicit iso-surfacing thresholds. We demonstrate that our method achieves high performance with little memory overhead, enabling interactive high quality rendering of complex AMR data sets on individual GPU workstations

AMM: Adaptive Multilinear Meshes

We present Adaptive Multilinear Meshes (AMM), a new framework that significantly reduces the memory footprint compared to existing data structures. AMM uses a hierarchy of cuboidal cells to create continuous, piecewise multilinear representation of uniformly sampled data. Furthermore, AMM can selectively relax or enforce constraints on conformity, continuity, and coverage, creating a highly adaptive and flexible representation to support a wide range of use cases. AMM supports incremental updates in both spatial resolution and numerical precision establishing the first practical data structure that can seamlessly explore the tradeoff between resolution and precision. We use tensor products of linear B-spline wavelets to create an adaptive representation and illustrate the advantages of our framework. AMM provides a simple interface for evaluating the function defined on the adaptive mesh, efficiently traversing the mesh, and manipulating the mesh, including incremental, partial updates. Our framework is easy to adopt for standard visualization and analysis tasks. As an example, we provide a VTK interface, through efficient on-demand conversion, which can be used directly by corresponding tools, such as VisIt, disseminating the advantages of faster processing and a smaller memory footprint to a wider audience. We demonstrate the advantages of our approach for simplifying scalar-valued data for commonly used visualization and analysis tasks using incremental construction, according to mixed resolution and precision data streams

Immersive ExaBrick: Visualizing Large AMR Data in the CAVE

Rendering large adaptive mesh refinement (AMR) data in real-time in virtual reality (VR) environments is a complex challenge that demands sophisticated techniques and tools. The proposed solution harnesses the ExaBrick framework and integrates it as a plugin in COVISE, a robust visualization system equipped with the VR-centric OpenCOVER render module. This setup enables direct navigation and interaction within the rendered volume in a VR environment. The user interface incorporates rendering options and functions, ensuring a smooth and interactive experience. We show that high-quality volume rendering of AMR data in VR environments at interactive rates is possible using GPUs

Meshless methods: theory and application in 3D fracture modelling with level sets

Accurate analysis of fracture is of vital importance yet methods for effetive 3D calculations are currently unsatisfactory. In this thesis, novel numerical techniques are developed which solve many of these problems. This thesis consists two major parts: firstly an investigation into the theory of meshless methods and secondly an innovative numerical framework for 3D fracture modelling using the element-free Galerkin method and the level set method. The former contributes to some fundamental issues related to accuracy and error control in meshless methods needing to be addressed for fracture modelling developed later namely, the modified weak form for imposition of essential boundary conditions, the use of orthogonal basis functions to obtain shape functions and error control in adaptive analysis. In the latter part, a simple and efficient numerical framework is developed to overcome the difficulties in current 3D fracture modelling. Modelling cracks in 3D remains a challenging topic in computational solid mechanics since the geometry of the crack surfaces can be difficult to describe unlike the case in 2D where cracks can be represented as combinations of lines or curves. Secondly, crack evolution requires numerical methods that can accommodate the moving geometry and a geometry description that maintains accuracy in successive computational steps. To overcome these problems, the level set method, a powerful numerical method for describing and tracking arbitrary motion of interfaces, is used to describe and capture the crack geometry and forms a local curvilinear coordinate system around the crack front. The geometry information is used in the stress analysis taken by the element-Free Galerkin method as well as in the computation of fracture parameters needed for crack propagation. Examples are tested and studied throughout the thesis addressing each of the above described issues