Kenneth Weiss

Lawrence Livermore National Laboratory | LLNL · Computing Applications and Research Department

Many foundational visualization techniques including isosurfacing, direct volume rendering and texture mapping rely on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus within the visualization community on techniques that efficiently generate and encode globally continuous functions defined by the...

We introduce the Stellar decomposition, a model for efficient topological data structures over a broad range of simplicial and cell complexes. A Stellar decomposition of a complex is a collection of regions indexing the complex’s vertices and cells such that each region has sufficient information to locally reconstruct the star of its vertices, i.e...

Point containment queries for regions bound by watertight geometric surfaces, i.e., closed and without self-intersections, can be evaluated straightforwardly with a number of well-studied algorithms. When this assumption on domain geometry is not met, such methods are either unusable, or prone to misclassifications that can lead to cascading errors...

This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We iteratively reduce the dimensionality of integration using the generalized Stokes theorem to line integrals over tri...

The Lawrence Livermore National Laboratory (LLNL) will soon have in place the El Capitan exascale supercomputer, based on AMD GPUs. As part of a multiyear effort under the NNSA Advanced Simulation and Computing (ASC) program, we have been developing MARBL, a next generation, performance portable multiphysics application based on high-order finite e...

On December 5, 2022, an indirect drive fusion implosion on the National Ignition Facility (NIF) achieved a target gain G target of 1.5. This is the first laboratory demonstration of exceeding “scientific breakeven” (or G target > 1 ) where 2.05 MJ of 351 nm laser light produced 3.1 MJ of total fusion yield, a result which significantly exceeds the...

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a...

With the introduction of advanced heterogeneous computing architectures based on GPU accelerators, large-scale production codes have had to rethink their numerical algorithms and incorporate new programming models and memory management strategies in order to run efficiently on the latest supercomputers. In this work we discuss our co-design strateg...

Power is an often-cited reason for moving to advanced architectures on the path to Exascale computing. This is due to the practical concern of delivering enough power to successfully site and operate these machines, as well as concerns over energy usage while running large simulations. Since accurate power measurements can be difficult to obtain, p...

With the introduction of advanced heterogeneous computing architectures based on GPU accelerators, large-scale production codes have had to rethink their numerical algorithms and incorporate new programming models and memory management strategies in order to run efficiently on the latest supercomputers. In this work we discuss our co-design strateg...

In this paper we describe the research and development activities in the Center for Efficient Exascale Discretization within the US Exascale Computing Project, targeting state-of-the-art high-order finite-element algorithms for high-order applications on GPU-accelerated platforms. We discuss the GPU developments in several components of the CEED so...

In this paper we describe the research and development activities in the Center for Efficient Exascale Discretization within the US Exascale Computing Project, targeting state-of-the-art high-order finite-element algorithms for high-order applications on GPU-accelerated platforms. We discuss the GPU developments in several components of the CEED so...

Multimaterial simulation codes model the flow of materials with differing physical properties over a computational domain. Due to the intrinsically complicated access and traversal patterns on the underlying material-based field data defined over its mesh cells, such codes require implementations to strike a careful balance between competing demand...

In an effort to guide optimizations and detect performance regressions, developers of large HPC codes must regularly collect and analyze application performance profiles across different hardware platforms and in a variety of program configurations. However, traditional performance profiling tools mostly focus on ad-hoc analysis of individual progr...

This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We iteratively reduce the dimensionality of integration using the generalized Stokes theorem to line integrals over tri...

This work presents spectral, mesh-free, Green’s theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find intermediate quadrature rules for line integrals along the region’s boundary curves corresponding to Green’s theorem. (...

We address the problem of performing efficient spatial and topological queries on large tetrahedral meshes with arbitrary topology and complex boundaries. Such meshes arise in several application domains, such as 3D Geographic Information Systems (GISs), scientific visualization, and finite element analysis. To this aim, we propose Tetrahedral tree...

This work presents spectral, mesh-free, Green's theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find intermediate quadrature rules for line integrals along the region's boundary curves corresponding to Green's theorem. (...

The main goal of this milestone was to help CEED-enabled ECP applications, including ExaSMR, MARBL, ExaWind and ExaAM, to improve their performance and capabilities on GPU systems like Summit and Lassen/Sierra. In addition, the CEED team also worked to: add and improve support for additional hardware and programming models in the CEED software comp...

We introduce the Stellar decomposition, a model for efficient topological data structures over a broad range of simplicial and cell complexes. A Stellar decomposition of a complex is a collection of regions indexing the complex's vertices and cells such that each region has sufficient information to locally reconstruct the star of its vertices, i.e...

Multimaterial numerical simulations typically embed the shape of their materials into the computational mesh by determining the volume fractions of each material within the mesh elements, which requires the means to numerically describe the material boundaries. In this paper, we present a mesh-agnostic technique for generating and querying an impli...

While the vast majority of mesh processing tools assume a manifold mesh, many available meshes do not satisfy these constraints due to geometric defects and non-manifold singularities. We propose an efficient technique, based on a simple and compact data structure, for verifying topological properties of arbitrary simplicial complexes and experimen...

We consider the problem of efficient computing and simplifying Morse complexes on a Triangulated Irregular Network (TIN) based on discrete Morse theory. We develop a compact encoding for the discrete Morse gradient field, defined by the terrain elevation, by attaching it to the triangles of the TIN. This encoding is suitable to be combined with any...

In this paper we describe a visualization system for enabling location-based navigation of a social blog network. Our visualization has three parts: a map, tabular, and matrix display, to facilitate several selected user tasks. We use coordinated visualizations with an interface based on the principles of overview, zoom and filter, and details-on-d...

We consider the problem of computing discrete Morse and Morse-Smale complexes on an unstructured tetrahedral mesh discretizing the domain of a 3D scalar field. We use a duality argument to define the cells of the descending Morse complex in terms of the supplied (primal) tetrahedral mesh and those of the ascending complex in terms of its dual mesh....

Several algorithms have recently been introduced for morphological analysis of scalar fields (terrains, static and dynamic volume data) based on a discrete version of Morse theory. However, despite the applicability of the theory to very general discretized domains, memory constraints have limited its practical usage to scalar fields defined on reg...

We investigate a morphological approach to the analysis and understanding of three-dimensional scalar fields, and we consider applications to 3D medical and molecular images as examples.We consider a discrete model of the scalar field obtained by discretizing its 3D domain into a tetrahedral mesh. In particular, our meshes correspond to approximati...

Hierarchical spatial decompositions are a basic modelling tool in a variety of application domains. Several papers on this subject deal with hierarchical simplicial decompositions generated through regular simplex bisection. Such decompositions, originally developed for finite elements, are extensively used as the basis for multi-resolution models...

We propose the PR-star octree as a combined spatial data structure for performing efficient topological queries on tetrahedral meshes. The PR-star octree augments the Point Region octree (PR Octree) with a list of tetrahedra incident to its indexed vertices, i.e. those in the star of its vertices. Thus, each leaf node encodes the minimal amount of...

We propose a compact, dimension-independent data structure for the manifold, non-manifold and non-regular simplicial complexes, that we call the Generalized Indexed Data structure with Adjacencies (IA∗ data structure). It encodes only top simplices, i.e., the ones that are not on the boundary of any other simplex, plus a suitable subset of the adja...

We present parallel algorithms for processing, extracting and rendering adaptively sampled regular terrain datasets represented as a multiresolution model defined by a super-square-based diamond hierarchy. This model represents a terrain as a nested triangle mesh generated through a series of longest edge bisections and encoded in an implicit hiera...

Figure 1: Three nested refinement domains for hierarchies of tetrahedra and diamonds. The descendant domain (left) is the limit shape of the domain covered by all descendants of a given diamond (colored). Due to the fractal nature of these shapes, we introduce the more conservative convex descendant domain (middle) and bounding box descendant domai...

We consider a model of a 3D image obtained by discretizing it into a multiresolution tetrahedral mesh known as a hierarchy of diamonds. This model enables us to extract crack-free approximations of the 3D image at any uniform or variable resolution, thus reducing the size of the data set without reducing the accuracy. A 3D intensity image is a scal...

Efficient multiresolution representations for isosurfaces and interval volumes are becoming increasingly important as the gap between volume data sizes and processing speed continues to widen. Our multiresolution scalar field model is a hierarchy of tetrahedral clusters generated by longest edge bisection that we call a hierarchy of diamonds. We pr...

Hierarchical spatial decompositions play a fundamental role in many disparate areas of scientific and mathematical computing since they enable adaptive sampling of large problem domains. Although the use of quadtrees, octrees, and their higher dimensional analogues is ubiquitous, these structures generate meshes with cracks, which can lead to disco...

Volumetric datasets are often modeled using a multiresolution approach based on a nested decomposition of the domain into a polyhedral mesh. Nested tetrahedral meshes generated through the longest edge bisection rule are commonly used to decompose regular volumetric datasets since they produce highly adaptive crack-free representations. Efficient r...

Nested simplicial meshes generated by the simplicial bisection decomposition proposed by Maubach (Mau95) have been widely used in 2D and 3D as multi-resolution models of terrains and three-dimensional scalar fields, They are an alternative to octree representation since they allow generating crack-free representations of the underlying field. On th...

Time-varying volumetric data arise in a variety of applica- tion domains, and thus several techniques for dealing with such data have been proposed in the literature. A time-varying dataset is typically modeled either as a collection of discrete snapshots of volumetric data, or as a four-dimensional dataset. This choice influences the operations th...

Bintrees based on longest edge bisection and hierarchies of diamonds are popular multiresolution techniques on regularly sampled terrain datasets. In this work, we consider Sparse Terrain Pyramids as a compact multiresolution representation for terrain datasets whose samples are a subset of those lying on a regular grid. While previous diamond-base...

Interval volumes are a generalization of isosurfaces that represent the set of points between two surfaces. In this paper, we present a compact multi-resolution representation for interval volume meshes extracted from regularly sampled volume data sets. The multi-resolution model is a hierarchical tetrahedral mesh whose updates are based on the lon...

In this paper, we report our newly developed 3D face modeling system with arbitrary expressions in a high level of detail using the topographic analysis and mesh instantiation process. Given a sequence of images of facial expressions at frontal views, we automatically generate 3D expressions at arbitrary views. Our face modeling system consists of...

We present a method for efficiently generating plausible dents and scratches due to collisions using bump maps instead of mesh deformation. We use a rigid body simulator based on that of Guendelman et al. [2003], with collisions detected by interpenetration ...