Robert M. Kirby

Volumetric parameterization and trivariate B-spline fitting using harmonic functions

We present a methodology based on discrete volumetric harmonic functions to parameterize a volumetric model in a way that it can be used to fit a single trivariate B-spline to data so that simulation attributes can also be modeled. The resulting model representation is suitable for isogeometric analysis [Hughes, T.J., Cottrell, J.A., B., Y., 2005. Isogeometric analysis: Cad, finite elements, nurbs, exact geometry, and mesh refinement. Computer Methods in Applied Mechanics and Engineering 194, 4135-4195]. Input data consists of both a closed triangle mesh representing the exterior geometric shape of the object and interior triangle meshes that can represent material attributes or other interior features. The trivariate B-spline geometric and attribute representations are generated from the resulting parameterization, creating trivariate B-spline material property representations over the same parameterization in a way that is related to [Martin, W., Cohen, E., 2001. Representation and extraction of volumetric attributes using trivariate splines. In: Symposium on Solid and Physical Modeling, pp. 234-240] but is suitable for application to a much larger family of shapes and attributes. The technique constructs a B-spline representation with guaranteed quality of approximation to the original data. Then we focus attention on a model of simulation interest, a femur, consisting of hard outer cortical bone and inner trabecular bone. The femur is a reasonably complex object to model with a single trivariate B-spline since the shape overhangs make it impossible to model by sweeping planar slices. The representation is used in an elastostatic isogeometric analysis, demonstrating its ability to suitably represent objects for isogeometric analysis.

Nektar++: An open-source spectral/hp element framework

Nektar++ is an open-source software framework designed to support the development of high-performance scalable solvers for partial differential equations using the spectral/hp element method. High-order methods are gaining prominence in several engineering and biomedical applications due to their improved accuracy over low-order techniques at reduced computational cost for a given number of degrees of freedom. However, their proliferation is often limited by their complexity, which makes these methods challenging to implement and use. Nektar++ is an initiative to overcome this limitation by encapsulating the mathematical complexities of the underlying method within an efficient C++ framework, making the techniques more accessible to the broader scientific and industrial communities. The software supports a variety of discretisation techniques and implementation strategies, supporting methods research as well as application-focused computation, and the multi-layered structure of the framework allows the user to embrace as much or as little of the complexity as they need. The libraries capture the mathematical constructs of spectral/hp element methods, while the associated collection of pre-written PDE solvers provides out-of-the-box application-level functionality and a template for users who wish to develop solutions for addressing questions in their own scientific domains. Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland No. of lines in distributed program, including test data, etc.: 1052456 No. of bytes in distributed program, including test data, etc.: 42851367 External routines: Boost, PFTW, MPI, BLAS, LAPACK and METIS (www.cs.umn.edu) Nature of problem: The Nektar++ framework is designed to enable the discretisation and solution of time-independent or time-dependent partial differential equations. Running time: The tests provided take a few minutes to run. Runtime in general depends on mesh size and total integration time.

Comparing 2D vector field visualization methods: a user study

In a user study comparing four visualization methods for three-dimensional vector data, participants used visualizations from each method to perform five simple but representative tasks: 1) determining whether a given point was a critical point, 2) determining the type of a critical point, 3) determining whether an integral curve would advect through two points, 4) determining whether swirling movement is present at a point, and 5) determining whether the vector field is moving faster at one point than another. The visualization methods were line and tube representations of integral curves with both monoscopic and stereoscopic viewing. While participants reported a preference for stereo lines, quantitative results showed performance among the tasks varied by method. Users performed all tasks better with methods that: 1) gave a clear representation with no perceived occlusion, 2) clearly visualized curve speed and direction information, and 3) provided fewer rich 3D cues (e.g., shading, polygonal arrows, overlap cues, and surface textures). These results provide quantitative support for anecdotal evidence on visualization methods. The tasks and testing framework also give a basis for comparing other visualization methods, for creating more effective methods, and for defining additional tasks to explore further the tradeoffs among the methods.

De-aliasing on non-uniform grids: algorithms and applications

We present de-aliasing rules to be used when evaluating non-linear terms with polynomial spectral methods on non-uniform grids analogous to the de-aliasing rules used in Fourier spectral methods. They are based upon the idea of super-collocation followed by a Galerkin projection of the non-linear terms. We demonstrate through numerical simulation that both accuracy and stability can be greatly enhanced through the use of this approach. We begin by deriving from the numerical quadrature rules used by Galerkin-type projection methods the number of quadrature points and weights needed for quadratic and cubic non-linearities. We then present a systematic study of the effects of super-collocation when using both a continuous Galerkin and a discontinuous Galerkin method to solve the one-dimensional viscous Burgers equation. We conclude by examining three direct numerical simulation flow examples: incompressible turbulent flow in a triangular duct, incompressible turbulent flow in a channel at Reτ = 395, and compressible flow past a pitching airfoil at Re = 45,000.

From h to p efficiently: Implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations

The spectral/hp element method can be considered as bridging the gap between the - traditionally low-order - finite element method on one side and spectral methods on the other side. Consequently, a major challenge which arises in implementing the spectral/hp element methods is to design algorithms that perform efficiently for both low- and high-order spectral/hp discretisations, as well as discretisations in the intermediate regime. In this paper, we explain how the judicious use of different implementation strategies can be employed to achieve high efficiency across a wide range of polynomial orders. Furthermore, based upon this efficient implementation, we analyse which spectral/hp discretisation (which specific combination of mesh-size h and polynomial order P) minimises the computational cost to solve an elliptic problem up to a predefined level of accuracy. We investigate this question for a set of both smooth and non-smooth problems.

Unconditionally stable discretizations of the immersed boundary equations

The immersed boundary (IB) method is known to require small timesteps to maintain stability when solved with an explicit or approximately implicit method. Many implicit methods have been proposed to try to mitigate this timestep restriction, but none are known to be unconditionally stable, and the observed instability of even some of the fully implicit methods is not well understood. In this paper, we prove that particular backward Euler and Crank-Nicolson-like discretizations of the nonlinear immersed boundary terms of the IB equations in conjunction with unsteady Stokes Flow can yield unconditionally stable methods. We also show that the position at which the spreading and interpolation operators are evaluated is not relevant to stability so as long as both operators are evaluated at the same location in time and space. We further demonstrate through computational tests that approximate projection methods (which do not provide a discretely divergence-free velocity field) appear to have a stabilizing influence for these problems; and that the implicit methods of this paper, when used with the full Navier-Stokes equations, are no longer subject to such a strict timestep restriction and can be run up to the CFL constraint of the advection terms.

Contour Boxplots: A Method for Characterizing Uncertainty in Feature Sets from Simulation Ensembles

Ensembles of numerical simulations are used in a variety of applications, such as meteorology or computational solid mechanics, in order to quantify the uncertainty or possible error in a model or simulation. Deriving robust statistics and visualizing the variability of an ensemble is a challenging task and is usually accomplished through direct visualization of ensemble members or by providing aggregate representations such as an average or pointwise probabilities. In many cases, the interesting quantities in a simulation are not dense fields, but are sets of features that are often represented as thresholds on physical or derived quantities. In this paper, we introduce a generalization of boxplots, called contour boxplots, for visualization and exploration of ensembles of contours or level sets of functions. Conventional boxplots have been widely used as an exploratory or communicative tool for data analysis, and they typically show the median, mean, confidence intervals, and outliers of a population. The proposed contour boxplots are a generalization of functional boxplots, which build on the notion of data depth. Data depth approximates the extent to which a particular sample is centrally located within its density function. This produces a center-outward ordering that gives rise to the statistical quantities that are essential to boxplots. Here we present a generalization of functional data depth to contours and demonstrate methods for displaying the resulting boxplots for two-dimensional simulation data in weather forecasting and computational fluid dynamics.

Formal verification of practical MPI programs

This paper considers the problem of formal verification of MPI programs operating under a fixed test harness for safety properties without building verification models. In our approach, we directly model-check the MPI/C source code, executing its interleavings with the help of a verification scheduler. Unfortunately, the total feasible number of interleavings is exponential, and impractical to examine even for our modest goals. Our earlier publications formalized and implemented a partial order reduction approach that avoided exploring equivalent interleavings, and presented a verification tool called ISP. This paper presents algorithmic and engineering innovations to ISP, including the use of OpenMP parallelization, that now enables it to handle practical MPI programs, including:(i)~ParMETIS - a widely used hypergraph partitioner, and (ii)~MADRE - a Memory Aware Data Re-distribution Engine, both developed outside our group. Over these benchmarks, ISP has automatically verified up to 14K lines of MPI/C code, producing error traces of deadlocks and assertion violations within seconds.

Particle-based Sampling and Meshing of Surfaces in Multimaterial Volumes

Methods that faithfully and robustly capture the geometry of complex material interfaces in labeled volume data are important for generating realistic and accurate visualizations and simulations of real-world objects. The generation of such multimaterial models from measured data poses two unique challenges: first, the surfaces must be well-sampled with regular, efficient tessellations that are consistent across material boundaries; and second, the resulting meshes must respect the nonmanifold geometry of the multimaterial interfaces. This paper proposes a strategy for sampling and meshing multimaterial volumes using dynamic particle systems, including a novel, differentiable representation of the material junctions that allows the particle system to explicitly sample corners, edges, and surfaces of material intersections. The distributions of particles are controlled by fundamental sampling constraints, allowing Delaunay-based meshing algorithms to reliably extract watertight meshes of consistently high-quality.

Sensorial and microbial effects of gaseous ozone on fresh scad (Trachurus trachurus).

The bactericidal activity of gaseous ozone was investigated using a commercial ozone generator. Five species of fish bacteria, Pseudomonas putida, Shewanella putrefaciens, Brochothrix thermosphacta, Enterobacter sp. and Lactobacillus plantarum, were inoculated on agar surfaces and exposed to different ozonation times in a gas chamber. Results showed ozone in relatively low concentrations (<0·27 × 10−3 g l−1) was an effective bactericide of vegetative cells of the five fish bacteria. The age of the cell culture was shown to influence the cell response following exposure. Survival rate was not linearly related to ozonation time, but exhibited biphasic death over an extended period. Similar bactericidal effects were observed on fish skin treated with ozone daily in the laboratory, with decreases of 1·0 log cfu cm−2 for the micro‐organisms studied. Whole fish treated daily in the laboratory using a commercial ozone generator showed improved scores for sensory analyses compared with the controls. The results were statistically significant. Fish treated on board ships were also analysed for microbiological and sensory changes. Controls were obtained from a similar vessel without the ozone facility in the hold. Similar trends to those recorded in the laboratory for the microbiological and sensory results on ozonated fish were observed.