Scalable Fast Multipole Methods on Heterogeneous Architecture

The N-body problem appears in many computational physics simulations. At each time step the computation involves an all-pairs sum whose complexity is quadratic, followed by an update of particle positions. This cost means that it is not practical to solve such dynamic N-body problems on large scale. To improve this situation, we use both algorithmic and hardware approaches. Our algorithmic approach is to use the Fast Multipole Method (FMM), which is a divide-and-conquer algorithm that performs a fast N-body sum using a spatial decomposition and is often used in a time-stepping or iterative loop, to reduce such quadratic complexity to linear with guaranteed accuracy. Our hardware approach is to use heterogeneous clusters, which comprised of nodes that contain multi-core CPUs tightly coupled with accelerators, such as graphics processors unit (GPU) as our underline parallel processing hardware, on which efficient implementations require highly non-trivial re-designed algorithms. In this dissertation, we fundamentally reconsider the FMM algorithms on heterogeneous architectures to achieve a significant improvement over recent/previous implementations in literature and to make the algorithm ready for use as a workhorse simulation tool for both time-dependent vortex flow problems and for boundary element methods. Our major contributions include: 1. Novel FMM data structures using parallel construction algorithms for dynamic problems. 2. A fast hetegenenous FMM algorithm for both single and multiple computing nodes. 3. An efficient inter-node communication management using fast parallel data structures. 4. A scalable FMM algorithm using novel Helmholz decomposition for Vortex Methods (VM). The proposed algorithms can handle non-uniform distributions with irregular partition shapes to achieve workload balance and their MPI-CUDA implementations are highly tuned up and demonstrate the state of the art performances

Doctor of Philosophy

dissertationVisualizing surfaces is a fundamental technique in computer science and is frequently used across a wide range of fields such as computer graphics, biology, engineering, and scientific visualization. In many cases, visualizing an interface between boundaries can provide meaningful analysis or simplification of complex data. Some examples include physical simulation for animation, multimaterial mesh extraction in biophysiology, flow on airfoils in aeronautics, and integral surfaces. However, the quest for high-quality visualization, coupled with increasingly complex data, comes with a high computational cost. Therefore, new techniques are needed to solve surface visualization problems within a reasonable amount of time while also providing sophisticated visuals that are meaningful to scientists and engineers. In this dissertation, novel techniques are presented to facilitate surface visualization. First, a particle system for mesh extraction is parallelized on the graphics processing unit (GPU) with a red-black update scheme to achieve an order of magnitude speed-up over a central processing unit (CPU) implementation. Next, extending the red-black technique to multiple materials showed inefficiencies on the GPU. Therefore, we borrow the underlying data structure from the closest point method, the closest point embedding, and the particle system solver is switched to hierarchical octree-based approach on the GPU. Third, to demonstrate that the closest point embedding is a fast, flexible data structure for surface particles, it is adapted to unsteady surface flow visualization at near-interactive speeds. Finally, the closest point embedding is a three-dimensional dense structure that does not scale well. Therefore, we introduce a closest point sparse octree that allows the closest point embedding to scale to higher resolution. Further, we demonstrate unsteady line integral convolution using the closest point method

Unsteady wake modelling for tidal current turbines

The authors present a numerical model for three-dimensional unsteady wake calculations for tidal turbines. Since wakes are characterised by the shedding of a vortex sheet from the rotor blades, the model is based on the vorticity transport equations. A vortex sheet may be considered a jump contact discontinuity in tangential velocity with, in inviscid hydrodynamic terms, certain kinematic and dynamic conditions across the sheet. The kinematic condition is that the sheet is a stream surface with zero normal fluid velocity; the dynamic condition is that the pressure is equal on either side of the sheet. The dynamic condition is explicitly satisfied at the trailing edge only, via an approximation of the Kutta condition. The shed vorticity is the span-wise derivative of bound circulation, and the trailed vorticity is the time derivative of bound circulation, and is convected downstream from the rotors using a finite-volume solution of vorticity transport equations thus satisfying the kinematic conditions. Owing to an absence in the literature of pressure data for marine turbines, results from the code are presented for the NREL-UAE Phase IV turbine. Axial flow cases show a close match in pressure coefficients at various spanwise stations; however, yawed flow cases demonstrate the shortcomings of a modelling strategy lacking viscosity

Dynamic simulation of smoke diffusion and gas pollution

Gas pollution is a common phenomenon in natural life. Aiming at the low efficiency of simulating smoke diffusion based on physical model and the poor effect of drawing gas pollution based on empirical model, a hybrid model method is proposed to draw the dynamic gas pollution caused by smoke diffusion. Firstly, the semi Lagrangian method is used to model the smoke, and the k-d tree is introduced to improve the computational efficiency; secondly, to solve the problem of insufficient details in smoke simulation, the fluctuating wind field based on linear filter method is introduced into the external force term to optimize the trajectory of smoke particles; the bidirectional shot function combined with the real smoke texture is selected for rendering to avoid the problem of obvious particle sense and significantly improve the smoke diffusion details; then, the optimized Gaussian plume model is introduced to establish the relationship between the physical model and the empirical model, and the pollution attenuation formula and the optimized Perlin noise are used to improve the lack of details of global gas pollution and increase the realism of gas pollution changes; by improving the time axis algorithm, the problem of fixed gas pollution color is solved, and the dynamic gradual gas pollution is obtained. Finally, several groups of analysis and comparison experiments are designed. The results show that this method can draw a realistic dynamic gas pollution scene in real-time

Flow simulation with locally-refined LBM

We simulate 3D fluid flow by a locally-refined lattice Boltzmann method (LBM) on graphics hardware. A low resolution LBM simulation running on a coarse grid models global flow behavior of the entire domain with low consumption of computational resources. For regions of interest where small visual details are desired, LBM simulations are performed on fine grids, which are separate grids superposed on the coarse one. The flow properties on boundaries of the fine grids are determined by the global simulation on the coarse grid. Thus, the locally refined fine-grid simulations follow the global fluid behavior, and model the desired small-scale and turbulent flow motion with their denser numerical discretization. A fine grid can be initiated and terminated at any time while the global simulation is running. It can also move inside the domain with a moving object to capture small-scale vortices caused by the object. Besides the performance improvement due to the adaptive simulation, the locally-refined LBM is suitable for acceleration on contemporary graphics hardware (GPU), since it involves only local and linear computations. Therefore, our approach achieves fast and adaptive 3D flow simulation for computer games and other interactive applications

Reviews on Physically Based Controllable Fluid Animation

In computer graphics animation, animation tools are required for fluid-like motions which are controllable by users or animator, since applying the techniques to commercial animations such as advertisement and film. Many developments have been proposed to model controllable fluid simulation with the need in realistic motion, robustness, adaptation, and support more required control model. Physically based models for different states of substances have been applied in general in order to permit animators to almost effortlessly create interesting, realistic, and sensible animation of natural phenomena such as water flow, smoke spread, etc. In this paper, we introduce the methods for simulation based on physical model and the techniques for control the flow of fluid, especially focus on particle based method. We then discuss the existing control methods within three performances; control ability, realism, and computation time. Finally, we give a brief of the current and trend of the research areas

Liquid surface tracking with error compensation

Our work concerns the combination of an Eulerian liquid simulation with a high-resolution surface tracker (e.g. the level set method or a Lagrangian triangle mesh). The naive application of a high-resolution surface tracker to a low-resolution velocity field can produce many visually disturbing physical and topological artifacts that limit their use in practice. We address these problems by defining an error function which compares the current state of the surface tracker to the set of physically valid surface states. By reducing this error with a gradient descent technique, we introduce a novel physics-based surface fairing method. Similarly, by treating this error function as a potential energy, we derive a new surface correction force that mimics the vortex sheet equations. We demonstrate our results with both level set and mesh-based surface trackers