Student Posters Repository

I use an advanced computational framework called Gkeyll to simulate plasma turbulence in the edge of magnetic confinement fusion experiments. Gkeyll uses the discontinuous Galerkin finite element method, which combines the benefits of finite element methods, such as high-order accuracy, with those of finite volume methods, including locality of data. To model the plasma, I use a gyrokinetic formulation, which averages over the fast gyro-motion of the charged particles and reduces the dimensionality of the probability distribution function. More specifically, I simulated the Texas Helimak experiment, which is useful for validating numerical codes due to its extensive diagnostics and simple, helical geometry, which is similar to the edge region of larger fusion devices. These were the first kinetic simulations of the Helimak and results agree fairly well with experimental data.

We introduce an integer programming formulation for ranking aggregation with ties and compare it to a modified version of a recently developed formulation. This new formulation provides computational advantages when solving large size problems. Moreover, we develop a refined social-choice related property for group decision-making, called the Generalized Condorcet Criterion, which can be regarded as a natural extension of the well-known Condorcet criterion and the Extended Condorcet criterion. Unlike its parent properties, the generalized Condorcet criterion is adequate for complete rankings with ties as well as for incomplete rankings. This property allows a simplification of solution process for very large instances of the NP-hard Kemeny ranking aggregation problem by using HPC techniques. To test the practical implications of this property, we sample complete rankings with and without ties from the Mallows statistical distribution of rank data to generate instances with differing degrees of collective cohesion. 

Core-collapse supernovae (CCSNe) - the explosive deaths of massive stars - are among the most important sites of element synthesis in the universe. Not only do they drive the chemical evolution of galaxies, the nucleosynthesis yields of CCSNe are also imprinted on some of the oldest stars. Our ability to predict these yields, however, is limited by the still unsolved question of the CCSN explosion mechanism. Spherically symmetric simulations fail to explode and multi-dimensional simulations, although crucial for uncovering the explosion mechanism, are computationally too demanding to study large samples of progenitor stars. The PUSH method induces explosions in otherwise non-exploding spherically symmetric simulations via parametrized heating. It also follows the evolution of the protoneutron star and the electron fraction of the ejecta - features vital for nucleosynthesis calculations. I will present the explosion energies, remnant masses and nucleosynthesis yields of 111 models, with masses between 10.8 and 120 solar masses, exploded successfully using PUSH. I will highlight broad trends that appear as a function of pre-explosion properties and compare predicted nucleosynthesis yields to available observational data. These yields will be extremely useful for modeling galactic chemical evolution to gain further insight into the nuclear history of our universe.

A geometrical Volume-of-Fluid (VoF) method approximates the interface that separates immiscible fluids as a set of piece wise planar elements, associated with cells of the discretized solution domain that contain both fluids. Geometrical intersection operations are used both on the piecewise planar interface approximation, and the cells of the discretized domain in order to numerically approximate the evolution of the interface. The geometrical VoF method is widely used for two-phase flow simulations, because it stringently conserves mass, allows for accurate calculation on surface tension forces, and is straightforward to implement in parallel in terms of simple message exchanges across process boundaries. Current research is focusing on the extensions of the geometrical VoF method to unstructured domain discretization, and dimensionally un-split geometrical transport algorithms, as well as a more accurate geometrical interface approximation. The unstructured discretization of the solution domain, and the un-split transport algorithm negatively affect the serial and parallel efficiency of the method. Therefore, there is a need for modern HPC techniques to be applied on the method implementation in order to improve its serial and parallel efficiency.

 Molecular dynamics simulation is a powerful tool to study biomolecules. However, sometimes their configurations get trapped in local minimum of free energy landscape and it prevents us from efficient simulations. To overcome this problem, replica-exchange method and replica-permutation method have been proposed. Replica-permutation method is an improved alternative of the replica-exchange method. However, volume cannot be changed in previous replica-permutation method. In this study, I developed the replica-permutation method in the isothermal-isobaric ensemble. The isothermal-isobaric replica-permutation method carries out many molecular dynamics simulations (replicas) at the same time, and sometimes the parameters such as temperatures and pressures are permuted among the replicas through MPI communication. The replica-permutation methods use the Suwa-Todo algorithm to permute parameter labels instead of the Metropolis algorithm so that the rejection rate can be minimized. I showed that the method enhances the sampling efficiency.

To enhance the productivity of HPC applications, I have been implementing a distributed shared memory (DSM) library, which can execute shared memory applications on distributed memory machines with minimal modifications. Although many people think that DSM is less scalable than distributed memory programming models including message passing or PGAS, I am trying to integrate several important ideas (e.g. self-invalidation, relaxed consistency) to build a scalable and efficient DSM library.

I am also developing a technique to accelerate communication libraries in multi-threading environments because it is increasingly important for DSM or other systems to efficiently manage the communications from multiple threads. Several researchers have proposed software offloading approaches to deal with resource contentions by the use of dedicated communication threads and lockless queues. However, software offloading techniques suffer from the heavy consumption of CPU resources because dedicated threads are spinning to monitor the queue. To solve this problem, I implemented a technique which can accomplish parallelized software offloading without spinning using a user-level thread library.

In solving complex symmetric linear systems arising from the edge finite element method with double precision number, we suffer from slow or no convergence of iterative methods. Here, in real number problems, high precision calculation improves the convergence of the iterative method. Therefore, we implement multiple-precision calculation, especially, double-double (DD) precision numbers, which is implemented with two double precision type variable.  As a result of numerical experiments, when solving the complex symmetric linear equation, we succeeded in improving the convergence of the iterative method by using high precision calculation, and by using mixed precision calculation with high precision calculation and double precision calculation, we succeeded in suppressing the increase of calculation time.Moreover, we succeeded in suppressing the influence of acceleration factor and relaxation coefficient in preconditioning matrix calculation by high precision calculation.Thereby, I succeeded in getting convergent solution stably. In future, we aim to realize more speedup by implementing parallelization, and utilizing high-performance computing technology using Intel AVX instruction and so on.

Our research is about exploring parallel multigrid methods to solve three dimensional Poisson equation on a cylindrical coordinate system which will be implemented in many/multicore processor environment. First, we try to investigate the iteration method that used as smoother. Our objective is to reduce as much as possible the serial part of the solver. While the other part of multigrid methods like in restriction and prolongation process is easier to parallelize, in many-core architectures, memory access pattern is not too friendly to straightforward implementation. Next, we also investigate the parallelization in multinode systems, where some node might idle while the other nodes still do some computation. In order to achieve that, we try to consider some key issues: (1) thread parallelism that related to scalability with core count, (2) data-parallelism exposure to explore vectorization capabilities and (3) data-locality aware techniques.

Coherent patterns are frequently observed in oceanic currents, planetary atmospheres, and many other natural contexts. Coherent patterns are considered Lagrangian if they are defined from the bulk motion of a fluid parcel. Studying Lagrangian motion enables the discovery of important transport properties of fluid flows and extracting coherent patterns reveals the robust material surfaces behind complex dynamics. Our framework for extracting coherent patterns is to study the spectra of Koopman operators acting on observables of the system. We modeled time-dependent double gyre and the idealized stratospheric flow using this framework.

Higher-order tensor renormalization group (HOTRG) is one of approximation methods for the partition function in physics. Bottleneck computation of HOTRG is a tensor contraction which is a generalization of matrix product. A tensor contraction is usually implemented by matrix products and tensor transportations which is a generalization of matrix transportation. Tensor transportations in HOTRG take a lot of time because it is complicated and applied to large tensors. In this research, we reduce computation time for the tensor transportations in HOTRG by optimizing tensor transportation procedure.