Bulletin of the American Physical Society
Annual Meeting of the Four Corners Section of the APS
Volume 59, Number 11
Friday–Saturday, October 17–18, 2014; Orem, Utah
Session K2: Materials Science IV: Computational Methods |
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Chair: Matt Kim, Quanterra Corp. Room: Science Building 246 |
Saturday, October 18, 2014 1:15PM - 1:39PM |
K2.00001: Rectangles Stink: Numerical Integration in DFT Codes Invited Speaker: Gus Hart The 1998 Nobel prize was given to Kohn and Pople for their development of Density Functional Theory. DFT allows one to do quantum-mechanical calculations for materials and has been developed into a powerful computational tool. Typical DFT calculations require a numerical integral over the electron states in the material. Even though this integral is a small piece of the overall calculation, it is a primary source of error when the material is metallic. Metals are particularly problematic for the basic rectangle integration rules used in DFT codes. I'll give a pedestrian review of DFT calculations, a basic introduction to numerical integration, and finish with a demonstration of a new integration method for metals. Improving the current integration method should lead to a 5000\% speedup in typical calculations. [Preview Abstract] |
Saturday, October 18, 2014 1:39PM - 1:51PM |
K2.00002: Materials Modeling and the Integration Problem Matthew Burbidge, Gus Hart The 1998 Nobel prize was given to Kohn and Pople for their development of Density Functional Theory. DFT allows one to do quantum-mechanical calculations for materials and has been developed into a powerful computational tool. Typical DFT calculations require a numerical integral over the electron states in the material. Even though this integral is a small piece of the overall calculation, it is a primary source of error. Through the use of a simple toy problem, we will explain the fundamentals of the integration problem. Further, we will show that there is much room for improvement in current DFT codes (such as VASP). Using our toy problem we can get some insight as to what is going wrong. The resolution of this integration problem will result in millions of CPU hours saved for a typical computational materials scientist. [Preview Abstract] |
Saturday, October 18, 2014 1:51PM - 2:03PM |
K2.00003: A simple spline solution to a 50 year old problem Jeremy Jorgensen As increasingly complex issues confront humanity (nuclear waste management, efficient fuel cells, water purifying systems, etc) it is progressively more important to find solutions. There are materials yet to be discovered that could solve these problems. Computers and density functional theory (DFT) enable scientists to predict new materials. Speeding up these codes would have a real impact on materials development. Modern DFT programs perform a slowly converging numeric integration. We plan to replace the current integration method, a standard rectangle method, by spline interpolation. This will increase computation speeds by up to 5,000\%, which will boost data processing speeds and increase the likelihood of novel materials being discovered. [Preview Abstract] |
Saturday, October 18, 2014 2:03PM - 2:15PM |
K2.00004: Robust Computational Physics and Automated Sanity Checks Conrad Rosenbrock A good computational physics course teaches students to say ``well that's completely wrong'' anytime the computer gives them a result. Once cast in doubt, it is the scientist's responsibility to convince themselves that the result is in fact correct. As programs become more complicated, it usually becomes more difficult to guarantee that the final output is right. I will present a new framework that automates the production of robust, high quality Fortran code. The talk will include a brief overview of good coding principles and a demonstration of the most useful features of the framework that help automate implementation of these principles. By providing an XML-based documentation standard and automated unit testing, fortpy\footnote{Conrad W. Rosenbrock \textit{Fortpy Auto-completion and Automated Unit Testing for Fortran: https://github.com/rosenbrockc/fortpy}} helps researchers ensure that their code produces accurate physics and is easier to use by others. [Preview Abstract] |
Saturday, October 18, 2014 2:15PM - 2:27PM |
K2.00005: Trimming a Combinatorical Tree Wiley Morgan, Rod Forcade, Gus Hart In computational material science, one frequently needs to know the number of unique atomic configurations in a structure. For example in an A$_{3}$B phase, two different kinds of atoms may be present on the B sites. In modeling possible alloys one needs to know the number of possible arrangements on the B sites. The obvious solution to this combinatorics problem is to generate the list of all possible configurations and then eliminate those that are symmetrically equivalent. This approach, however, suffers from a combinatoric explosion, particularly for large structures with more than two atom types. This happens even when there are a large number of symmetrically-equivalent configurations and only a few unique configurations that survive the elimination process. We developed a new algorithm that avoids this problem by not generating the entire list of configurations. Instead, it generates ``partial configurations'' and applies the symmetry operations without finding each ``complete'' configuration. This algorithm allows us to tackle much larger problems due to increases in computational efficiency. [Preview Abstract] |
Saturday, October 18, 2014 2:27PM - 2:39PM |
K2.00006: Tuning the Metropolis algorithm Spencer Hart, Derek Ostrom, Gus Hart The Metropolis algorithm is a method for simulating equilibrium states of systems. Metropolis Monte Carlo simulations are commonly used to explore material properties, such as transition temperatures. For complex systems, statistical convergence can be hard to achieve, making the results ambiguous. Increasing your sample size will increase the likelihood of convergence, but if the simulation already takes 20 days, increasing the runtime by an order of magnitude is impractical. In an effort to find the best ways to improve simulation results without just increasing runtime, we explored the effects of various computational parameters on a test case, 2D binary alloy model. These parameters include the number of random samples (called Monte Carlo steps), lattice size, and temperature step-size. We hope to use these results to improve simulations of more complex systems in the future. [Preview Abstract] |
Saturday, October 18, 2014 2:39PM - 2:51PM |
K2.00007: Wang Landau Sampling: Only a ``Random'' Walk in the Park? Derek Ostrom, Spencer Hart, Lance Nelson, Gus Hart For years the Metropolis algorithm has been the king of random sampling (Monte Carlo) in computational methods. However, one method, Wang Landau sampling, promises to be a powerful replacement to the famous Metropolis algorithm. I explore the usefulness of the Metropolis algorithm with both the magnetic and alloy Ising models and show the validity of the Wang Landau sampling with the magnetic Ising as well as show the results of the previously untested alloy Ising. The usefulness of the Wang Landau sampling is evident in its ability to map the density of states of these models. From the density of states the free energy and entropy can be computed directly. In materials science, finding the entropy is arguably the most important and most difficult piece of information one can gain about a system. This method hopes to make material simulations more effective, hopefully giving a boost to the materials simulation community producing results faster for the world to use. [Preview Abstract] |
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