Kirk E. Jordan

Multiphysics simulations: Challenges and opportunities

We consider multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity, and “architectural” includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

Modeling the performance of an algebraic multigrid cycle on HPC platforms

Now that the performance of individual cores has plateaued, future supercomputers will depend upon increasing parallelism for performance. Processor counts are now in the hundreds of thousands for the largest machines and will soon be in the millions. There is an urgent need to model application performance at these scales and to understand what changes need to be made to ensure continued scalability. This paper considers algebraic multigrid (AMG), a popular and highly efficient iterative solver for large sparse linear systems that is used in many applications. We discuss the challenges for AMG on current parallel computers and future exascale architectures, and we present a performance model for an AMG solve cycle as well as performance measurements on several massively-parallel platforms.

Singular operators in multiwavelet bases

We review some recent results on multiwavelet methods for solving integral and partial differential equations and present an efficient representation of operators using discontinuous multiwavelet bases, including the case for singular integral operators. Numerical calculus using these representations produces fast O(N) methods for multiscale solution of integral equations when combined with low separation rank methods. Using this formulation, we compute the Hilbert transform and solve the Poisson and SchrA¶dinger equations. For a fixed order of multiwavelets and for arbitrary but finite- precision computations, the computational complexity is O(N). The computational structures are similar to fast multipole methods but are more generic in yielding fast O(N) algorithm development.

Modeling the Performance of an Algebraic Multigrid Cycle Using Hybrid MPI/OpenMP

The rise of multicore cluster architectures has led to intense interest in using a combination of MPI and OpenMP to more effectively program these machines. We present a performance model for hybrid implementation of the solve cycle of algebraic multigrid (AMG), a popular iterative solver for large sparse linear systems and a key component of many scientific simulations. We validate the model on two leading parallel platforms, and discuss implications for applications programmed in a hybrid model on future machines.

Undergraduate Computational Science and Engineering Education

It is widely acknowledged that computational science and engineering (CSE) will play a critical role in the future of the scientific discovery process and engineering design. However, in recent years computational skills have been deemphasized in the curricula of many undergraduate programs in science and engineering. There is a clear need to provide training in CSE fundamentals at the undergraduate level. An undergraduate CSE program can train students for careers in industry, education, and for graduate CSE study. The courses developed for such a program will have an impact throughout the science, technology, engineering, and mathematics (STEM) undergraduate curriculum. This paper outlines the content of a CSE curriculum, the skills needed by successful graduates, the structure and experiences of some recently developed CSE undergraduate programs, and the potential career paths following a CSE undergraduate education.

Modeling time and topology for animation and visualization with examples on parametric geometry

The art of animation relies upon modeling objects that change over time. A sequence of static images is displayed to produce an illusion of motion. Even for simple cases, a careful analysis exposes that formal topological guarantees are often lacking. This absence of rigor can result in subtle, but significant, topological flaws. A new modeling approach is proposed to integrate topological rigor with a continuous model of time. Examples will be given for Bezier curves, while indicating extensions to a richer class of parametric curves and surfaces. Applications to scientific visualization for molecular modeling are discussed. Prototype animations are available for viewing over the web.

Parallel interactive visualization of 3D mantle convection

In 3D simulation of thermal convective flows that change with time, each run can generate gigabytes of data. A client server visualization tool called pV3, running on a parallel computer, allows data exploration during computation instead of by postprocessing. While pV3 has been primarily used in the area of flow visualization designed with aerospace applications in mind, it has easily been applied in other flow visualization areas, such as geoscience. It has also been used for 3D wave propagation problems, including seismic waves and electromagnetics. More importantly, many of the concepts of pV3s client server interactive parallel visualization model could be used as a prototype for other application areas, such as enhanced MRI in medicine. The key to this kind of interactive visualization lies in being able to scale the compute part of the visualization as well as the application is scaled, while still minimizing network traffic. The article discusses the use of pV3 for investigating thermal convection in the interior of the Earth. pV3 was used to help understand details of the physics of variable viscosity and phase transitions in high Rayleigh number convection.

A service composition framework for market-oriented high performance computing cloud

Despite the success High Performance Computing (HPC) across a number of application domains, the adoption of HPC resources and applications is still limited, primarily due to its high capital cost, system complexity, application availability, and service delivery model. Recently, several research efforts have shown that the emerging Cloud Computing service model can improve on-demand access to HPC capacity as utility. This paper introduces a framework for on-demand composing and deploying available HPC applications as services on HPC clouds. The composition is enabled by an ontology that describes dependencies and relationships among HPC software and resources.

A computational model for overcoming drug resistance using selective dual-inhibitors for aurora kinase A and its T217D variant.

The human Aurora kinase-A (AK-A) is an essential mitotic regulator that is frequently overexpressed in several cancers. The recent development of several novel AK-A inhibitors has been driven by the well-established association of this target with cancer development and progression. However, resistance and cross-reactivity with similar kinases demands an improvement in our understanding of key molecular interactions between the Aurora kinase-A substrate binding pocket and potential inhibitors. Here, we describe the implementation of state-of-the-art virtual screening techniques to discover a novel set of Aurora kinase-A ligands that are predicted to strongly bind not only to the wild type protein, but also to the T217D mutation that exhibits resistance to existing inhibitors. Furthermore, a subset of these computationally screened ligands was shown to be more selective toward the mutant variant over the wild type protein. The description of these selective subsets of ligands provides a unique pharmacological tool for the design of new drug regimens aimed at overcoming both kinase cross-reactivity and drug resistance associated with the Aurora kinase-A T217D mutation.

Toward a Standard Protocol for Micelle Simulation.

In this paper, we present protocols for simulating micelles using dissipative particle dynamics (and in principle molecular dynamics) that we expect to be appropriate for computing micelle properties for a wide range of surfactant molecules. The protocols address challenges in equilibrating and sampling, specifically when kinetics can be very different with changes in surfactant concentration, and with minor changes in molecular size and structure, even using the same force field parameters. We demonstrate that detection of equilibrium can be automated and is robust, for the molecules in this study and others we have considered. In order to quantify the degree of sampling obtained during simulations, metrics to assess the degree of molecular exchange among micellar material are presented, and the use of correlation times are prescribed to assess sampling and for statistical uncertainty estimates on the relevant simulation observables. We show that the computational challenges facing the measurement of the critical micelle concentration (CMC) are somewhat different for high and low CMC materials. While a specific choice is not recommended here, we demonstrate that various methods give values that are consistent in terms of trends, even if not numerically equivalent.