A General-Purpose Element-Based Approach to Compute Dispersion Relations in Periodic Materials with Existing Finite Element Codes

The numerical determination of dispersion relations in periodic materials via the finite element method is a difficult task in most standard codes. Here, we propose a novel technique which allows the computation of these band structures from local elemental subroutines in contrast with existing methods which impose Bloch boundary conditions on the global arrays. The proposed local approach is thus readily applicable to several physical contexts and space dimensionalities. Here we present the details of this element-based algorithm and provide verification results for three different kinematic assumptions applied to phononic crystals in a classical and a micropolar elastic medium. The paper also includes in the form of supplementary material, a fully-coded user subroutine and a test-problem to be used in a commercial finite element code.

Exploring versioned distributed arrays for resilience in scientific applications

Exascale studies project reliability challenges for future HPC systems. We present the Global View Resilience (GVR) system, a library for portable resilience. GVR begins with a subset of the Global Arrays interface, and adds new capabilities to create versions, name versions, and compute on version data. Applications can focus versioning where and when it is most productive, and customize for each application structure independently. This control is portable, and its embedding in application source makes it natural to express and easy to maintain. The ability to name multiple versions and “partially materialize” them efficiently makes ambitious forward-recovery based on “data slices” across versions or data structures both easy to express and efficient. Using several large applications (OpenMC, preconditioned conjugate gradient (PCG) solver, ddcMD, and Chombo), we evaluate the programming effort to add resilience. The required changes are small (< 2% lines of code (LOC)), localized and machine-independent, and perhaps most important, require no software architecture changes. We also measure the overhead of adding GVR versioning and show that overheads < 2% are generally achieved. This overhead suggests that GVR can be implemented in large-scale codes and support portable error recovery with modest investment and runtime impact. Our results are drawn from both IBM BG/Q and Cray XC30 experiments, demonstrating portability. We also present two case studies of flexible error recovery, illustrating how GVR can be used for multi-version rollback recovery, and several different forward-recovery schemes. GVR’s multi-version enables applications to survive latent errors (silent data corruption) with significant detection latency, and forward recovery can make that recovery extremely efficient. Our results suggest that GVR is scalable, portable, and efficient. GVR interfaces are flexible, supporting a variety of recovery schemes, and altogether GVR embodies a gentle-slope path to tolerate growing error rates in future extreme-scale systems.