Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part I: template-based generic programming

An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++ language to transform a given calculation into one that can compute a variety of additional quantities that are necessary for many state-of-the-art simulation and analysis algorithms. An approach for incorporating these ideas into complex simulation codes through general graph-based assembly is also presented. These ideas have been implemented within a set of packages in the Trilinos framework and are demonstrated on a simple problem from chemical engineering

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part II: application to partial differential equations

A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application

Distributed-Pair Programming can work well and is not just Distributed Pair-Programming

Background: Distributed Pair Programming can be performed via screensharing or via a distributed IDE. The latter offers the freedom of concurrent editing (which may be helpful or damaging) and has even more awareness deficits than screen sharing. Objective: Characterize how competent distributed pair programmers may handle this additional freedom and these additional awareness deficits and characterize the impacts on the pair programming process. Method: A revelatory case study, based on direct observation of a single, highly competent distributed pair of industrial software developers during a 3-day collaboration. We use recordings of these sessions and conceptualize the phenomena seen. Results: 1. Skilled pairs may bridge the awareness deficits without visible obstruction of the overall process. 2. Skilled pairs may use the additional editing freedom in a useful limited fashion, resulting in potentially better fluency of the process than local pair programming. Conclusion: When applied skillfully in an appropriate context, distributed-pair programming can (not will!) work at least as well as local pair programming

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented

Power Law Scaling for a System of Interacting Units with Complex Internal Structure

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits. We consider the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. To test the model, we identify a large data base spanning 20 years, and find that the model correctly predicts a variety of empirical results.Comment: 4 pages with 4 postscript figures (uses Revtex 3.1, Latex2e, multicol.sty, epsf.sty and rotate.sty). Submitted to PR

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented

Albany: Using Component-based Design to Develop a Flexible, Generic Multiphysics Analysis Code

Abstract: Albany is a multiphysics code constructed by assembling a set of reusable, general components. It is an implicit, unstructured grid finite element code that hosts a set of advanced features that are readily combined within a single analysis run. Albany uses template-based generic programming methods to provide extensibility and flexibility; it employs a generic residual evaluation interface to support the easy addition and modification of physics. This interface is coupled to powerful automatic differentiation utilities that are used to implement efficient nonlinear solvers and preconditioners, and also to enable sensitivity analysis and embedded uncertainty quantification capabilities as part of the forward solve. The flexible application programming interfaces in Albany couple to two different adaptive mesh libraries; it internally employs generic integration machinery that supports tetrahedral, hexahedral, and hybrid meshes of user specified order. We present the overall design of Albany, and focus on the specifics of the integration of many of its advanced features. As Albany and the components that form it are openly available on the internet, it is our goal that the reader might find some of the design concepts useful in their own work. Albany results in a code that enables the rapid development of parallel, numerically efficient multiphysics software tools. In discussing the features and details of the integration of many of the components involved, we show the reader the wide variety of solution components that are available and what is possible when they are combined within a simulation capability. Key Words: partial differential equations, finite element analysis, template-based generic programmin

MPAS-Albany Land Ice (MALI): a variable-resolution ice sheet model for Earth system modeling using Voronoi grids

We introduce MPAS-Albany Land Ice (MALI) v6.0, a new variable-resolution land ice model that uses unstructured Voronoi grids on a plane or sphere. MALI is built using the Model for Prediction Across Scales (MPAS) framework for developing variable-resolution Earth system model components and the Albany multi-physics code base for the solution of coupled systems of partial differential equations, which itself makes use of Trilinos solver libraries. MALI includes a three-dimensional first-order momentum balance solver (Blatter–Pattyn) by linking to the Albany-LI ice sheet velocity solver and an explicit shallow ice velocity solver. The evolution of ice geometry and tracers is handled through an explicit first-order horizontal advection scheme with vertical remapping. The evolution of ice temperature is treated using operator splitting of vertical diffusion and horizontal advection and can be configured to use either a temperature or enthalpy formulation. MALI includes a mass-conserving subglacial hydrology model that supports distributed and/or channelized drainage and can optionally be coupled to ice dynamics. Options for calving include eigencalving, which assumes that the calving rate is proportional to extensional strain rates. MALI is evaluated against commonly used exact solutions and community benchmark experiments and shows the expected accuracy. Results for the MISMIP3d benchmark experiments with MALI's Blatter–Pattyn solver fall between published results from Stokes and L1L2 models as expected. We use the model to simulate a semi-realistic Antarctic ice sheet problem following the initMIP protocol and using 2&thinsp;km resolution in marine ice sheet regions. MALI is the glacier component of the Energy Exascale Earth System Model (E3SM) version 1, and we describe current and planned coupling to other E3SM components.</p

Opposite polarities of ENSO drive distinct patterns of coral bleaching potentials in the southeast Indian Ocean.

Episodic anomalously warm sea surface temperature (SST) extremes, or marine heatwaves (MHWs), amplify ocean warming effects and may lead to severe impacts on marine ecosystems. MHW-induced coral bleaching events have been observed frequently in recent decades in the southeast Indian Ocean (SEIO), a region traditionally regarded to have resilience to global warming. In this study, we assess the contribution of El Niño-Southern Oscillation (ENSO) to MHWs across the mostly understudied reefs in the SEIO. We find that in extended summer months, the MHWs at tropical and subtropical reefs (divided at ~20°S) are driven by opposite ENSO polarities: MHWs are more likely to occur at the tropical reefs during eastern Pacific El Niño, driven by enhanced solar radiation and weaker Australian Monsoon, some likely alleviated by positive Indian Ocean Dipole events, and at the subtropical reefs during central Pacific La Niña, mainly caused by increased horizontal heat transport, and in some cases reinforced by local air-sea interactions. Madden-Julian Oscillations (MJO) also modulate the MHW occurrences. Projected future increases in ENSO and MJO intensity with greenhouse warming will enhance thermal stress across the SEIO. Implementing forecasting systems of MHWs can be used to anticipate future coral bleaching patterns and prepare management responses

Prospective Evaluation of TMVR for Failed Surgical Annuloplasty Rings: MITRAL Trial Valve-in-Ring Arm 1-Year Outcomes

OBJECTIVES: The authors report 1-year outcomes of high-risk patients with failed surgical annuloplasty rings undergoing transseptal mitral valve-in-ring (MViR) with the SAPIEN 3 aortic transcatheter heart valve (THV). BACKGROUND: The MITRAL (Mitral Implantation of Transcatheter Valves) trial is the first prospective study evaluating transseptal MViR with the SAPIEN 3 aortic THV in high-risk patients with failed surgical annuloplasty rings. METHODS: Prospective enrollment of high-risk patients with symptomatic moderate to severe or severe mitral regurgitation (MR) or severe mitral stenosis and failed annuloplasty rings at 13 U.S. sites. The primary safety endpoint was technical success. The primary THV performance endpoint was absence of MR grade ≥2+ or mean mitral valve gradient ≥10 mm Hg (30 days and 1 year). Secondary endpoints included procedural success and all-cause mortality (30 days and 1 year). RESULTS: Thirty patients were enrolled between January 2016 and October 2017 (median age 71.5 years [interquartile range: 67.0 to 76.8 years], 36.7% women, median Society of Thoracic Surgeons score 7.6% [interquartile range: 5.1% to 11.8%], 76.7% in New York Heart Association functional class III or IV). Technical success was 66.7% (driven primarily by need for a second valve in 6 patients). There was no intraprocedural mortality or conversion to surgery. The primary performance endpoint was achieved in 85.7% of survivors at 30 days (24 of 28) and 89.5% of patients alive at 1 year with echocardiographic data available (17 of 19). All-cause mortality at 30 days was 6.7% and at 1 year was 23.3%. Among survivors at 1-year follow-up, 84.2% were in New York Heart Association functional class I or II, the median mean mitral valve gradient was 6.0 mm Hg (interquartile range: 4.7 to 7.3 mm Hg), and all had ≤1+ MR. CONCLUSIONS: Transseptal MViR was associated with a 30-day mortality rate lower than predicted by the Society of Thoracic Surgeons score. At 1 year, transseptal MViR was associated with symptom improvement and stable THV performance