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

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

Domain-specific implementation of high-order Discontinuous Galerkin methods in spherical geometry

In recent years, domain-specific languages (DSLs) have achieved significant success in large-scale efforts to reimplement existing meteorological models in a performance portable manner. The dynamical cores of these models are based on finite difference and finite volume schemes, and existing DSLs are generally limited to supporting only these numerical methods. In the meantime, there have been numerous attempts to use high-order Discontinuous Galerkin (DG) methods for atmospheric dynamics, which are currently largely unsupported in main-stream DSLs. In order to link these developments, we present two domain-specific languages which extend the existing GridTools (GT) ecosystem to high-order DG discretization. The first is a C++-based DSL called G4GT, which, despite being no longer supported, gave us the impetus to implement extensions to the subsequent Python-based production DSL called GT4Py to support the operations needed for DG solvers. As a proof of concept, the shallow water equations in spherical geometry are implemented in both DSLs, thus providing a blueprint for the application of domain-specific languages to the development of global atmospheric models. We believe this is the first GPU-capable DSL implementation of DG in spherical geometry. The results demonstrate that a DSL designed for finite difference/volume methods can be successfully extended to implement a DG solver, while preserving the performance-portability of the DSL.ISSN:0010-4655ISSN:1879-294

Doctor of Philosophy

dissertationThe increase in computational power of supercomputers is enabling complex scientific phenomena to be simulated at ever-increasing resolution and fidelity. With these simulations routinely producing large volumes of data, performing efficient I/O at this scale has become a very difficult task. Large-scale parallel writes are challenging due to the complex interdependencies between I/O middleware and hardware. Analytic-appropriate reads are traditionally hindered by bottlenecks in I/O access. Moreover, the two components of I/O, data generation from simulations (writes) and data exploration for analysis and visualization (reads), have substantially different data access requirements. Parallel writes, performed on supercomputers, often deploy aggregation strategies to permit large-sized contiguous access. Analysis and visualization tasks, usually performed on computationally modest resources, require fast access to localized subsets or multiresolution representations of the data. This dissertation tackles the problem of parallel I/O while bridging the gap between large-scale writes and analytics-appropriate reads. The focus of this work is to develop an end-to-end adaptive-resolution data movement framework that provides efficient I/O, while supporting the full spectrum of modern HPC hardware. This is achieved by developing technology for highly scalable and tunable parallel I/O, applicable to both traditional parallel data formats and multiresolution data formats, which are directly appropriate for analysis and visualization. To demonstrate the efficacy of the approach, a novel library (PIDX) is developed that is highly tunable and capable of adaptive-resolution parallel I/O to a multiresolution data format. Adaptive resolution storage and I/O, which allows subsets of a simulation to be accessed at varying spatial resolutions, can yield significant improvements to both the storage performance and I/O time. The library provides a set of parameters that controls the storage format and the nature of data aggregation across he network; further, a machine learning-based model is constructed that tunes these parameters for the maximum throughput. This work is empirically demonstrated by showing parallel I/O scaling up to 768K cores within a framework flexible enough to handle adaptive resolution I/O