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

A Block Preconditioner for an Exact Penalty Formulation for Stationary MHD

The magnetohydrodynamics (MHD) equations are used to model the flow of electrically conducting fluids in such applications as liquid metals and plasmas. This system of non-self adjoint, nonlinear PDEs couples the Navier-Stokes equations for fluids and Maxwell's equations for electromagnetics. There has been recent interest in fully coupled solvers for the MHD system because they allow for fast steady-state solutions that do not require pseudo-time stepping. When the fully coupled system is discretized, the strong coupling can make the resulting algebraic systems difficult to solve, requiring effective preconditioning of iterative methods for efficiency. In this work, we consider a finite element discretization of an exact penalty formulation for the stationary MHD equations. This formulation has the benefit of implicitly enforcing the divergence free condition on the magnetic field without requiring a Lagrange multiplier. We consider extending block preconditioning techniques developed for the Navier-Stokes equations to the full MHD system. We analyze operators arising in block decompositions from a continuous perspective and apply arguments based on the existence of approximate commutators to develop new preconditioners that account for the physical coupling. This results in a family of parameterized block preconditioners for both Picard and Newton linearizations. We develop an automated method for choosing the relevant parameters and demonstrate the robustness of these preconditioners for a range of the physical non-dimensional parameters and with respect to mesh refinement

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

Robust Large-scale Parallel Nonlinear Solvers for Simulation

This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia

Final report on LDRD project : coupling strategies for multi-physics applications.

Many current and future modeling applications at Sandia including ASC milestones will critically depend on the simultaneous solution of vastly different physical phenomena. Issues due to code coupling are often not addressed, understood, or even recognized. The objectives of the LDRD has been both in theory and in code development. We will show that we have provided a fundamental analysis of coupling, i.e., when strong coupling vs. a successive substitution strategy is needed. We have enabled the implementation of tighter coupling strategies through additions to the NOX and Sierra code suites to make coupling strategies available now. We have leveraged existing functionality to do this. Specifically, we have built into NOX the capability to handle fully coupled simulations from multiple codes, and we have also built into NOX the capability to handle Jacobi Free Newton Krylov simulations that link multiple applications. We show how this capability may be accessed from within the Sierra Framework as well as from outside of Sierra. The critical impact from this LDRD is that we have shown how and have delivered strategies for enabling strong Newton-based coupling while respecting the modularity of existing codes. This will facilitate the use of these codes in a coupled manner to solve multi-physic applications