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Harnessing modern parallel computing resources to achieve complex multiphysics simulations is a daunting task. The Multiphysics Object Oriented Simulation Environment (MOOSE) aims to enable such development by providing simplified interfaces for specification of partial differential equations, boundary conditions, material properties, and all aspects of a simulation without the need to consider the parallel, adaptive, nonlinear, finite-element solve that is handled internally. Through the use of interfaces and inheritance, each portion of a simulation becomes reusable and composable in a manner that allows disparate research groups to share code and create an ecosystem of growing capability that lowers the barrier for the creation of multiphysics simulation codes. Included within the framework is a unique capability for building multiscale, multiphysics simulations through simultaneous execution of multiple sub-applications with data transfers between the scales. Other capabilities include automatic differentiation, scaling to a large number of processors, hybrid parallelism, and mesh adaptivity. To date, MOOSE-based applications have been created in areas of science and engineering such as nuclear physics, geothermal science, magneto-hydrodynamics, seismic events, compressible and incompressible fluid flow, microstructure evolution, and advanced manufacturing processes.

SUMMARYA variational formulation and C 1 finite element scheme with adaptive mesh refinement and coarsening are developed for phase-separation processes described by the Cahn-Hilliard diffuse interface model of transport in a mixture or alloy. The adaptive scheme is guided by a Laplacian jump indicator based on the corresponding term arising from the weak formulation of the fourth-order non-linear problem, and is implemented in a parallel solution framework. It is then applied to resolve complex evolving interfacial solution behavior for 2D and 3D simulations of the classic spinodal decomposition problem from a random initial mixture and to other phase-transformation applications of interest. Simulation results and adaptive performance are discussed. The scheme permits efficient, robust multiscale resolution and interface characterization.

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Abstract. The progression of scientific computing resources has enabled the numerical approximation of mathematical models describing complex physical phenomena. A significant portion of researcher time is typically dedicated to the development of software to compute the numerical solutions. This work describes a flexible C++ software framework, built on the libMesh finite element library, designed to alleviate developer burden and provide easy access to modern computational algorithms, including quantity-of-interest-driven parallel adaptive mesh refinement on unstructured grids and adjoint-based sensitivities. Other software environments are highlighted and the current work motivated; in particular, the present work is an attempt to balance software infrastructure and user flexibility. The applicable class of problems and design of the software components is discussed in detail. Several examples demonstrate the effectiveness of the design, including applications that incorporate uncertainty. Current and planned developments are discussed.

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SUMMARYSome interesting properties of composite basis functions for C 1 macroelements are investigated, including their use for constructing conforming C 1 function spaces on non-conforming adaptively refined meshes. Of particular interest is the classical cubic Hsieh-Clough-Tocher 3-split triangle because of its simplicity and convergence properties in fourth-order problems, as compared with the Powell-Sabin-Heindl 6-split and 12-split triangles. A posteriori error indicators for adaptive refinement are developed. Numerical experiments demonstrate convergence rates, and adaptive refinement performance based on a simplified error indicator is tested. Extensibility to analogous three-dimensional tetrahedral elements is briefly discussed.

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