Proliferation of degrees-of-freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data structure of their continuous Galerkin counterparts. The new method uses local, element-wise problems to project a continuous finite element space into a given discontinuous space, and then applies a discontinuous Galerkin formulation. The projection leads to parameterization of the discontinuous degrees-of-freedom by their continuous counterparts and has a variational multiscale interpretation. This significantly reduces the computational burden and, at the same time, little or no degradation of the solution occurs. In fact, the new method produces improved solutions compared with the traditional discontinuous Galerkin method in some situations.
Controlled seeding of perturbations is employed to study the evolution of wire array z-pinch implosion instabilities which strongly impact x-ray production when the 3D plasma stagnates on axis. Wires modulated in radius exhibit locally enhanced magnetic field and imploding bubble formation at discontinuities in wire radius due to the perturbed current path. Wires coated with localized spectroscopic dopants are used to track turbulent material flow. Experiments and MHD modeling offer insight into the behavior of z-pinch instabilities.
The absence of agreed definitions and metrics for supercomputer RAS obscures meaningful discussion of the issues involved, hinders their solution, and increases total system cost. Seeking to foster a common basis for communication about supercomputer RAS, [1] proposed a general system state model, definitions, and measurements based on the SEMI-E10 specification [2] used in the semiconductor manufacturing industry. This document enumerates the platform-specific details necessary to apply that general framework to the Red Storm system at Sandia National Laboratories. Familiarity with [1] is a strong prerequisite for understanding of this document, as is familiarity with the Red Storm RAS subsystem (although to a much lesser degree). Given the current pre-production status of Red Storm, this document does not specify actual policy or practice, but rather proposes a framework by which to measure RAS performance on Red Storm.
The success of Lagrangian contact modeling leads one to believe that important aspects of this capability may be used for multi-material modeling when only a portion of the simulation can be represented in a Lagrangian frame. We review current experience with two dual mesh technologies where one of these meshes is a Lagrangian mesh and the other is an Arbitrary Lagrangian/Eulerian (ALE) mesh. These methods are cast in the framework of an operator-split ALE algorithm where a Lagrangian step is followed by a remesh/remap step. An interface-coupled methodology is considered first. This technique is applicable to problems involving contact between materials of dissimilar compliance. The technique models the more compliant (soft) material as ALE while the less compliant (hard) material and associated interface are modeled in a Lagrangian fashion. Loads are transferred between the hard and soft materials via explicit transient dynamics contact algorithms. The use of these contact algorithms remove the requirement of node-tonode matching at the soft-hard interface. In the context of the operator-split ALE algorithm, a single Lagrangian step is performed using a mesh to mesh contact algorithm. At the end of the Lagrangian step the meshes will be slightly offset at the interface but non-interpenetrating. The ALE mesh nodes at the interface are then remeshed to their initial location relative to the Lagrangian body faces and the ALE mesh is smoothed, translated and rotated to follow Lagrangian body. Robust remeshing in the ALE region is required for success of this algorithm, and we describe current work in this area. The second method is an overlapping grid methodology that requires mapping of information between a Lagrangian mesh and an ALE mesh. The Lagrangian mesh describes a relatively hard body that interacts with softer material contained in the ALE mesh. A predicted solution for the velocity field is performed independently on both meshes. Element-centered velocity and momentum are transferred between the meshes using the volume transfer capability implemented in contact algorithms. Data from the ALE mesh is mapped to a phantom mesh that surrounds the Lagrangian mesh, providing for the reaction to the predicted motion of the Lagrangian material. Data from the Lagrangian mesh is mapped directly to the ALE mesh. A momentum balance is performed on both meshes to adjust the velocity field to account for the interaction of the material from the other mesh. Subsequent, remeshing and remapping of the ALE mesh is performed to allow large deformation of the softer material. We overview current progress using this approach and discuss avenues for future research and development.
We provide a common framework for compatible discretizations using algebraic topology to guide our analysis. The main concept is the natural inner product on cochains, which induces a combinatorial Hodge theory. The framework comprises of mutually consistent operations of differentiation and integration, has a discrete Stokes theorem, and preserves the invariants of the DeRham cohomology groups. The latter allows for an elementary calculation of the kernel of the discrete Laplacian. Our framework provides an abstraction that includes examples of compatible finite element, finite volume and finite difference methods. We describe how these methods result from the choice of a reconstruction operator and when they are equivalent.
The overlap of computation and communication has long been considered to be a significant performance benefit for applications. Similarly, the ability of the Message Passing Interface (MPI) to make independent progress (that is, to make progress on outstanding communication operations while not in the MPI library) is also believed to yield performance benefits. Using an intelligent network interface to offload the work required to support overlap and independent progress is thought to be an ideal solution, but the benefits of this approach have not been studied in depth at the application level. This lack of analysis is complicated by the fact that most MPI implementations do not sufficiently support overlap or independent progress. Recent work has demonstrated a quantifiable advantage for an MPI implementation that uses offload to provide overlap and independent progress. The study is conducted on two different platforms with each having two MPI implementations (one with and one without independent progress). Thus, identical network hardware and virtually identical software stacks are used. Furthermore, one platform, ASCI Red, allows further separation of features such as overlap and offload. Thus, this paper extends previous work by further qualifying the source of the performance advantage: offload, overlap, or independent progress.
In this paper, we analyze the relationship between pool maintenance schemes, long-term memory mechanisms, and search space structure, with the goal of placing metaheuristic design on a more concrete foundation.
