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The purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest. In particular, the conservation properties of both synchronous and asynchronous variational integrators (AVIs) are discussed in detail. We present selected numerical examples which… (More)

We describe a new class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation to each other; (ii) the algorithms derive from a spacetime… (More)

Recently, graphics processing units (GPUs) have had great success in accelerating many numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are… (More)

Discontinuous Galerkin (DG) finite-element methods for secondand fourth-order elliptic problems were introduced about three decades ago. These methods stem from the hybrid methods developed by Pian and his coworker [25]. At the time of their introduction, DG methods were generally called interior penalty methods, and were considered by Baker [4], Douglas… (More)

- Adrian J. Lew, M. Ortiz
- 2002

We present an artificial viscosity scheme tailored to finite-deformation Lagrangian calculations of shocks in materials with or without strength on unstructured tetrahedral meshes of arbitrary order. The artificial viscous stresses are deviatoric and satisfy material-frame indifference exactly. We have assessed the performance of the method on selected… (More)

- Alex Ten Eyck, Fatih Celiker, Adrian J. Lew
- 2008

The goal of this paper is to motivate, introduce and demonstrate a novel approach to stabilizing Discontinuous Galerkin (DG) methods in nonlinear elasticity problems. The stabilization term adapts to the solution of the problem by locally changing the size of a penalty term on the appearance of discontinuities, with the goal of better approximating the… (More)

- Alex Ten Eyck, Fatih Celiker, Adrian J. Lew
- 2008

This is the second of two papers in which we motivate, introduce and analyze a new type of strategy for the stabilization of discontinuous Galerkin (DG) methods in nonlinear elastic problems. The foremost goal behind it is to enhance the robustness of the method without deteriorating the accuracy of the resulting solutions. Its distinctive property is that… (More)

- Adrian J. Lew
- 2003

This paper presents a scalable parallel variational time integration algorithm for nonlinear elastodynamics with the distinguishing feature of allowing each element in the mesh to have a possibly different time step. Furthermore, the algorithm is obtained from a discrete variational principle, and hence it is termed Parallel Asynchronous Variational… (More)

We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our approach is the use of a universal mesh: a stationary background mesh containing the domain of interest for all times… (More)

We propose a family of methods for simulating two-dimensional incompressible, low Reynolds number flow around a moving obstacle whose motion is prescribed. The methods make use of a universal mesh: a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle’s… (More)