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286
On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 219 (4 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems
 Internat. J. Numer. Methods Engrg
, 1999
"... The purpose of this work is twofold. First, we demonstrate analytically that the classical Newmark family as well as related integration algorithms are variational in the sense of the Veselov formulation of discrete mechanics. Such variational algorithms are well known to be symplectic and momentum ..."
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Cited by 97 (35 self)
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The purpose of this work is twofold. First, we demonstrate analytically that the classical Newmark family as well as related integration algorithms are variational in the sense of the Veselov formulation of discrete mechanics. Such variational algorithms are well known to be symplectic and momentum preserving and to often have excellent global energy behavior. This analytical result is verified through numerical examples and is believed to be one of the primary reasons that this class of algorithms performs so well. Second, we develop algorithms for mechanical systems with forcing, and in particular, for dissipative systems. In this case, we develop integrators that are based on a discretization of the Lagrange d’Alembert principle as well as on a variational formulation of dissipation. It is demonstrated that these types of structured integrators have good numerical behavior in terms of obtaining the correct amounts by which
Nonreflecting Boundary Conditions For Time Dependent Scattering
 SIAM J. Appl. Math
, 1996
"... An exact nonreflecting boundary condition was derived previously for use with the time dependent wave equation in three space dimensions [1]. Here it is shown how to combine that boundary condition with finite difference methods and finite element methods. Uniqueness of the solution is proved, stabi ..."
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Cited by 55 (2 self)
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An exact nonreflecting boundary condition was derived previously for use with the time dependent wave equation in three space dimensions [1]. Here it is shown how to combine that boundary condition with finite difference methods and finite element methods. Uniqueness of the solution is proved, stability issues are discussed, and improvements are proposed for numerical computation. Numerical examples are presented which demonstrate the improvement in accuracy over standard methods. 1 Supported by an IBM graduate fellowship (grote@cims.nyu.edu). 2 Supported in part by AFOSR, NSF, and ONR (keller@math.stanford.edu). 1 Introduction We wish to calculate numerically the time dependent field u(x; t) scattered from a bounded scattering region in threedimensional space. In this region, there may be one or more scatterers, and the equation for u may have variable coefficients and nonlinear terms. As usual, we surround the scattering region by an artificial boundary B, and confine the comp...
Variational time integrators
 Int. J. Numer. Methods Eng
"... 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 de ..."
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Cited by 51 (10 self)
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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 demonstrate the excellent accuracy, conservation and convergence characteristics of AVIs. In these tests, AVIs are found to result in substantial speedups, at equal accuracy, relative to explicit Newmark. A mathematical proof of convergence of the AVIs is also presented in this paper. Finally, we develop the subject of horizontal variations and configurational forces in discrete dynamics. This theory leads to exact pathindependent characterizations of the configurational forces acting on discrete systems. Notable examples are the configurational forces acting on material nodes in a finite element discretisation; and the Jintegral at the tip of a crack in
FEAP  A Finite Element Analysis Program
"... This manual serves as a supplement to the FEAP User manual [1] available at the web ..."
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Cited by 37 (0 self)
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This manual serves as a supplement to the FEAP User manual [1] available at the web
Benchmark control problems for seismically excited nonlinear buildings.
 Journal of Engineering Mechanics,
, 2004
"... Abstract This paper presents the problem definition and guidelines of a set of benchmark control problems for seismically excited nonlinear buildings. Focusing on three typical steel structures, 3, 9and 20story buildings designed for the SAC project for the Los Angeles, California region, the go ..."
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Cited by 30 (3 self)
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Abstract This paper presents the problem definition and guidelines of a set of benchmark control problems for seismically excited nonlinear buildings. Focusing on three typical steel structures, 3, 9and 20story buildings designed for the SAC project for the Los Angeles, California region, the goal of this study is to provide a clear basis to evaluate the efficacy of various structural control strategies. A nonlinear evaluation model has been developed that portrays the salient features of the structural system. Evaluation criteria and control constraints are presented for the design problems. The task of each participant in this benchmark study is to define (including sensors and control algorithms), evaluate and report on their proposed control strategies. These strategies may be either passive, active, semiactive or a combination thereof. The benchmark control problems will then facilitate direct comparison of the relative merits of the various control strategies. To illustrate some of the design challenges, a sample control strategy employing active control with a linear quadratic Gaussian (LQG) control algorithm is applied to the 20story structure.
Decomposition Contact Response (DCR) for Explicit Finite Element Dynamics
 INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
, 2005
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Structure Preservation For Constrained Dynamics With Super Partitioned Additive RungeKutta Methods
 SIAM J. Sci. Comput
, 1998
"... A broad class of partitioned differential equations with possible algebraic constraints is considered, including Hamiltonian and mechanical systems with holonomic constraints. For mechanical systems a formulation eliminating the Coriolis forces and closely related to the EulerLagrange equations is ..."
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Cited by 22 (9 self)
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A broad class of partitioned differential equations with possible algebraic constraints is considered, including Hamiltonian and mechanical systems with holonomic constraints. For mechanical systems a formulation eliminating the Coriolis forces and closely related to the EulerLagrange equations is presented. A new class of integrators is defined: the super partitioned additive RungeKutta (SPARK) methods. This class is based on the partitioning of the system into different variables and on the splitting of the differential equations into different terms. A linear stability and convergence analysis of these methods is given. SPARK methods allowing the direct preservation of certain properties are characterized. Different structures and invariants are considered: the manifold of constraints, symplecticness, reversibility, contractivity, dilatation, energy, momentum, and quadratic invariants. With respect to linear stability and structurepreservation, the class of sstage Lobatto IIIABCC* SPARK methods is of special interest. Controllable numerical damping can be introduced by the use of additional parameters. Some issues related to the implementation of a reversible variable stepsize strategy are discussed.
A Multiscale Approach to Meshbased Surface Tension Flows
"... Figure 1: Our method allows us to efficiently simulate complex surface tension phenomena such as this crown splash. The small scales are handled with our surface approach, while the larger scales are computed with the Eulerian simulation. For the shown simulation, our method requires only 22.3 secon ..."
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Cited by 19 (6 self)
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Figure 1: Our method allows us to efficiently simulate complex surface tension phenomena such as this crown splash. The small scales are handled with our surface approach, while the larger scales are computed with the Eulerian simulation. For the shown simulation, our method requires only 22.3 seconds per frame on average. We present an approach to simulate flows driven by surface tension based on triangle meshes. Our method consists of two simulation layers: the first layer is an Eulerian method for simulating surface tension forces that is free from typical strict time step constraints. The second simulation layer is a Lagrangian finite element method that simulates subgrid scale wave details on the fluid surface. The surface wave simulation employs an unconditionally stable, symplectic time integration method that allows for a high propagation speed due to strong surface tension. Our approach can naturally separate the grid and subgrid scales based on a volumepreserving mean curvature flow. As our model for the subgrid dynamics enforces a local conservation of mass, it leads to realistic pinch off and merging effects. In addition to this method for simulating dynamic surface tension effects, we also present an efficient nonoscillatory approximation for capturing damped surface tension behavior. These approaches allow us to efficiently simulate complex phenomena associated with strong surface tension, such as RayleighPlateau instabilities and crown splashes, in a short amount of time.