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1

Ruas, Vitoriano. A quadratic finite element method for solving biharmonic problems in IRn. Rio de Janeiro, Brasil: Pontifícia Universidade Catolica do Rio de Janeiro, 1986.

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2

Lin-Jun, Hou, and Langley Research Center, eds. Periodic trim solutions with hp-version finite elements in time: Final report. Atlanta, Ga: School of Aerospace Engineering, Georgia Institute of Technology, 1990.

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3

Golla, David Frank. Dynamics of viscoelastic structures: a time-domain finite element formulation. [Downsview, Ont.]: [Institute for Aerospace Studies], 1985.

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4

Golla, D. F. Dynamics of viscoelastic structures - a time-domain, finite element formulation. [S.l.]: [s.n.], 1985.

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5

United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., ed. Time-domain finite elements in optimal control with application to launch-vehicle guidance. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1991.

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6

United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., ed. Time-domain finite elements in optimal control with application to launch-vehicle guidance. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1991.

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7

Golla, David Frank. Dynamics of viscoelastic structures: A time-domain finite element formulation. [Downsview, Ont.]: Institute for Aerospace Studies, 1986.

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8

George, Alan. An analysis of spectral envelope-reduction via quadratic assignment problems. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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9

George, Alan. An analysis of spectral envelope-reduction via quadratic assignment problems. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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10

Bless, Robert R. Time-domain finite elements in optimal control with application to launch-vehicle guidance. Hampton, Va: Langley Research Center, 1991.

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11

Li, Jichun. Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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12

1934-, Craig Roy R., and Lyndon B. Johnson Space Center., eds. A decentralized linear quadratic control design method for flexible structures: Interim report. Austin, Texas: Center for Aeromechanics Research, University of Texas at Austin, 1990.

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13

Mei, C. Modeling of structural-acoustic interaction using coupled FE/BE method and control of interior acoustic pressure using piezoelectric actuators: Final report for the period ending August, 1997 under research grant NAG1-1684. Norfolk, Va: Dept. of Aerospace Engineering, College of Engineering & Technology, Old Dominion University, 1997.

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14

Yacheng, Shi, and United States. National Aeronautics and Space Administration., eds. Modeling of structural-acoustic interaction using coupled FE/BE method and control of interior acoustic pressure using piezoelectric actuators: Final report for the period ending August, 1997 under research grant NAG1-1684. Norfolk, Va: Dept. of Aerospace Engineering, College of Engineering & Technology, Old Dominion University, 1997.

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15

Yacheng, Shi, and United States. National Aeronautics and Space Administration., eds. Modeling of structural-acoustic interaction using coupled FE/BE method and control of interior acoustic pressure using piezoelectric actuators: Final report for the period ending August, 1997 under research grant NAG1-1684. Norfolk, Va: Dept. of Aerospace Engineering, College of Engineering & Technology, Old Dominion University, 1997.

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16

Yacheng, Shi, and United States. National Aeronautics and Space Administration., eds. Modeling of structural-acoustic interaction using coupled FE/BE method and control of interior acoustic pressure using piezoelectric actuators: Final report for the period ending August, 1997 under research grant NAG1-1684. Norfolk, Va: Dept. of Aerospace Engineering, College of Engineering & Technology, Old Dominion University, 1997.

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17

Ostachowicz, W. M. Guided waves in structures for SHM: The time-domain spectral element method. Chichester, West Sussex: Wiley, 2012.

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18

Gherlone, Marco. Dynamic shape reconstruction of three-dimensional frame structures using the inverse finite element method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2011.

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19

P, Chen C., and United States. National Aeronautics and Space Administration., eds. A two-layer multiple-time-scale turbulence model and grid independence study. [Washington, D.C.]: National Aeronautics and Space Administration, 1989.

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20

United States. National Aeronautics and Space Administration., ed. Applications of parallel computation in micro-mechanics and finite element method: Final report ... time period: October 1, 1993 to May 31, 1996. [Washington, DC: National Aeronautics and Space Administration, 1996.

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21

United States. National Aeronautics and Space Administration., ed. Parallel aeroelastic computations for wing and wing-body configurations: Annual report for the period of time July 1993-July 1994. San Jose, CA: MCAT Institute, 1994.

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22

ZnO bao mo zhi bei ji qi guang, dian xing neng yan jiu. Shanghai Shi: Shanghai da xue chu ban she, 2010.

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23

Li, Jichun, and Yunqing Huang. Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials. Springer, 2015.

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24

A two-layer multiple-time-scale turbulence model and grid independence study. [Washington, D.C.]: National Aeronautics and Space Administration, 1989.

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25

Boudreau, Joseph F., and Eric S. Swanson. Continuum dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0019.

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Abstract:
The theory and application of a variety of methods to solve partial differential equations are introduced in this chapter. These methods rely on representing continuous quantities with discrete approximations. The resulting finite difference equations are solved using algorithms that stress different traits, such as stability or accuracy. The Crank-Nicolson method is described and extended to multidimensional partial differential equations via the technique of operator splitting. An application to the time-dependent Schrödinger equation, via scattering from a barrier, follows. Methods for solving boundary value problems are explored next. One of these is the ubiquitous fast Fourier transform which permits the accurate solution of problems with simple boundary conditions. Lastly, the finite element method that is central to modern engineering is developed. Methods for generating finite element meshes and estimating errors are also discussed.
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