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Littérature scientifique sur le sujet « Higher Order Method »

Auteur : Grafiati

Publié le 6 septembre 2023

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Articles de revues sur le sujet "Higher Order Method"

1

You-zhong, Guo, Liu Zeng-rong, Jiang Xia-mei, and Han Zhi-bin. "Higher-order Melnikov method." Applied Mathematics and Mechanics 12, no. 1 (1991): 21–32. http://dx.doi.org/10.1007/bf02018063.

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Chin, Wei-Ngan, and John Darlington. "A higher-order removal method." Lisp and Symbolic Computation 9, no. 4 (1996): 287–322. http://dx.doi.org/10.1007/bf01806315.

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Amat, Sergio, and Sonia Busquier. "On a higher order Secant method." Applied Mathematics and Computation 141, no. 2-3 (2003): 321–29. http://dx.doi.org/10.1016/s0096-3003(02)00257-6.

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Kim, Oleksiy S., and Peter Meincke. "Adaptive Integral Method for Higher Order Method of Moments." IEEE Transactions on Antennas and Propagation 56, no. 8 (2008): 2298–305. http://dx.doi.org/10.1109/tap.2008.926759.

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A. Ashour, Ola. "Basic Steffensen's Method of Higher-Order Convergence." International Journal of Advanced Engineering Research and Science 8, no. 4 (2021): 184–91. http://dx.doi.org/10.22161/ijaers.84.22.

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Seong Keun Yi and 변경희. "Higher Order Quantification Method for PLS Correlation." Journal of Product Research 29, no. 3 (2011): 143–49. http://dx.doi.org/10.36345/kacst.2011.29.3.013.

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Keierleber, C. W., and B. T. Rosson. "Higher-Order Implicit Dynamic Time Integration Method." Journal of Structural Engineering 131, no. 8 (2005): 1267–76. http://dx.doi.org/10.1061/(asce)0733-9445(2005)131:8(1267).

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Chen, Ji, Zhu Wang, and Yinchao Chen. "Higher-order alternative direction implicit FDTD method." Electronics Letters 38, no. 22 (2002): 1321. http://dx.doi.org/10.1049/el:20020911.

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Fu, W., and E. L. Tan. "Compact higher-order split-step FDTD method." Electronics Letters 41, no. 7 (2005): 397. http://dx.doi.org/10.1049/el:20057927.

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Shim, Hyungseop. "Higher-order α-method in computational plasticity". KSCE Journal of Civil Engineering 9, № 3 (2005): 255–59. http://dx.doi.org/10.1007/bf02829054.

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Thèses sur le sujet "Higher Order Method"

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KUSAKARI, Keiichirou. "Higher-Order Path Orders Based on Computability." Institute of Electronics, Information and Communication Engineers, 2004. http://hdl.handle.net/2237/14973.

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Eng, Ju-Ling. "Higher order finite-difference time-domain method." Connect to resource, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1165607826.

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Zhu, Xuemei. "A higher-order panel method for third-harmonic diffraction problems." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43339.

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Sykes, James Henry Carleton University Dissertation Engineering Mechanical and Aerospace. "A higher order panel method for linearized unsteady subsonic aerodynamics." Ottawa, 1994.

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Ben, Romdhane Mohamed. "Higher-Degree Immersed Finite Elements for Second-Order Elliptic Interface Problems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/39258.

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A wide range of applications involve interface problems. In most of the cases, mathematical modeling of these interface problems leads to partial differential equations with non-smooth or discontinuous inputs and solutions, especially across material interfaces. Different numerical methods have been developed to solve these kinds of problems and handle the non-smooth behavior of the input data and/or the solution across the interface. The main focus of our work is the immersed finite element method to obtain optimal numerical solutions for interface problems. In this thesis, we present piecewise quadratic immersed finite element (IFE) spaces that are used with an immersed finite element (IFE) method with interior penalty (IP) for solving two-dimensional second-order elliptic interface problems without requiring the mesh to be aligned with the material interfaces. An analysis of the constructed IFE spaces and their dimensions is presented. Shape functions of Lagrange and hierarchical types are constructed for these spaces, and a proof for the existence is established. The interpolation errors in the proposed piecewise quadratic spaces yield optimal <i>O</i>(h³) and <i>O</i>(h²) convergence rates, respectively, in the L² and broken H¹ norms under mesh refinement. Furthermore, numerical results are presented to validate our theory and show the optimality of our quadratic IFE method. Our approach in this thesis is, first, to establish a theory for the simplified case of a linear interface. After that, we extend the framework to quadratic interfaces. We, then, describe a general procedure for handling arbitrary interfaces occurring in real physical practical applications and present computational examples showing the optimality of the proposed method. Furthermore, we investigate a general procedure for extending our quadratic IFE spaces to <i>p</i>-th degree and construct hierarchical shape functions for <i>p</i>=3.<br>Ph. D.

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Li, Ming-Sang. "Higher order laminated composite plate analysis by hybrid finite element method." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/40145.

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Maniar, Hiren Dayalal. "A three dimensional higher order panel method based on B-splines." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/11127.

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Bonhaus, Daryl Lawrence. "A Higher Order Accurate Finite Element Method for Viscous Compressible Flows." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/29458.

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The Streamline Upwind/Petrov-Galerkin (SU/PG) method is applied to higher-order finite-element discretizations of the Euler equations in one dimension and the Navier-Stokes equations in two dimensions. The unknown flow quantities are discretized on meshes of triangular elements using triangular Bezier patches. The nonlinear residual equations are solved using an approximate Newton method with a pseudotime term. The resulting linear system is solved using the Generalized Minimum Residual algorithm with block diagonal preconditioning. The exact solutions of Ringleb flow and Couette flow are used to quantitatively establish the spatial convergence rate of each discretization. Examples of inviscid flows including subsonic flow past a parabolic bump on a wall and subsonic and transonic flows past a NACA 0012 airfoil and laminar flows including flow past a a flat plate and flow past a NACA 0012 airfoil are included to qualitatively evaluate the accuracy of the discretiza-tions. The scheme achieves higher order accuracy without modification. Based on the test cases presented, significant improvement of the solution can be expected using the higher-order schemes with little or no increase in computational requirements. The nonlinear sys-tem also converges at a higher rate as the order of accuracy is increased for the same num-ber of degrees of freedom; however, the linear system becomes more difficult to solve. Several avenues of future research based on the results of the study are identified, includ-ing improvement of the SU/PG formulation, development of more general grid generation strategies for higher order elements, the addition of a turbulence model to extend the method to high Reynolds number flows, and extension of the method to three-dimensional flows. An appendix is included in which the method is applied to inviscid flows in three dimensions. The three-dimensional results are preliminary but consistent with the findings based on the two-dimensional scheme.<br>Ph. D.

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Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1205350171405-81971.

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A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this work<br>In der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben

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Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Forschungszentrum caesar, 2007. https://tud.qucosa.de/id/qucosa%3A24054.

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A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this work.<br>In der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben.

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Livres sur le sujet "Higher Order Method"

1

Karel, Segeth, and Dolez̆el Ivo, eds. Higher-order finite element methods. Chapman & Hall/CRC, 2004.

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2

Yan, Jue. Local discontinuous Galerkin methods for partial differential equations with higher order derivates. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.

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3

Reddy, J. N. A higher-order theory for geometrically nonlinear analysis of composite laminates. Langley Research Center, 1987.

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4

Yeh, Chou, and Langley Research Center, eds. On higher order dynamics in lattice-based models using Chapman-Enskog method. National Aeronautics and Space Administration, Langley Research Center, 1999.

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5

Zhang, Yu. Higher Order Basis Based Integral Equation Solver (HOBBIES). John Wiley & Sons Inc., 2012.

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6

Pierce, Donald A. Practical use of higher-order asymptotics for multiparameter exponential families. Dept. of Statistics, Oregon State University, 1991.

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Pierce, Donald A. Practical use of higher-order asymptotics for multiparameter exponential families. Dept. of Statistics, Oregon State University, 1991.

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8

Zhang, Yu. Higher Order Basis Based Integral Equation Solver (HOBBIES). John Wiley & Sons Inc., 2012.

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9

O, Demuren Ayodeji, Carpenter Mark, and Institute for Computer Applications in Science and Engineering., eds. Higher-order compact schemes for numerical simulation of incompressible flows. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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O, Demuren A., Carpenter Mark, and Institute for Computer Applications in Science and Engineering., eds. Higher-order compact schemes for numerical simulation of incompressible flows. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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Chapitres de livres sur le sujet "Higher Order Method"

1

Taigbenu, Akpofure E. "Higher-Order Elements." In The Green Element Method. Springer US, 1999. http://dx.doi.org/10.1007/978-1-4757-6738-4_9.

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Rabczuk, Timon, Huilong Ren, and Xiaoying Zhuang. "Higher Order Nonlocal Operator Method." In Computational Methods Based on Peridynamics and Nonlocal Operators. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20906-2_5.

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Ketcheson, D. I., and R. J. LeVeque. "WENOCLAW: A Higher Order Wave Propagation Method." In Hyperbolic Problems: Theory, Numerics, Applications. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75712-2_60.

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Kaveh, A. "Optimal Force Method for FEMS: Higher Order Elements." In Computational Structural Analysis and Finite Element Methods. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02964-1_7.

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Nishio, S., T. Okuno, and S. Morikawa. "Higher Order Approximation for Spatio-Temporal Derivative Method." In Flow Visualization VI. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-84824-7_129.

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Hone, A. N. W., and G. R. W. Quispel. "Analogues of Kahan’s Method for Higher Order Equations of Higher Degree." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-57000-2_9.

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Zhang, Cui, Brian R. Becker, Mark R. Heckman, Karl Levitt, and Ron A. Olsson. "A hierarchical method for reasoning about distributed programming languages." In Higher Order Logic Theorem Proving and Its Applications. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60275-5_78.

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Kowarsch, Ulrich, Constantin Oehrle, Martin Hollands, Manuel Keßler, and Ewald Krämer. "Computation of Helicopter Phenomena Using a Higher Order Method." In High Performance Computing in Science and Engineering ‘13. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02165-2_29.

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Hatano, Yasuo, Hidema Tanaka, and Toshinobu Kaneko. "An Optimized Algebraic Method for Higher Order Differential Attack." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44828-4_8.

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Busch, Holger. "A practical method for reasoning about distributed systems in a theorem prover." In Higher Order Logic Theorem Proving and Its Applications. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60275-5_60.

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Actes de conférences sur le sujet "Higher Order Method"

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Turner, James. "Beyond Newton's Method: Generalized Higher-Order Approximation Methods." In AIAA/AAS Astrodynamics Specialist Conference and Exhibit. American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-6272.

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Kim, Cheolwan, H. Chang, and Jang Yeon Lee. "Compact Higher-order Discontinuous Galerkin Method." In 11th AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-2824.

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Mansar, S., M. Boumahdi, and P. Julien. "New Deconvolution Method Using Higher Order Statistics." In 57th EAEG Meeting. EAGE Publications BV, 1995. http://dx.doi.org/10.3997/2214-4609.201409338.

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Zhang, Yan, Shan-wei Lu, Jun Zhang, and Ming-hua Xue. "3-D Higher-Order ADI-FDTD Method." In 2007 Asia-Pacific Microwave Conference (APMC '07). IEEE, 2007. http://dx.doi.org/10.1109/apmc.2007.4554548.

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Kim, O. S., and P. Meincke. "Adaptive integral method for higher-order hierarchical method of moments." In 2006 1st European Conference on Antennas and Propagation (EuCAP). IEEE, 2006. http://dx.doi.org/10.1109/eucap.2006.4584498.

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Tirkas, P. A., C. A. Balanis, and R. A. Renaut. "Higher-order absorbing boundary conditions in FDTD method." In IEEE Antennas and Propagation Society International Symposium 1992 Digest. IEEE, 1992. http://dx.doi.org/10.1109/aps.1992.221878.

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"Optimization of bilinear systems using higher-order method." In Proceedings of the 1999 American Control Conference. IEEE, 1999. http://dx.doi.org/10.1109/acc.1999.783171.

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Nelson, D. J., and D. C. Smith. "A higher order method for concentrating the STFT." In Optics & Photonics 2005, edited by Franklin T. Luk. SPIE, 2005. http://dx.doi.org/10.1117/12.618153.

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Rasedee, Ahmad Fadly Nurullah, Hazizah Mohd Ijam, Mohammad Hasan Abdul Sathar, et al. "Block variable order step size method for solving higher order orbital problems." In PROCEEDINGS OF THE 13TH IMT-GT INTERNATIONAL CONFERENCE ON MATHEMATICS, STATISTICS AND THEIR APPLICATIONS (ICMSA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5012174.

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Borries, Oscar, Peter Meincke, Erik Jorgensen, Stig Busk Sorensen, and Per Christian Hansen. "Improved Multilevel Fast Multipole Method for Higher-Order discretizations." In 2014 8th European Conference on Antennas and Propagation (EuCAP). IEEE, 2014. http://dx.doi.org/10.1109/eucap.2014.6902611.

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Rapports d'organisations sur le sujet "Higher Order Method"

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Brooks, Stephen. Higher-Order Corrections to Optimisers based on Newton's Method. Office of Scientific and Technical Information (OSTI), 2023. http://dx.doi.org/10.2172/1991087.

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2

Jiang, W., and Benjamin W. Spencer. Modeling 3D PCMI using the Extended Finite Element Method with higher order elements. Office of Scientific and Technical Information (OSTI), 2017. http://dx.doi.org/10.2172/1409274.

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3

GHARAKHANI, ADRIN. A Higher Order Vorticity Redistribution Method for 3-D Diffusion In Free Space. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/766240.

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4

Lieberman, Evan, Xiaodong Liu, Nathaniel Ray Morgan, Darby Jon Luscher, and Donald E. Burton. A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics and reactive materials. Office of Scientific and Technical Information (OSTI), 2019. http://dx.doi.org/10.2172/1492638.

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5

Iwashige, Kengo, and Takashi Ikeda. Numerical simulation of stratified shear flow using a higher order Taylor series expansion method. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/115072.

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6

Osborne, A. R. Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics: Building Blocks for a Higher Order Method. Defense Technical Information Center, 2006. http://dx.doi.org/10.21236/ada612395.

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7

Baboi, Nicoleta. IMPEDANCE MEASUREMENT SETUP FOR HIGHER-ORDER MODE STUDIES IN NLC ACCELERATING STRUCTURES WITH THE WIRE METHOD. Office of Scientific and Technical Information (OSTI), 2002. http://dx.doi.org/10.2172/801788.

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Haddock, John E., Reyhaneh Rahbar-Rastegar, M. Reza Pouranian, Miguel Montoya, and Harsh Patel. Implementing the Superpave 5 Asphalt Mixture Design Method in Indiana. Purdue University, 2020. http://dx.doi.org/10.5703/1288284317127.

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Recent research developments have indicated that asphalt mixture durability and pavement life can be increased by modifying the Superpave asphalt mixture design method to achieve an in-place density of 95%, approximately 2% higher than the density requirements of conventionally designed Superpave mixtures. Doing so requires increasing the design air voids content to 5% and making changes to the mixture aggregate gradation so that effective binder content is not lowered. After successful laboratory testing of this modified mixture design method, known as Superpave 5, two controlled field trials and one full scale demonstration project, the Indiana Department of Transportation (INDOT) let 12 trial projects across the six INDOT districts based on the design method. The Purdue University research team was tasked with observing the implementation of the Superpave 5 mixture design method, documenting the construction and completing an in-depth analysis of the quality control and quality assurance (QC/QA) data obtained from the projects. QC and QA data for each construction project were examined using various statistical metrics to determine construction performance with respect to INDOT Superpave 5 specifications. The data indicate that, on average, the contractors achieved 5% laboratory air voids, which coincides with the Superpave 5 recommendation of 5%. However, on average, the as-constructed mat density of 93.8% is roughly 1% less than the INDOT Superpave 5 specification. It is recommended that INDOT monitor performance of the Superpave 5 mixtures and implement some type of additional training for contractor personnel, in order to help them increase their understanding of Superpave 5 concepts and how best to implement the design method in their operation.

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9

Yager, Ronald R. On Methods for Higher Order Information Fusion. Defense Technical Information Center, 2005. http://dx.doi.org/10.21236/ada430888.

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Wollaber, Allan Benton, HyeongKae Park, Robert Byron Lowrie, Rick M. Rauenzahn, and Mathew Allen Cleveland. Rad-Hydro with a High-Order, Low-Order Method. Office of Scientific and Technical Information (OSTI), 2015. http://dx.doi.org/10.2172/1207754.

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