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Publications of John A. Trangenstein    :chronological  alphabetical  combined listing:

%% Books   
@book{fds71097,
   Author = {J. Trangenstein},
   Title = {Numerical Solution of Hyperbolic Partial Differential
             Equations},
   Publisher = {Cambridge University Press},
   Year = {2007},
   Month = {December},
   ISBN = {052187727X},
   Abstract = {Numerical Solution of Hyperbolic Partial Differential
             Equations is a new type of graduate textbook, with both
             print and interactive electronic components (on CD). It is a
             comprehensive presentation of modern shock-capturing
             methods, including both finite volume and finite element
             methods, covering the theory of hyperbolic conservation laws
             and the theory of the numerical methods. The range of
             applications is broad enough to engage most engineering
             disciplines and many areas of applied mathematics. Classical
             techniques for judging the qualitative performance of the
             schemes are used to motivate the development of classical
             higher-order methods. The interactive CD gives access to the
             computer code used to create all of the text's figures, and
             lets readers run simulations, choosing their own input
             parameters; the CD displays the results of the experiments
             as movies. Consequently, students can gain an appreciation
             for both the dynamics of the problem application, and the
             growth of numerical errors.},
   Key = {fds71097}
}


%% Papers Published   
@article{fds287423,
   Author = {Trangenstein, JA and Kim, C},
   Title = {Operator splitting and adaptive mesh refinement for the
             Luo-Rudy I model},
   Journal = {Journal of Computational Physics},
   Volume = {196},
   Number = {2},
   Pages = {645-679},
   Publisher = {Elsevier BV},
   Year = {2004},
   Month = {May},
   ISSN = {0021-9991},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000221400700010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {We apply second-order operator splitting to the Luo-Rudy I
             model for electrical wave propagation in the heart. The
             purpose of the operator splitting is to separate the
             nonlinear but local reaction computations from the linear
             but globally coupled diffusion computations. This approach
             allows us to use local nonlinear iterations for the stiff
             nonlinear reactions and to solve global linear systems for
             the implicit treatment of diffusion. For computational
             efficiency, we use dynamically adaptive mesh refinement
             (AMR), involving hierarchies of unions of grid patches on
             distinct levels of refinement. The linear system for the
             discretization of the diffusion on the composite AMR grid is
             formulated via standard conforming finite elements on unions
             grid patches within a level of refinement and aligned mortar
             elements along interfaces between levels of refinement. The
             linear systems are solved iteratively by preconditioned
             conjugate gradients. Our preconditioner uses multiplicative
             domain decomposition between levels of refinement; the
             smoother involves algebraic additive domain decomposition
             between patches within a level of refinement, and
             Gauss-Seidel iteration within grid patches. Numerical
             results are presented in 1D and 2D, including spiral waves.
             © 2003 Elsevier Inc. All rights reserved.},
   Doi = {10.1016/j.jcp.2003.11.014},
   Key = {fds287423}
}

@article{fds28834,
   Author = {J.A. Trangenstein and John A. Trangenstein and Chisup Kim},
   Title = {Operator Splitting and Adaptive Mesh Refinement for the
             Luo-Rudy I Model},
   Journal = {Journal of Computational Physics},
   Volume = {196},
   Pages = {645-679},
   Publisher = {Elsevier},
   Year = {2004},
   Keywords = {reaction-diffusion, • excitable media, • adaptive
             mesh refinement, • operator splitting, • finite
             elements, • multigrid, • domain
             decomposition},
   Abstract = {We apply second-order operator splitting to the Luo-Rudy I
             model for electrical wave propagation in the heart. The
             purpose of the operator splitting is to separate the
             nonlinear but local reaction computations from the linear
             but globally coupled diffusion computations. This approach
             allows us to use {\em local nonlinear} iterations for the
             stiff nonlinear reactions, and to solve {\em global linear}
             systems for the implicit treatment of diffusion. For
             computational efficiency, we use dynamically adaptive mesh
             refinement (AMR), involving hierarchies of unions of grid
             patches on distinct levels of refinement. The linear system
             for the discretization of the diffusion on the composite AMR
             grid is formulated via standard conforming finite elements
             on unions grid patches within a level of refinement, and
             aligned mortar elements along interfaces between levels of
             refinement. The linear systems are solved iteratively by
             preconditioned conjugate gradients. Our preconditioner uses
             multiplicative domain decomposition between levels of
             refinement; the smoother involves algebraic additive domain
             decomposition between patches within a level of refinement,
             and Gauss-Seidel iteration within grid patches. Numerical
             results are presented in 1D and 2D, including spiral
             waves.},
   Key = {fds28834}
}

@article{fds287424,
   Author = {Trangenstein, JA},
   Title = {Multi-scale iterative techniques and adaptive mesh
             refinement for flow in porous media},
   Journal = {Advances in Water Resources},
   Volume = {25},
   Number = {8-12},
   Pages = {1175-1213},
   Publisher = {Elsevier BV},
   Year = {2002},
   Month = {August},
   ISSN = {0309-1708},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000180073300015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {Multi-component flow in porous media involves localized
             phenomena that could be due to several features, such as
             concentration fronts, wells or geometry of the media. Our
             approach to treating the localized phenomena is to use
             high-resolution discretization methods in combination with
             adaptive mesh refinement (AMR). The purpose of AMR is to
             concentrate the computational work near the regions of
             interest in the flow. When properly designed, AMR can
             significantly reduce the computational effort required to
             obtain a desired level of accuracy in the simulation.
             Necessarily, AMR requires appropriate techniques for
             communication between length scales in a hierarchy. The
             selection of appropriate scaling rules as well as
             computationally efficient data structures is essential to
             the success of the overall method. However, the emphasis
             here is on the development of e.cient techniques for solving
             linear systems that arise in the numerical discretization of
             an elliptic equation for the incompressible pressure field.
             In this paper, the combined AMR technique has been applied
             to a two-component single-phase model for miscible flooding.
             Numerical results are discussed in one-dimensional and
             two-dimensional. © 2002 Elsevier Science Ltd. All rights
             reserved.},
   Doi = {10.1016/S0309-1708(02)00053-2},
   Key = {fds287424}
}

@article{04068006912,
   Author = {Trangenstein, John A. and Bi, Zhuoxin},
   Title = {Multi-Scale Iterative Techniques and Adaptive Mesh
             Refinement for Miscible Displacement Simulation},
   Journal = {Proceedings - SPE Symposium on Improved Oil
             Recovery},
   Pages = {924 - 936},
   Address = {Tulsa, OK, United States},
   Year = {2002},
   Keywords = {Petroleum reservoirs;Solubility;Object oriented
             programming;Radioactive tracers;Aquifers;Vectors;Linear
             systems;Computer simulation;},
   Abstract = {Many enhanced oil recovery processes in reservoir
             engineering involve localized phenomena that could be due to
             several features, such as injection fronts, wells or
             reservoir heterogeneity. In order to reach sufficient
             accuracy in field-scale simulation, the localized phenomena
             need to be resolved and modeled in appropriate
             scale-dependent ways. Our approach to treating the localized
             phenomena is to use high-resolution discretization methods
             in combination with dynamically adaptive mesh refinement
             (AMR). The purpose of adaptive mesh refinement is to
             concentrate the computational work near the regions of
             interest in the displacement processes, which may evolve
             constantly in space. Adaptive mesh refinement requires
             appropriate techniques for data communication in a hierarchy
             of dynamically adaptive mesh. The selection of appropriate
             scaling rules as well as computationally efficient data
             structures is essential to the success of the overall
             method. We have exploited the object-oriented features of
             C++ for the AMR program structure and data management, while
             numerically intensive routines are implemented in FORTRAN.
             It turned out that adaptive mesh refinement can
             significantly reduce the computational cost required to
             obtain a desired level of accuracy in the simulation.
             However, the emphasis here is on the development of
             efficient techniques for solving linear systems that arise
             in the numerical discretization of an elliptic equation for
             the incompressible pressure field. We use a conjugate
             gradient algorithm preconditioned by multiplicative domain
             decomposition between refinement levels, in which additive
             domain decomposition and incomplete Cholesky factorization
             were employed as "smoothers". In this paper, the combined
             adaptive mesh refinement technique has been applied to a
             single-phase tracer transport model for miscible flooding.
             Numerical results demonstrating the effectiveness of the
             method are presented and discussed.},
   Key = {04068006912}
}

@article{fds287425,
   Author = {Bi, Z and Higdon, D and Lee, H and Trangenstein, J},
   Title = {Upscaling Tensorial Permeability Fields Based on {G}Gaussian
             Markov Random Field Models and the Hybrid Mixed Finite
             Element Method},
   Journal = {Spe Journal},
   Year = {2002},
   url = {http://www.math.duke.edu/~johnt/spepaper2002.ps},
   Key = {fds287425}
}

@article{6216174,
   Author = {Garaizar, FX and Trangenstein, J},
   Title = {Adaptive Mesh Refinement and Front-Tracking for Shear Bands
             in an Antiplane Shear Model},
   Journal = {Siam Journal on Scientific Computing},
   Volume = {20},
   Number = {2},
   Pages = {750-779},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1998},
   Month = {January},
   url = {http://dx.doi.org/10.1137/S1064827597319271},
   Keywords = {granular flow;granular materials;mesh generation;physics
             computing;plastic deformation;tracking;},
   Abstract = {We describe a numerical algorithm for the study of
             shear-band formation and growth in a 2D antiplane shear of
             granular materials. The algorithm combines front-tracking
             techniques and adaptive mesh refinement. Tracking provides a
             more careful evolution of the band when coupled with special
             techniques to advance the ends of the shear band in the
             presence of a loss of hyperbolicity. The adaptive mesh
             refinement allows the computational effort to be
             concentrated in important areas of the deformation, such as
             the shear band and the elastic relief wave. The main
             challenges are the problems related to shear bands that
             extend across several grid patches and the effects that a
             nonhyperbolic growth rate of the shear bands has in the
             refinement process. We give examples of the success of the
             algorithm for various levels of refinement},
   Doi = {10.1137/s1064827597319271},
   Key = {6216174}
}

@article{98013996894,
   Author = {Miller, CT and Christakos, G and Imhoff, PT and McBride, JF and Pedit,
             JA and Trangenstein, JA},
   Title = {Multiphase flow and transport modeling in heterogeneous
             porous media: Challenges and approaches},
   Journal = {Advances in Water Resources},
   Volume = {21},
   Number = {2},
   Pages = {77-120},
   Publisher = {Elsevier BV},
   Year = {1998},
   Month = {January},
   ISSN = {0309-1708},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000071536500002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {Porous materials;Pressure;Transport properties;Hydraulic
             conductivity;Mass transfer;Random processes;Computational
             methods;Mathematical models;Saturation (materials
             composition);Phase interfaces;},
   Abstract = {We review the current status of modeling multiphase systems,
             including balance equation formulation, constitutive
             relations for both pressure-saturation-conductivity and
             interphase mass transfer, and stochastic and computational
             issues. We discuss weaknesses and inconsistencies of current
             approaches based on theoretical, computational, and
             experimental evidence. Where possible, we suggest new or
             evolving approaches. Copyright © 1997 Elsevier Science
             Limited.},
   Doi = {10.1016/S0309-1708(96)00036-X},
   Key = {98013996894}
}

@article{97113919459,
   Author = {Hornung, RD and Trangenstein, JA},
   Title = {Adaptive mesh refinement and multilevel iteration for flow
             in porous media},
   Journal = {Journal of Computational Physics},
   Volume = {136},
   Number = {2},
   Pages = {522-545},
   Publisher = {Elsevier BV},
   Year = {1997},
   Month = {September},
   ISSN = {0021-9991},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1997XZ45000020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {An adaptive local mesh refinement algorithm originally
             developed for unsteady gas dynamics by M. J. Berger is
             extended to incompressible flow in porous media. Multilevel
             iteration and domain decomposition methods are introduced to
             accommodate the elliptic/parabolic aspects of the flow
             equations. The algorithm is applied to a two-phase polymer
             flooding model consisting of a system of nonlinear
             hyperbolic mass conservation equations coupled to an
             elliptic pressure equation. While the various numerical
             methods used have been presented previously, our emphasis is
             on their consistent combination within the adaptive mesh
             refinement framework to treat important problems in porous
             media flow. To achieve efficient, easily maintainable code,
             we have exploited the features of object-oriented
             programming for the overall program structure and data
             management. Examples of algorithmic performance and
             computational results are provided. © 1997 Academic
             Press.},
   Doi = {10.1006/jcph.1997.5779},
   Key = {97113919459}
}

@article{97043606580,
   Author = {Garaizar, FX and Trangenstein, J},
   Title = {Front Tracking for Shear Bands in an Antiplane Shear
             Model},
   Journal = {Journal of Computational Physics},
   Volume = {131},
   Number = {1},
   Pages = {54-69},
   Publisher = {Elsevier BV},
   Year = {1997},
   Month = {February},
   url = {http://dx.doi.org/10.1006/jcph.1996.5456},
   Doi = {10.1006/jcph.1996.5456},
   Key = {97043606580}
}

@article{96083296598,
   Author = {Khan, SA and Pope, GA and Trangenstein, JA},
   Title = {Micellar/polymer physical-property models for contaminant
             cleanup problems and enhanced oil recovery},
   Journal = {Transport in Porous Media},
   Volume = {24},
   Number = {1},
   Pages = {35-79},
   Publisher = {Springer Nature},
   Year = {1996},
   Month = {January},
   ISSN = {0169-3913},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1996UZ43900002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {Mathematical models;Micelles;Polymers;Flow of
             fluids;Impurities;Enhanced recovery;Computer
             simulation;Calculations;Surface active agents;},
   Abstract = {Previous pseudo-phase representations of micellar/polymer
             phase behavior have been highly successful in simulating
             enhanced oil recovery processes using conventional numerical
             methods. These models allowed for a variety of physical
             phenomena, such as the formation of one to three phases, the
             effect of salinity and co-solvents on the phase behavior,
             adsorption of several of the chemical species, capillary
             desaturation, and polymer shear thinning and permeability
             reduction. In order to extend these models to either
             higher-order simulation techniques or to contaminant
             transport problems, it is necessary to remove previous
             discontinuities in the model behavior and to improve the
             predictions as concentrations become infinitesimal. In this
             paper, we provide a complete description of a revised model
             that avoids the problems of the previous model, and we show
             how to implement the computations in a numerically stable
             fashion. Computational results from a North Sea pilot study
             are presented. © 1996 Kluwer Academic Publishers.},
   Doi = {10.1007/BF00175603},
   Key = {96083296598}
}

@article{5033123,
   Author = {Trangenstein, JA},
   Title = {Adaptive Mesh Refinement for Wave Propagation in Nonlinear
             Solids},
   Journal = {Siam Journal on Scientific Computing},
   Volume = {16},
   Number = {4},
   Pages = {819-839},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1995},
   Month = {July},
   ISSN = {1064-8275},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1995RF58400004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {equations of state;finite difference methods;fluid
             dynamics;wave propagation;},
   Abstract = {The adaptive mesh refinement algorithm for unsteady gas
             dynamics is extended to nonlinear solids. Several
             modifications to the original algorithm are forced by the
             dissimilarities in the forms of the gas and solid equations
             of state. The variety of forms of the solid constitutive
             laws motivates the development of several abstractions that
             are implemented through object-oriented programming.
             Examples of the performance of the scheme are provided by
             two numerical examples},
   Doi = {10.1137/0916048},
   Key = {5033123}
}

@article{94041255724,
   Author = {Trangenstein, JA},
   Title = {A second-order Godunov algorithm for two-dimensional solid
             mechanics},
   Journal = {Computational Mechanics},
   Volume = {13},
   Number = {5},
   Pages = {343-359},
   Publisher = {Springer Nature},
   Year = {1994},
   Month = {September},
   url = {http://dx.doi.org/10.1007/BF00512588},
   Keywords = {Solids;Mechanics;Wave transmission;Deformation;Equations of
             motion;Convergence of numerical methods;Finite element
             method;Approximation theory;Computational
             complexity;Equations of state;},
   Abstract = {The second-order Godunov method is extended to dynamic wave
             propagation in two-dimensional solids undergoing nonlinear
             finite deformation. It is shown that this explicit method is
             linearly stable for timesteps satisfying the standard CFL
             condition, does not support the development of hourglass
             modes, and handles non-reflecting boundaries very naturally.
             The computational cost is essentially one evaluation of the
             kinetic equation of state per cell and timestep, the same as
             explicit finite element methods employing reduced
             quadrature. © 1994 Springer-Verlag.},
   Doi = {10.1007/BF00512588},
   Key = {94041255724}
}

@article{95032624249,
   Author = {Khan, S.A. and Trangenstein, J.A. and Horning, R.D. and Holing, Kent and Schilling, B.E.R.},
   Title = {Application of adaptive mesh-refinement with a new
             higher-order method in simulation of a north sea
             micellar/polymer flood},
   Journal = {Proceedings of the SPE Symposium on Reservoir
             Simulation},
   Pages = {531 - 543},
   Address = {San Antonio, TX, USA},
   Year = {1994},
   Keywords = {Petroleum reservoir evaluation;Computational
             methods;Micelles;Polymers;Finite difference
             method;Costs;Surface active agents;Simulators;},
   Abstract = {This paper demonstrates the application of a higher-order
             Godunov method and adaptive mesh-refinement to a
             three-phase, seven-component, micellar/polymer (MP) model
             and use in the simulation of an MP flood designed for North
             Sea conditions. Conventional one-point upstream weighting
             with globally fine mesh is too expensive for obtaining a
             reasonable level of accuracy for field-scale simulations.
             The use of higher-order Godunov method with adaptive
             mesh-refinement not only results in significant reduction in
             computational times but also reveals more numerical details
             of the displacement process due to higher-order accuracy.
             Comparisons are also made between the first- and
             second-order Godunov methods under field-scale design
             conditions with and without adaptive mesh-refinement.},
   Key = {95032624249}
}

@article{4294599,
   Author = {Trangenstein, JA and Pember, RB},
   Title = {Numerical algorithms for strong discontinuities in
             elastic-plastic solids},
   Journal = {Journal of Computational Physics},
   Volume = {103},
   Number = {1},
   Pages = {63-89},
   Publisher = {Elsevier BV},
   Year = {1992},
   Month = {January},
   ISSN = {0021-9991},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992JV66900004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {elastic waves;elastoplasticity;numerical
             analysis;},
   Abstract = {In this paper the implementation of second-order Godunov
             methods for dynamic wave propagation in one-dimensional
             elastic-plastic solids is investigated. First, the
             Lagrangian form of the algorithm is reviewed, and then the
             algorithm is extended to the Eulerian frame of reference.
             This extension requires additional evolution equations to
             handle the history of the material along particle paths.
             Both the Lagrangian and Eulerian versions of the algorithm
             require appropriately accurate approximations to the
             solution of Riemann problems, in order to represent the
             interaction of waves at cell boundaries. Two inexpensive
             approximations to the solution of the Riemann problem are
             constructed, and the resulting algorithms are tested against
             the analytic solution of the Riemann problem for
             longitudinal motion in an elastic-plastic bar. These
             approximations to the Riemann problem are shown to work
             well, even for strong discontinuities. Finally, the
             numerical experience gained from the simple longitudinal bar
             problem is used to design an algorithm for strong shocks
             predicted by a realistic soil model. © 1992.},
   Doi = {10.1016/0021-9991(92)90326-T},
   Key = {4294599}
}

@article{92121461002,
   Author = {Trangenstein, J.A.},
   Title = {Analysis of a model and sequential numerical method for
             thermal reservoir simulation},
   Journal = {Proceedings of the Conference on the Mathematics of Oil
             Recovery},
   Pages = {359 -},
   Address = {Cambridge, Engl},
   Year = {1992},
   Key = {92121461002}
}

@article{3865816,
   Author = {Trangenstein, JA and Pember, RB},
   Title = {The Riemann Problem for Longitudinal Motion in an
             Elastic-Plastic Bar},
   Journal = {Siam Journal on Scientific and Statistical
             Computing},
   Volume = {12},
   Number = {1},
   Pages = {180-207},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1991},
   Month = {January},
   ISSN = {0196-5204},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1991EW35600010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {elasticity;elastoplasticity;},
   Abstract = {The analytical solution to the Riemann problem for the
             Antman-Szymczak model of longitudinal motion in an
             elastic-plastic bar is constructed. The model involves two
             surfaces corresponding to plastic yield in tension and
             compression, and exhibits the appropriate limiting behavior
             for total compressions. The solution of the Riemann problem
             involves discontinuous changes in characteristic speeds due
             to transitions from elastic to plastic response.
             Illustrations are presented, in both state-space and
             self-similar coordinates, of the variety of possible
             solutions to the Riemann problem for possible use with
             numerical algorithms},
   Doi = {10.1137/0912010},
   Key = {3865816}
}

@article{3704156,
   Author = {Trangenstein, JA},
   Title = {A second-order algorithm for the dynamic response of
             soils},
   Journal = {Impact of Computing in Science and Engineering},
   Volume = {2},
   Number = {1},
   Pages = {1-39},
   Publisher = {Elsevier BV},
   Year = {1990},
   Month = {January},
   url = {http://dx.doi.org/10.1016/0899-8248(90)90002-R},
   Keywords = {civil engineering computing;deformation;differential
             equations;geophysics computing;soil;},
   Abstract = {In this paper we describe a formally second-order algorithm
             for the dynamic response of one-dimensional soils and rock.
             There are two kinds of equations describing the motion of
             the material: the partial differential equations expressing
             conservation of momentum, and the kinetic equation of state
             relating the stress to the deformation. The stress-rate
             equations for the kinetic equation of state are formulated
             as a constrained system of ordinary differential equations
             and are integrated implicitly in time, both for stability
             and for satisfaction of the yield constraints. The equations
             of motion are formulated as a first-order system of
             hyperbolic conservation laws and integrated explicitly by
             means of a second-order version of Godunov's method. Because
             the motion can develop both smooth waves and shocks, special
             care has been taken to design a numerical method that is
             second-order in smooth waves and yet reduces to a stable
             low-order method near discontinuities. We present numerical
             results for both the integration of the equation of state
             and the equations of motion, in order to demonstrate the
             features of the method. © 1990.},
   Doi = {10.1016/0899-8248(90)90002-R},
   Key = {3704156}
}

@article{3834403,
   Author = {Glass, I.I. and Kaca, J. and Zhang, D.L. and Glaz, H.M. and Bell, J.B. and Trangenstein, J.A. and Collins,
             J.P.},
   Title = {Diffraction of planar shock waves over half-diamond and
             semicircular cylinders: an experimental and numerical
             comparison},
   Journal = {AIP Conf. Proc. (USA)},
   Number = {208},
   Pages = {246 - 51},
   Address = {Bethlehem, PA, USA},
   Year = {1990},
   Keywords = {diffraction;electromagnetic wave interferometry;shock
             waves;},
   Abstract = {The problem of an incident planar shock interacting with a
             downstream obstacle is studied; half-diamond and
             semicircular cylinders are chosen for the obstacles.
             Experimental data is taken from the UTIAS shock tube
             facility; in particular; infinite-fringe interferograms are
             analyzed which provides full flowfield data. Numerical
             results are obtained using a new unsplit version of the
             second-order Eulerian Godunov scheme for inviscid gas
             dynamics which is capable of computing on general, body
             conforming meshes. Detailed comparisons of the two
             techniques are offered, and excellent agreement is
             confirmed},
   Key = {3834403}
}

@article{3547392,
   Author = {Trangenstein, JA and Bell, JB},
   Title = {Mathematical Structure of Compositional Reservoir
             Simulation},
   Journal = {Siam Journal on Scientific and Statistical
             Computing},
   Volume = {10},
   Number = {5},
   Pages = {817-845},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1989},
   Month = {September},
   ISSN = {0196-5204},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1989AM02600001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {chemical technology;numerical methods;petroleum
             industry;two-phase flow;},
   Abstract = {Multicomponent two-phase isothermal fluid flow in petroleum
             reservoirs is described. The fluid-flow model consists of
             component conservation equations. Darcy's law for the
             volumetric flow rates, balance between the fluid volume and
             the rock void, and the conditions of thermodynamic
             equilibrium that determine the distribution of the chemical
             components into phases. Thermodynamic equilibrium is
             described by means of a mathematical model for the chemical
             potentials of each component in each phase of the fluid. The
             flow equations are manipulated to form a pressure equation
             and a modified component-conservation equation: these form
             the basis for the sequential method. It is shown that the
             pressure equation is parabolic under reasonable assumptions
             on the thermodynamic equilibrium model, and that the
             component-conservation equations are hyperbolic in the
             absence of diffusive forces such as capillary pressure and
             mixing. A numerical method based on the sequential
             formulation of the flow equations is outlined and used to
             illustrate the kinds of flow behavior that occur during
             miscible gas injection},
   Doi = {10.1137/0910049},
   Key = {3547392}
}

@article{88040048974,
   Author = {Trangenstein, JA},
   Title = {Customized minimization techniques for phase equilibrium
             computations in reservoir simulation},
   Journal = {Chemical Engineering Science},
   Volume = {42},
   Number = {12},
   Pages = {2847-2863},
   Publisher = {Elsevier BV},
   Year = {1987},
   Month = {January},
   ISSN = {0009-2509},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1987L461100004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {COMPUTER PROGRAMMING - Algorithms;FLOW OF FLUIDS - Computer
             Simulation;OIL WELL PRODUCTION - Enhanced
             Recovery;},
   Abstract = {This paper discusses a minimization algorithm for the
             solution of the Gibbs free energy minimization problem
             involving at most two phases. There are three major aspects
             to this paper. The first is the selection of descent
             directions and step lengths in order to handle the poorly
             scaled phase equilibrium problems associated with mixtures
             near bubble points and critical points. The second is the
             prevention of convergence to trivial solutions in both the
             Gibbs free energy minimization problem for two-phase
             mixtures and the associated phase stability test for
             single-phase mixtures. The third is the use of effective
             convergence criteria to obtain either the desired level of
             accuracy in the solution or the maximum accuracy allowed by
             the problem and the computer. © 1987.},
   Doi = {10.1016/0009-2509(87)87051-3},
   Key = {88040048974}
}

@article{87050080444,
   Author = {Subramanian, G and Trangenstein, JA and Mochizuki, S and Shen,
             EIC},
   Title = {EFFICIENT FLUID BEHAVIOR COMPUTATIONS IN A SEQUENTIAL
             COMPOSITIONAL RESERVOIR SIMULATOR.},
   Journal = {Society of Petroleum Engineers of Aime, (Paper)
             Spe},
   Pages = {321-327},
   Address = {San Antonio, TX, USA},
   Year = {1987},
   Month = {January},
   Keywords = {OIL WELLS;OIL WELL PRODUCTION;FLOW OF FLUIDS -
             Multiphase;},
   Abstract = {A compositional reservoir simulator using a sequential
             formulation of the fluid flow and phase equilibrium
             equations requires that the phase equilibrium and associated
             derivatives of the dependent phase equilibrium variables
             with respect to the pressure and moles of individual
             components be computed every time step for all the grid
             blocks in the system. The phase equilibrium calculations are
             computation intensive, since they solve a nonlinear system
             of equations and are thus iterative in nature. This paper
             describes techniques for implementing the phase equilibrium
             and the associated derivative calculations in a sequential
             compositional reservoir simulator designed for large
             reservoir models.},
   Key = {87050080444}
}

@article{87020024439,
   Author = {Bell, JB and Trangenstein, JA and Shubin, GR},
   Title = {Conservation Laws of Mixed Type Describing Three-Phase Flow
             in Porous Media},
   Journal = {Siam Journal on Applied Mathematics},
   Volume = {46},
   Number = {6},
   Pages = {1000-1017},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1986},
   Month = {December},
   ISSN = {0036-1399},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1986F083900004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {MATHEMATICAL TECHNIQUES;PETROLEUM RESERVOIR ENGINEERING -
             Computer Simulation;},
   Abstract = {In this paper we examine the mathematical structure of a
             model for three-phase, incompressible flow in a porous
             medium. We show that, in the absence of diffusive forces,
             the system of conservation laws describing the flow is not
             necessarily hyperbolic. We present an example in which there
             is an elliptic region in saturation space for reasonable
             relative permeability data. A linearized analysis shows that
             in nonhyperbolic regions solutions grow exponentially.
             However, the nonhyperbolic region, if present, will be of
             limited extent which inherently limits the exponential
             growth. To examine these nonlinear effects we resort to fine
             grid numerical experiments with a suitably dissipative
             numerical method. These experiments indicate that the
             solutions of Riemann problems remain well behaved in spite
             of the presence of a linearly unstable elliptic region in
             saturation space. These results are relevant to modeling
             fluid flow in petroleum reservoirs.},
   Doi = {10.1137/0146059},
   Key = {87020024439}
}

@article{85110169321,
   Author = {Trangenstein John and A},
   Title = {MINIMIZATION OF GIBBS FREE ENERGY IN COMPOSITIONAL RESERVOIR
             SIMULATION.},
   Journal = {Society of Petroleum Engineers of Aime, (Paper)
             Spe},
   Pages = {233-246},
   Address = {Dallas, TX, USA},
   Year = {1985},
   Keywords = {FLOW OF FLUIDS - Two Phase;MATHEMATICAL TECHNIQUES - Phase
             Space Methods;},
   Abstract = {This paper describes the formulation of vapor-liquid phase
             equilibrium as a linearly constrained minimization problem.
             It also describes a second minimization problem designed to
             test for local phase stability. Vectorized unconstrained
             minimization techniques can be used to solve this pair of
             constrained minimization problems. The methods of this paper
             are applied to liquid-vapor equilibria for mixtures both far
             from and near to the phase boundary. Significant
             improvements over the standard successive substitution
             algorithm are demonstrated.},
   Key = {85110169321}
}

@article{83020003109,
   Author = {TRANGENSTEIN, J. A. and READ, H. E.},
   Title = {INELASTIC RESPONSE CHARACTERISTICS OF THE NEW ENDOCHRONIC
             THEORY WITH SINGULAR KERNEL.},
   Volume = {18},
   Number = {11},
   Pages = {947 - 956},
   Year = {1982},
   Keywords = {STRESSES - ANALYSIS;},
   Abstract = {THE CONSTITUTIVE RESPONSE PREDICTED BY THE NEW ENDOCHRONIC
             THEORY WITH SINGULAR KERNEL FOR NON-PROPORTIONAL LOADING
             INVOLVING AN ABRUPT CHANGE IN THE LOADING DIRECTION IN
             STRESS SPACE IS INVESTIGATED ANALYTICALLY. FOR SUCH LOADING,
             THE RESPONSE IS DETERMINED, AS A FUNCTION OF THE ANGLE
             BETWEEN THE ORIGINAL AND THE REVISED LOADING DIRECTIONS, FOR
             INFINITESIMAL LOADING INCREMENTS IN THE REVISED DIRECTION.
             IT IS SHOWN THAT THE NEW ENDOCHRONIC THEORY DIFFERS IN
             IMPORTANT AND FUNDAMENTAL WAYS FROM CLASSICAL PLASTICITY
             WITH HARDENING. FOR INFINITESIMAL DEFORMATIONS, THE TWO
             THEORIES EXHIBIT SIMILARRESPONSE CHARACTERISTICS ONLY UNDER
             VERY SPECIALIZED CONDITIONS. FOR FINITE DEFORMATIONS, THE
             NEW ENDOCHRONIC THEORY LEADS TO PLASTIC FLOW FOR ALL LOADING
             DIRECTIONS, WHILE THE TYPE OF RESPONSE PREDICTED BY
             CLASSICAL PLASTICITY THEORY DEPENDS UPON THE DIRECTION OF
             LOADING.},
   Key = {83020003109}
}

@article{1158810,
   Author = {Trangenstein, JA},
   Title = {A Finite Element Method for the Tricomi Problem in the
             Elliptic Region},
   Journal = {Siam Journal on Numerical Analysis},
   Volume = {14},
   Number = {6},
   Pages = {1066-1077},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1977},
   Month = {December},
   ISSN = {0036-1429},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1977EC70900009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {finite element analysis;},
   Abstract = {The Tricomi problem is divided into an elliptic problem,
             involving a nonlocal boundary condition on a line of
             parabolic degeneracy, and a hyperbolic problem. The author
             converts the elliptic problem into an equivalent variational
             form, shows it to be well-posed, and applies the finite
             element method. Error estimates in weighted Sobolev spaces
             are proved},
   Doi = {10.1137/0714073},
   Key = {1158810}
}

@article{972653,
   Author = {More, JJ and Trangenstein, JA},
   Title = {On the global convergence of broydens method},
   Journal = {Mathematics of Computation},
   Volume = {30},
   Number = {135},
   Pages = {523-540},
   Publisher = {American Mathematical Society (AMS)},
   Year = {1976},
   Month = {January},
   url = {http://dx.doi.org/10.1090/S0025-5718-1976-0418451-2},
   Keywords = {convergence of numerical methods;nonlinear
             equations;},
   Abstract = {We consider Broyden's 1965 method for solving nonlinear
             equations. If the mapping is linear, then a simple
             modification of this method guarantees global and Q- super
             linear convergence. For nonlinear mappings it is shown that
             the hybrid strategy for nonlinear equations due to Powell
             leads to R-super linear convergence provided the search
             directions form a uniformly linearly independent sequence.
             We then explore this last concept and its connection with
             Broyden's method. Finally, we point out how the above
             results extend to Powell's symmetric version of Broyden's
             method. © 1976, American Mathematical Society.},
   Doi = {10.1090/S0025-5718-1976-0418451-2},
   Key = {972653}
}

@article{fds9499,
   Author = {X. Garaizar and John Trangenstein},
   Title = {Adaptive Mesh Refinement and Front Tracking for shear bands
             in Granular Flow},
   Journal = {SIAM Journal on Scientific Computing, vol. 20, (1999), pp.
             750-779},
   Key = {fds9499}
}

@article{fds9037,
   Author = {G. Christakos and P.T. Imhoff and John F. McBride and C.T. Miller and Joseph A. Pedit and John Trangenstein},
   Title = {Multiple Flow and Transport Modeling in Heterogeneous Porous
             Media: Challenges and Approaches},
   Journal = {Advances in Water Resources 21(1998), 77-120.},
   Key = {fds9037}
}

@article{fds9498,
   Author = {F. X. Garaizar and John Trangenstein},
   Title = {Front Tracking for Shear Bands in an Antiplane Shear
             Model},
   Journal = {J. Comp. Phys., vol.131, (1998), pp. 54-69},
   Key = {fds9498}
}

@article{fds9018,
   Author = {R. Hornung and John Trangenstein},
   Title = {Adaptive Mesh Refinement and Multilevel Iteration for Flow
             in Porous Media},
   Journal = {Journal of Computational Physics, 136, 522-545.},
   Key = {fds9018}
}

@article{fds9024,
   Author = {S. A. Khan and G.A. Pope and John Trangenstein},
   Title = {Micellar/Polymer Physical Property Models for Contaminant
             Cleanup Problems and Enhanced Oil Recovery},
   Journal = {Transport in Porous Media 24(1996), 35-79.},
   Key = {fds9024}
}

@article{fds9021,
   Author = {John Trangenstein},
   Title = {Adaptive Mesh Refinement for Wave Propagation in Nonlinear
             Solids},
   Journal = {SIAM J. Sci. Comput. 16(1995), 819-839.},
   Key = {fds9021}
}

@article{fds9022,
   Author = {F. Xabier Garaizar and John Trangenstein},
   Title = {Tracking of Shear Bands in an Antiplane Shear
             Model},
   Journal = {Proceedings of the International Conference on Hyperbolic
             Equations, SUNY Stony Brook.},
   Key = {fds9022}
}

@article{fds9023,
   Author = {S. A. Khan and K. Holing and R.D. Hornung and B.E.R. Schilling and John
             Trangenstein},
   Title = {Application of Adaptive Mesh-Refinement with a New
             Higher-Order Method in Simulation of a North Sea
             Micellar/Polymer Flood, SPE 29145},
   Journal = {Proceedings of the SPE Symposium on Reservoir
             Simulation},
   Key = {fds9023}
}

@article{fds9020,
   Author = {John Trangenstein},
   Title = {A Second-Order Godunov Algorithm for Two-Dimensional Solid
             Mechanics},
   Journal = {Computational Mechanics, 13(1994) pp. 343-359.},
   Key = {fds9020}
}

@article{fds9492,
   Author = {Richard Pember and John Trangenstein},
   Title = {Numerical Algorithms for Strong Discontinuities in
             Elastic-Plastic Solids},
   Journal = {J. Comp. Phys., vol. 103, (1992), pp. 63-89},
   Key = {fds9492}
}

@article{fds9487,
   Author = {Philip Colella and John Trangenstein},
   Title = {A Higher-Order Godunov Method for Modeling Finite
             Deformation in Elastic-Plastic Solids},
   Journal = {Comm. Pure Appl. Math., vol. XLIV, (1991), pp.
             41-100},
   Key = {fds9487}
}

@article{fds9488,
   Author = {Richard Pember and John Trangenstein},
   Title = {The Riemann Problem for Longitudinal Motion in an
             Elastic-Plastic Bar},
   Journal = {SIAM J. Sci. Stat. Comput., vol. 12, (1991), pp.
             180-207},
   Key = {fds9488}
}

@article{fds9497,
   Author = {John Trangenstein},
   Title = {A Comparison of Two Numerical Methods for Shocks in
             One-Dimensional Elastic-Plastic Solids},
   Journal = {Viscous Profiles and Numerical Methods for Shock Waves,
             Michael Shearer (editor), SIAM (1991).},
   Key = {fds9497}
}

@article{fds9489,
   Author = {John Trangenstein},
   Title = {A Second-Order Algorithm for the Dynamic Response of
             Soils},
   Journal = {IMPACT of Computing in Science and Engineering, vol. 2,
             (1990), pp. 1-39},
   Key = {fds9489}
}

@article{fds9491,
   Author = {Kent Holing and Birgitte Schilling and John
             Trangenstein},
   Title = {The Use of Second-Order Godunov-Type Methods for Simulating
             EOR Processes in Realistic Reservoir Models},
   Journal = {Second European Conference on the Mathematics of Oil
             Recovery, E. Guerillot and O. Guillon (ed.) (1990),
             101-111},
   Key = {fds9491}
}

@article{fds9480,
   Author = {John B. Bell and John Trangenstein},
   Title = {Mathematical Structure of the Black-Oil Model for Petroleum
             Reservoir Simulation},
   Journal = {SIAM J. Appl. Math., vol.49, (1989), pp.
             749-783},
   Key = {fds9480}
}

@article{fds9481,
   Author = {John B. Bell and John Trangenstein},
   Title = {Mathematical Structure of Compositional Reservoir
             Simulation},
   Journal = {SIAM J. Sci. Stat. Comput., vol. 10, (1989), pp.
             817-845},
   Key = {fds9481}
}

@article{fds9483,
   Author = {John B. Bell and Philip Colella and John Trangenstein},
   Title = {Higher-Order Godunov Methods for General Systems of
             Hyperbolic Conservation Laws},
   Journal = {J. Comp. Phys., vol.82, (1989), pp. 362-397},
   Key = {fds9483}
}

@article{fds9485,
   Author = {Michael Shearer and John Trangenstein},
   Title = {Loss of Real Characteristics for Models of Three-Phase Flow
             in a Porous Medium},
   Journal = {Transport in Porous Media, vol. 4, (1989), pp.
             499-525},
   Key = {fds9485}
}

@article{fds9486,
   Author = {John Trangenstein},
   Title = {Three-Phase Flow with Gravity},
   Journal = {Contemporary Mathematics, vol.100, (1989), pp.
             147-160},
   Key = {fds9486}
}

@article{fds9490,
   Author = {John Trangenstein},
   Title = {Analysis of a Model and Sequential numerical Method for
             Thermal Reservoir Simulation},
   Journal = {Second European Conference on the Mathematics of Oil
             Recovery, P.R. King (ed.), Institute for Mathematics and Its
             Applications, Cambridge University, 1989},
   Key = {fds9490}
}

@article{fds9496,
   Author = {I.I. Glass and J. Kaca and D.L. Zhang and H.M. Glaz and J. Trangenstein and J.B. Bell and},
   Title = {Diffraction of Planar Shock Waves over Half-Diamond and
             Semicircular Cyliners: an Experimental and Numerical
             Comparisond},
   Journal = {Proceedings of the Seventeenth International Symposium on
             Shock Waves and Shock Tubes, July 17-21,
             1989.},
   Key = {fds9496}
}

@article{fds9479,
   Author = {Myron B. Allen and Alda Behie and John Trangenstein},
   Title = {Multiphase Flow in Porous Media: Mechanics, Mathematics and
             Numerics},
   Journal = {Springer-Verlag Lecture Notes in Engineering 34,
             (1988)},
   Key = {fds9479}
}

@article{fds9495,
   Author = {J. Bell and P. Colella and John Trangenstein and M.
             Welcome},
   Title = {Godunov Methods and Adaptive Algorithms for Unsteady Fluid
             Dynamics},
   Journal = {Eleventh International Conference on Numerical Methods in
             Fluid Dynamics, Williamsburg, Virginia, 1988.},
   Key = {fds9495}
}

@article{fds9478,
   Author = {John Trangenstein},
   Title = {Customized Minimization Techniques for Phase Equilibrium
             Computations in Reservoir Simulation},
   Journal = {Chemical Engineering Science, vol.42, (1987), pp.
             2847-2863},
   Key = {fds9478}
}

@article{fds9494,
   Author = {John Bell and Phillip Colella and John Trangenstein and Michael
             Welcome},
   Title = {Adaptive Methods for High Mach Number Reacting
             Flow},
   Journal = {AIAA Eighth Computational Fluid Dynamics Conference,
             Honolulu, Hawaii, 1987.},
   Key = {fds9494}
}

@article{fds9476,
   Author = {John B. Bell and Gregory R. Shubin and John
             Trangenstein},
   Title = {a Method for Reducing Numerical Dispersion in Two-Phase
             Black-Oil Reservoir Simulation},
   Journal = {J. Comp. Phys., vol. 65, (1986), pp. 71-106},
   Key = {fds9476}
}

@article{fds9477,
   Author = {John B. Bell and Gregory R. Shubin and John
             Trangenstein},
   Title = {Conservation Laws of Mixed Type Describing Three-Phase Flow
             in Porous Media},
   Journal = {SIAM J. Applied Math., vol. 46, (1986), pp.
             1000-1017},
   Key = {fds9477}
}

@article{fds9475,
   Author = {John Trangenstein},
   Title = {Minimization of Gibbs Free Energy in Compositional Reservoir
             Simulation},
   Journal = {Eighth SPE Symposium on Reservoir Simulation, SPE 13520,
             Dallas, 1985},
   Key = {fds9475}
}

@article{fds9474,
   Author = {H.E. Read and John Trangenstein},
   Title = {The Inelastic Response Characteristics of the New
             Endochronic Theory with Singular Kernel},
   Journal = {International Journal of Solids and Structures, vol. 18,
             (1982), pp. 947-956},
   Key = {fds9474}
}

@article{fds9473,
   Author = {W.B. Gragg and R.J. LeVeque and John Trangenstein},
   Title = {Numerically Stable Methods for Updating Regressions},
   Journal = {J. American Statistical Association, vol. 74, (1979), pp.
             161-168},
   Key = {fds9473}
}

@article{fds9472,
   Author = {John Trangenstein},
   Title = {Finite Element Method for the Tricomi Problem in the
             Elliptic Region},
   Journal = {SIAM J. Num. Anal., vol. 14, (1977), pp.
             1066-1077},
   Key = {fds9472}
}

@article{fds9471,
   Author = {J. J. More and John Trangenstein},
   Title = {On the Global Convergence of Broyden's Method},
   Journal = {Mathematics of Computation, vol. 30, (1976), pp.
             523-540},
   Key = {fds9471}
}


%% Preprints   
@article{fds10153,
   Author = {John Trangenstein and Zhuoxin Bi},
   Title = {Multi_Scale Iterative Techniques and Adaptive Mesh
             Refinement for Miscible Displacement Simulation},
   url = {http://www.math.duke.edu/~johnt/spe75232.ps},
   Abstract = {Accepted for presentation at SPE spring meeting,
             2002},
   Key = {fds10153}
}

@article{fds9028,
   Author = {Bill Allard and John Trangenstein},
   Title = {On the Performance of a Distributed Object Oriented Adaptive
             Mesh Refinement Code},
   Key = {fds9028}
}

 

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