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Fast sweeping methods for hyperbolic systems of conservation laws at steady state.

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Title: Fast sweeping methods for hyperbolic systems of conservation laws at steady state.
Authors: Engquist, Björn1 engquist@math.utexas.edu, Froese, Brittany D.1 bfroese@math.utexas.edu, Tsai, Yen-Hsi Richard1 ytsai@math.utexas.edu
Source: Journal of Computational Physics. Dec2013, Vol. 255, p316-338. 23p.
Subjects: Fast sweeping methods (Mathematics), Hyperbolic functions, Conservation laws (Mathematics), Hamilton-Jacobi equations, Information theory, Stochastic convergence
Abstract: Abstract: Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton–Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of conservation laws. By exploiting the flow of information along characteristics, these fast sweeping methods can compute solutions very efficiently. Furthermore, the methods capture shocks sharply by directly imposing the Rankine–Hugoniot shock conditions. We present convergence analysis and numerics for several one- and two-dimensional examples to illustrate the use and advantages of this approach. [Copyright &y& Elsevier]
Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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An: 90594579
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  Data: Fast sweeping methods for hyperbolic systems of conservation laws at steady state.
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  Data: <searchLink fieldCode="AR" term="%22Engquist%2C+Björn%22">Engquist, Björn</searchLink><relatesTo>1</relatesTo><i> engquist@math.utexas.edu</i><br /><searchLink fieldCode="AR" term="%22Froese%2C+Brittany+D%2E%22">Froese, Brittany D.</searchLink><relatesTo>1</relatesTo><i> bfroese@math.utexas.edu</i><br /><searchLink fieldCode="AR" term="%22Tsai%2C+Yen-Hsi+Richard%22">Tsai, Yen-Hsi Richard</searchLink><relatesTo>1</relatesTo><i> ytsai@math.utexas.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Dec2013, Vol. 255, p316-338. 23p.
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  Data: <searchLink fieldCode="DE" term="%22Fast+sweeping+methods+%28Mathematics%29%22">Fast sweeping methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Hyperbolic+functions%22">Hyperbolic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Conservation+laws+%28Mathematics%29%22">Conservation laws (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Hamilton-Jacobi+equations%22">Hamilton-Jacobi equations</searchLink><br /><searchLink fieldCode="DE" term="%22Information+theory%22">Information theory</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+convergence%22">Stochastic convergence</searchLink>
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  Data: Abstract: Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton–Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of conservation laws. By exploiting the flow of information along characteristics, these fast sweeping methods can compute solutions very efficiently. Furthermore, the methods capture shocks sharply by directly imposing the Rankine–Hugoniot shock conditions. We present convergence analysis and numerics for several one- and two-dimensional examples to illustrate the use and advantages of this approach. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jcp.2013.08.036
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      – Code: eng
        Text: English
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        PageCount: 23
        StartPage: 316
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      – SubjectFull: Fast sweeping methods (Mathematics)
        Type: general
      – SubjectFull: Hyperbolic functions
        Type: general
      – SubjectFull: Conservation laws (Mathematics)
        Type: general
      – SubjectFull: Hamilton-Jacobi equations
        Type: general
      – SubjectFull: Information theory
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      – SubjectFull: Stochastic convergence
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      – TitleFull: Fast sweeping methods for hyperbolic systems of conservation laws at steady state.
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              Text: Dec2013
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