Patched based methods for adaptive mesh refinement solutions of partial differential equations

Saltzman, J

doi:10.2172/584924

Title: Patched based methods for adaptive mesh refinement solutions of partial differential equations

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Abstract

This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year`s school which is ``Multiscale Methods and Wavelets in Numerical Simulation.`` The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.

Authors:: Saltzman, J

Publication Date:: Tue Sep 02 00:00:00 EDT 1997

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Assistant Secretary for Human Resources and Administration, Washington, DC (United States)

OSTI Identifier:: 584924

Report Number(s):: RI/RD-92-116
ON: DE98001101; TRN: AHC29808%%64

DOE Contract Number:: W-7405-ENG-36

Resource Type:: Technical Report

Resource Relation:: Other Information: PBD: 2 Sep 1997

Country of Publication:: United States

Language:: English

Subject:: 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; PARTIAL DIFFERENTIAL EQUATIONS; MESH GENERATION; PARALLEL PROCESSING; NUMERICAL SOLUTION; PROGRAMMING LANGUAGES; ALGORITHMS; CONSERVATION LAWS

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                    Saltzman, J. Patched based methods for adaptive mesh refinement solutions of partial differential equations.  United States: N. p., 1997. 
        Web.  doi:10.2172/584924.

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                    Saltzman, J. Patched based methods for adaptive mesh refinement solutions of partial differential equations.  United States.  https://doi.org/10.2172/584924

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                    Saltzman, J. 1997.  
        "Patched based methods for adaptive mesh refinement solutions of partial differential equations".  United States.  https://doi.org/10.2172/584924.  https://www.osti.gov/servlets/purl/584924.

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@article{osti_584924,

  title        = {Patched based methods for adaptive mesh refinement solutions of partial differential equations},

  author       = {Saltzman, J},

  abstractNote = {This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year`s school which is ``Multiscale Methods and Wavelets in Numerical Simulation.`` The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.},

  doi          = {10.2172/584924},

  url          = {https://www.osti.gov/biblio/584924},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Tue Sep 02 00:00:00 EDT 1997},

  month        = {Tue Sep 02 00:00:00 EDT 1997}

}

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