Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems

Baczewski, Andrew David; Dault, Daniel L.; Shanker, Balasubramaniam

doi:10.1109/TAP.2012.2207037

Title: Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems

Abstract

We present an algorithm for the fast and efficient solution of integral equations that arise in the analysis of scattering from periodic arrays of PEC objects, such as multiband frequency selective surfaces (FSS) or metamaterial structures. Our approach relies upon the method of Accelerated Cartesian Expansions (ACE) to rapidly evaluate the requisite potential integrals. ACE is analogous to FMM in that it can be used to accelerate the matrix vector product used in the solution of systems discretized using MoM. Here, ACE provides linear scaling in both CPU time and memory. Details regarding the implementation of this method within the context of periodic systems are provided, as well as results that establish error convergence and scalability. In addition, we also demonstrate the applicability of this algorithm by studying several exemplary electrically dense systems.

Authors:

Baczewski, Andrew David ^[1]; Dault, Daniel L. ^[1]; Shanker, Balasubramaniam ^[1]

Michigan State Univ., East Lansing, MI (United States)

Publication Date:: Tue Jul 03 00:00:00 EDT 2012

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1252694

Report Number(s):: SAND-2016-1049J
Journal ID: ISSN 0018-926X; 619142

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: IEEE Transactions on Antennas and Propagation

Additional Journal Information:: Journal Volume: 60; Journal Issue: 9; Journal ID: ISSN 0018-926X

Publisher:: IEEE

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; fast methods; integral equations; periodic structures; frequency; selective surfaces

Citation Formats


                    Baczewski, Andrew David, Dault, Daniel L., and Shanker, Balasubramaniam. Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems.  United States: N. p., 2012. 
Web.  doi:10.1109/TAP.2012.2207037.

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                    Baczewski, Andrew David, Dault, Daniel L., & Shanker, Balasubramaniam. Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems.  United States.  https://doi.org/10.1109/TAP.2012.2207037

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                    Baczewski, Andrew David, Dault, Daniel L., and Shanker, Balasubramaniam. Tue .  
"Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems".  United States.  https://doi.org/10.1109/TAP.2012.2207037.  https://www.osti.gov/servlets/purl/1252694.

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@article{osti_1252694,

  title        = {Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems},

  author       = {Baczewski, Andrew David and Dault, Daniel L. and Shanker, Balasubramaniam},

  abstractNote = {We present an algorithm for the fast and efficient solution of integral equations that arise in the analysis of scattering from periodic arrays of PEC objects, such as multiband frequency selective surfaces (FSS) or metamaterial structures. Our approach relies upon the method of Accelerated Cartesian Expansions (ACE) to rapidly evaluate the requisite potential integrals. ACE is analogous to FMM in that it can be used to accelerate the matrix vector product used in the solution of systems discretized using MoM. Here, ACE provides linear scaling in both CPU time and memory. Details regarding the implementation of this method within the context of periodic systems are provided, as well as results that establish error convergence and scalability. In addition, we also demonstrate the applicability of this algorithm by studying several exemplary electrically dense systems.},

  doi          = {10.1109/TAP.2012.2207037},

  journal      = {IEEE Transactions on Antennas and Propagation},

  number       = 9,

  volume       = 60,

  place        = {United States},

  year         = {Tue Jul 03 00:00:00 EDT 2012},

  month        = {Tue Jul 03 00:00:00 EDT 2012}

}

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