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Application of adaptive cross approximation combined with compressedsensing to fast solution of electromagnetic scatteringproblems of electrically large objects over wide angles

  • School of Electronics and Information Engineering, Hefei Normal University, Hefei 230601, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.04.007
  • Received Date: 10 December 2014
  • Accepted Date: 06 March 2015
  • Rev Recd Date: 06 March 2015
  • Publish Date: 30 April 2015
    Abstract

  • Abstract

    Fast analysis of electromagnetic scattering properties of various objects, especially electrically large objects over a wide angle, is always a difficult problem in computational electromagnetics. A new solution using compressed sensing in conjunction with adaptive cross approximation was proposed, and a new incident source including different angle information was constructed based on compressed sensing theory, which could reduce the number of computation times for method of moments. Meanwhile, adaptive cross approximation technique was also introduced to method of moments to form a low rank decomposition of the impedance matrix. Thus a new scheme was finally formed to rapidly analyze electromagnetic scattering problems for electrically large objects over a wide angle. Numerical results show that this solution can reduce operation time effectively while retaining the accuracy of calculation results.

    Abstract

    Fast analysis of electromagnetic scattering properties of various objects, especially electrically large objects over a wide angle, is always a difficult problem in computational electromagnetics. A new solution using compressed sensing in conjunction with adaptive cross approximation was proposed, and a new incident source including different angle information was constructed based on compressed sensing theory, which could reduce the number of computation times for method of moments. Meanwhile, adaptive cross approximation technique was also introduced to method of moments to form a low rank decomposition of the impedance matrix. Thus a new scheme was finally formed to rapidly analyze electromagnetic scattering problems for electrically large objects over a wide angle. Numerical results show that this solution can reduce operation time effectively while retaining the accuracy of calculation results.
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    • References(19)
  • [1]
    Yoshida K, Nishimura N, Kobayashi S. Application of new fastmultipole boundary integral equation method to crack problems in 3D[J]. Engineering Analysis with Boundary Elements, 2001, 25(4-5): 239-247.
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    [5]
    Frederix K, van Barel M. Solving a large dense linear system by adaptive cross approximation[J]. Journal of Computational and Applied Mathematics, 2010, 234(11): 3181-3195.
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    Zhang L H, Ma C. Low-rank decomposition and Laplacian group sparse coding for image classification[J]. Neurocomputing, 2014, 135(5): 339-347.
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    Makarov S. MoM antenna simulations, with Matlab: RWG basis functions[J]. IEEE Transactions on Antennas and Propagation, 2001, 43(5): 100-107.
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    Fang L Y, Li S T. An efficient dictionary learning algorithm for sparse representation[C]// Chinese Conference on Pattern Recognition. Chongqing, China: IEEE Press, 2010: 1-5.
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    Yu Y,Petropulu A P, Poor H V. Measurement matrix design for compressive sensing-based MIMO radar[J]. IEEE Transactions on Signal Processing, 2011, 59(11): 5338-5352.
    [14]
    Yan S,Sarin V, Shi W P. Sparse transformations and preconditioners for 3-D capacitance extraction[J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2005, 24(9): 1420-1426.
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    Candès E, Romberg J, Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.
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    Saad Y, Schultz M H. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems[J]. SIAM Journal of Scientific Statistical Computing, 1986, 7(3): 856-869.
    [17]
    Konidaris G, Osentoski S. Value function approximation in reinforcement learning using the Fourier basis[R]. USA: Autonomous Learning Laboratory, Computer Science Department, University of Massachusetts Amherst, 2008.
    [18]
    Cao X Y, Chen M S, Wu X L. Sparse transform matrices and their application in the calculation of electromagnetic scattering problems[J]. Chinese Physics Letters, 2013, 30(2): 028401(1-5).
    [19]
    Cai T T, Wang L. Orthogonal matching pursuit for sparse signal recovery with noise[J]. IEEE Transactions on Information Theory, 2011, 57(7): 4680-4688.)
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    [1]
    Yoshida K, Nishimura N, Kobayashi S. Application of new fastmultipole boundary integral equation method to crack problems in 3D[J]. Engineering Analysis with Boundary Elements, 2001, 25(4-5): 239-247.
    [2]
    Ewe W B, Li L W, Chang C S, et al. AIM analysis of scattering and radiation by arbitrary surface-wire configurations[J]. IEEE Transactions Antennas Propagation, 2007, 55(1): 162-166.
    [3]
    Sun E Y, Rusch W V T. Time-domain physical-optics[J]. IEEE Transactions on Antennas and Propagation, 1994, 42(1): 9-15.
    [4]
    Ling H, Chou R, Lee S W. Shooting and bouncing rays: Calculating RCS of an arbitrary cavity[J]. IEEE Transactions on Antennas and Propagation, 1989, 37(2): 194-205.
    [5]
    Frederix K, van Barel M. Solving a large dense linear system by adaptive cross approximation[J]. Journal of Computational and Applied Mathematics, 2010, 234(11): 3181-3195.
    [6]
    Zhang L H, Ma C. Low-rank decomposition and Laplacian group sparse coding for image classification[J]. Neurocomputing, 2014, 135(5): 339-347.
    [7]
    Makarov S. MoM antenna simulations, with Matlab: RWG basis functions[J]. IEEE Transactions on Antennas and Propagation, 2001, 43(5): 100-107.
    [8]
    杜红梅, 陈明生, 吴先良, 等. 应用压缩传感求解宽角度电磁散射问题[J].计算物理, 2012, 29(3): 394-398.
    Du H M, Chen M S, Wu X L, et al. Compressive sensing for solution of electromagnetic scattering over wide angles[J]. Chinese Journal of Computational Physics, 2012, 29(3): 394-398.
    [9]
    Markovsky I. Structured low-rank approximation and its applications[J]. Automatica, 2008, 44(4): 891-909.
    [10]
    Bebendorf M. Adaptive cross approximation of multivariate functions[J]. Constructive Approximation, 2011, 34(2): 149-179.
    [11]
    Tamayo J M,Heldring A, Rius J M. Application of multilevel adaptive cross approximation (MLACA) to electromagnetic scattering and radiation problems[C]// International Conference on Electromagnetics in Advanced Applications. Torino, Italy: INSPEC, 2009:178-181.
    [12]
    Fang L Y, Li S T. An efficient dictionary learning algorithm for sparse representation[C]// Chinese Conference on Pattern Recognition. Chongqing, China: IEEE Press, 2010: 1-5.
    [13]
    Yu Y,Petropulu A P, Poor H V. Measurement matrix design for compressive sensing-based MIMO radar[J]. IEEE Transactions on Signal Processing, 2011, 59(11): 5338-5352.
    [14]
    Yan S,Sarin V, Shi W P. Sparse transformations and preconditioners for 3-D capacitance extraction[J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2005, 24(9): 1420-1426.
    [15]
    Candès E, Romberg J, Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.
    [16]
    Saad Y, Schultz M H. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems[J]. SIAM Journal of Scientific Statistical Computing, 1986, 7(3): 856-869.
    [17]
    Konidaris G, Osentoski S. Value function approximation in reinforcement learning using the Fourier basis[R]. USA: Autonomous Learning Laboratory, Computer Science Department, University of Massachusetts Amherst, 2008.
    [18]
    Cao X Y, Chen M S, Wu X L. Sparse transform matrices and their application in the calculation of electromagnetic scattering problems[J]. Chinese Physics Letters, 2013, 30(2): 028401(1-5).
    [19]
    Cai T T, Wang L. Orthogonal matching pursuit for sparse signal recovery with noise[J]. IEEE Transactions on Information Theory, 2011, 57(7): 4680-4688.)
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