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Suppression of spurious eigenvalues for spherical cavity eigenproblem using CHEEF method

This paper presents the CHEEF method for suppressing spurious eigenvalues in the eigenproblem of a spherical cavity. The method utilizes null-field boundary integral equation formulation.

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Suppression of spurious eigenvalues for spherical cavity eigenproblem using CHEEF method

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  1. Suppression of spurious eigenvalues for spherical cavity eigenproblem using CHEEF method 陳正宗 陳義麟 李家瑋 1

  2. z y x CHEEF Point Problem statement • Governing equation • : Laplacian operator • : Domain of cavity • k : wave number 2

  3. Null-field BIE Where U(s,x) is the fundamental solution, U(s,x) satisfied the following equation Where is the Dirac delta function 3

  4. Eigenproblem For the Dirichlet B.C., u=0, The Neumann B.C., t=0. 4

  5. Degenerate kernel Where is the first kind n-th order spherical Bessel function, is the second kind n-th order spherical Bessel function. is the Legendre Polynomial function is the Neumann factor, ( , when m=0, , when m>0) 5

  6. Spherical harmonics of density function Where and are the undetermined coefficient. 6

  7. For the Dirichlet B.C. The orthogonality of Legendre Polynomial function 7

  8. The eigenequation is The true eigenequation is The spurious eigenequation is 8

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