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

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

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

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

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

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

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

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