We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Conver- gence rates of several orders are obtained fo...We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Conver- gence rates of several orders are obtained for fractional Sobolev spaces H^-1/2 （or H00^-l/2）. Main tools are the approximation properties of the discretization basis, the construction of a suitable Hilbert scale for weighted L2-spaces and local regularity estimates. Numerical experiments are provided to validate our claims,展开更多
We extend classic Sommerfeld and Silver-Muller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions.If x=(x1,x2,x3)...We extend classic Sommerfeld and Silver-Muller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions.If x=(x1,x2,x3)∈R^(3),with x_(3)denoting the direction orthogonal to the layers,standard conditions only hold for the outer layers in the region|x_(3)|>||x||^(γ),forγ∈(1/4,1/2)and x large.For|x_(3)|<||x||^(γ)and inside the slab,asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.展开更多
文摘We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Conver- gence rates of several orders are obtained for fractional Sobolev spaces H^-1/2 （or H00^-l/2）. Main tools are the approximation properties of the discretization basis, the construction of a suitable Hilbert scale for weighted L2-spaces and local regularity estimates. Numerical experiments are provided to validate our claims,
文摘We extend classic Sommerfeld and Silver-Muller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions.If x=(x1,x2,x3)∈R^(3),with x_(3)denoting the direction orthogonal to the layers,standard conditions only hold for the outer layers in the region|x_(3)|>||x||^(γ),forγ∈(1/4,1/2)and x large.For|x_(3)|<||x||^(γ)and inside the slab,asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.
