An Investigation of Restarted GMRES Method by Using Flexible Starting Vectors

We discuss a variant of restarted GMRES method that allows changes of the restarting vector at each cycle of iterations.The merit of the variant is that previously generated information can be utilized to select a new starting vector,such that the occurrence of stagnation be mitigated or the convergence be accelerated.The more appealing utilization of the new method is in conjunction with a harmonic Ritz vector as the starting vector,which is discussed in detail.Numerical experiments are carried out to demonstrate that the proposed procedure can effectively mitigate the occurrence of stagnation due to the presence of small eigenvalues in modulus.

Cylindrical vector beam-excited frequency-tunable second harmonic generation in a plasmonic octamer

We report a method to tune the second harmonic generation(SHG) frequency of a metallic octamer by employing cylindrical vector beams as the excitation. Our method exploits the ability to spatially match the polarization state of excitations with the fundamental target plasmonic modes, enabling flexible control of the SHG resonant frequency.It is found that SHG of the octamer is enhanced over a broad band(400 nm) by changing the excitation from the linearly polarized Gaussian beam to radially and azimuthally polarized beams. More strikingly, when subjected to an azimuthally polarized beam, the SHG intensity of the octamer becomes 30 times stronger than that for the linearly polarized beam even in the presence of Fano resonance.

On Basis and Pure Nash Equilibrium of Finite Pure Harmonic Games

This paper investigates the basis and pure Nash equilibrium of finite pure harmonic games(FPHGs) based on the vector space structure. First, a new criterion is proposed for the construction of pure harmonic subspace, based on which, a more concise basis is constructed for the pure harmonic subspace. Second, based on the new basis of FPHGs and auxiliary harmonic vector, a more easily verifiable criterion is presented for the existence of pure Nash equilibrium in basis FPHGs. Third,by constructing a pure Nash equilibrium cubic matrix, the verification of pure Nash equilibrium in three-player FPHGs is given.

BOUNDARY INTEGRAL EQUATIONS FOR ISOTROPIC LINEAR ELASTICITY

This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam´e coefficients in the form of a bounded domain of arbitrary shape surrounded by a background material.In the simple case of a spherical inclusion,the vector spherical harmonics consist of eigenfunctions of the single and double layer boundary operators and we provide their spectra.Further,in the case of many spherical inclusions with isotropic materials,each with its own set of Lam´e parameters,we propose an integral equation and a subsequent Galerkin discretization using the vector spherical harmonics and apply the discretization to several numerical test cases.