论文标题
对声波问题的等几何搭配矩阵的光谱特性的数值研究
A numerical study of the spectral properties of Isogeometric collocation matrices for acoustic wave problems
论文作者
论文摘要
本文侧重于及时使用等几何分析（IGA）搭配方法在空间和NEWMARK方法中及时使用的声波问题的质量和刚度矩阵的光谱特性。报道了参考平方域中的特征值和条件数量的广泛数值结果，并具有dirichlet，neumann和吸收边界条件，改变多项式$ p $，网状尺寸$ h $，定期$ k $，iga nivetization $ k $，iga nivetization $ g $Δt$δt$Δt$ $Δ$β$β$β$;关于矩阵的稀疏性和相对于自由度D.O.F.的稀疏性和特征值分布的结果。 NZ的非零条目数量也被报道。结果与与Dirichlet边界条件相关的IGA Galerkin矩阵的可用光谱估计值可比，在某些情况下，IgA搭配结果优于相应的IgA Galerkin估计。
This paper focuses on the spectral properties of the mass and stiffness matrices for acoustic wave problems discretized with Isogeometric analysis (IGA) collocation methods in space and Newmark methods in time. Extensive numerical results are reported for the eigenvalues and condition numbers of the acoustic mass and stiffness matrices in the reference square domain with Dirichlet, Neumann and absorbing boundary conditions, varying the polynomial degree $p$, mesh size $h$, regularity $k$, of the IGA discretization and the time step $Δt$ and parameter $β$ of the Newmark method. Results on the sparsity of the matrices and the eigenvalue distribution with respect to the degrees of freedom d.o.f. and the number of nonzero entries nz are also reported. The results are comparable with the available spectral estimates for IGA Galerkin matrices associated to the Poisson problem with Dirichlet boundary conditions, and in some cases the IGA collocation results are better than the corresponding IGA Galerkin estimates.
