Second order elliptic equation is a class of mathematical model for scientific computing, such as convex-diffusion, oil-reservoir simulation, etc. Based on intrinsic symmetrizable property, a new concept on positively...Second order elliptic equation is a class of mathematical model for scientific computing, such as convex-diffusion, oil-reservoir simulation, etc. Based on intrinsic symmetrizable property, a new concept on positively symmetrizable matrix is proposed in this paper. We point that for such kind of equation systems, it is possible to adopt special preconditioning CG algorithm, e.g. [1]-[3], instead of the usual iteration procedure for general non-symmetry systems, such as GMRES [3]-[4] ) BiCGSTAB [5]. Numerical tests show the new algorithm is effective for solving this kind of second order elliptic discrete systems.展开更多
We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for -Δu = u3 , when the finite-dimensional subspace is taken as the eigensubspace corresponding t...We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for -Δu = u3 , when the finite-dimensional subspace is taken as the eigensubspace corresponding to an N-fold eigenvalue of -Δ, the discretized problem has at least 3N-1 distinct nonzero solutions. We also present a related result on the multiplicities of eigenvalues of -Δ.展开更多
文摘Second order elliptic equation is a class of mathematical model for scientific computing, such as convex-diffusion, oil-reservoir simulation, etc. Based on intrinsic symmetrizable property, a new concept on positively symmetrizable matrix is proposed in this paper. We point that for such kind of equation systems, it is possible to adopt special preconditioning CG algorithm, e.g. [1]-[3], instead of the usual iteration procedure for general non-symmetry systems, such as GMRES [3]-[4] ) BiCGSTAB [5]. Numerical tests show the new algorithm is effective for solving this kind of second order elliptic discrete systems.
基金supported by National Natural Science Foundation of China (Grant Nos.11171051 and 91230103)
文摘We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for -Δu = u3 , when the finite-dimensional subspace is taken as the eigensubspace corresponding to an N-fold eigenvalue of -Δ, the discretized problem has at least 3N-1 distinct nonzero solutions. We also present a related result on the multiplicities of eigenvalues of -Δ.
