Decay estimates of discretized Green's functions for Schrdinger type operators  

作　　者：LIN Lin LU Jianfeng 

机构地区：[1]Department of Mathematics,University of California at Berkeley,Berkeley,CA 94720,USA [2]Computational Research Division,Lawrence Berkeley National Laboratory,Berkeley,CA 94720,USA [3]Department of Mathematics,Duke University,Durham,NC 27708,USA [4]Department of Physics,Duke University,Durham,NC 27708,USA [5]Department of Chemistry,Duke University,Durham,NC 27708,USA

出　　处：《Science China Mathematics》2016年第8期1561-1578,共18页中国科学：数学（英文版）

基　　金：supported by Laboratory Directed Research and Development Funding from Berkeley Lab;provided by the Director,Office of Science,of the US Department of Energy(Grant No.DE-AC02-05CH11231);the Alfred P Sloan Foundation;the DOE Scientific Discovery through the Advanced Computing Program;the DOE Center for Applied Mathematics for Energy Research Applications Program;the National Science Foundation of USA(Grant Nos.DMS-1312659 and DMS-1454939)

摘　　要：For a sparse non-singular matrix A, generally A- 1 is a dense matrix. However, for a class of matrices, A-1 can be a matrix with off-diagonal decay properties, i.e., ｜Aij^-1｜ decays fast to 0 with respect to the increase of a properly defined distance between i and j. Here we consider the off-diagonal decay properties of discretized Green＇s functions for SchrSdinger type operators. We provide decay estimates for discretized Green＇s functions obtained from the finite difference discretization, and from a variant of the pseudo-spectral discretization. The asymptotic decay rate in our estimate is independent of the domain size and of the discretization parameter. We verify the decay estimate with numerical results for one-dimensional Schr6dinger type operators.For a sparse non-singular matrix A, generally A^(-1)is a dense matrix. However, for a class of matrices,A^(-1)can be a matrix with off-diagonal decay properties, i.e., |A_(ij)^(-1)| decays fast to 0 with respect to the increase of a properly defined distance between i and j. Here we consider the off-diagonal decay properties of discretized Green's functions for Schr¨odinger type operators. We provide decay estimates for discretized Green's functions obtained from the finite difference discretization, and from a variant of the pseudo-spectral discretization. The asymptotic decay rate in our estimate is independent of the domain size and of the discretization parameter.We verify the decay estimate with numerical results for one-dimensional Schr¨odinger type operators.

关 键 词：decay estimates Green＇s function SchrSdinger operator finite difference discretization pseudo-spectral discretization 

分 类 号：O175[理学—数学]