Stability at Nonconforming Grid Interfaces for a High Order Discretization of the Schrodinger Equation

被引：16

作者：

Nissen, A. ^{[1
]}

Kreiss, G. ^{[2
]}

Gerritsen, M. ^{[1
]}

机构：

[1] Stanford Univ, Dept Energy Resources Engn, Stanford, CA 94305 USA

[2] Uppsala Univ, Dept Informat Technol, Uppsala, Sweden

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2012年 / 53卷 / 03期

基金：

瑞典研究理事会;

关键词：

Schrodinger equation; Finite difference methods; Summation-by-parts operator; Stability; Grid interface; FINITE-DIFFERENCE METHODS; ADAPTIVE MESH REFINEMENT; PARTS OPERATORS; BOUNDARY; ACCURATE; APPROXIMATIONS; SUMMATION; SCHEMES;

D O I：

10.1007/s10915-012-9586-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we extend the results from our earlier work on stable boundary closures for the Schrodinger equation using the summation-by-parts-simultaneous approximation term (SBP-SAT) method to include stability and accuracy at nonconforming grid interfaces. Stability at the grid interface is shown by the energy method, and the estimates are generalized to multiple dimensions. The accuracy of the grid interface coupling is investigated using normal mode analysis for operators of 2nd and 4th order formal interior accuracy. We show that full accuracy is retained for the 2nd and 4th order operators. The accuracy results are extended to 6th and 8th order operators by numerical simulations, in which case two orders of accuracy is gained with respect to the lower order approximation close to the interface.

引用

页码：528 / 551

页数：24

共 21 条

[1] [Anonymous], 1995, Time-Dependent Problems and Difference Methods
[2] ADAPTIVE MESH REFINEMENT FOR HYPERBOLIC PARTIAL-DIFFERENTIAL EQUATIONS
BERGER, MJ
OLIGER, J
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1984, 53 (03) : 484 - 512
[3] Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators
Carpenter, Mark H.
Nordstrom, Jan
Gottlieb, David
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2010, 45 (1-3) : 118 - 150
[4] TIME-STABLE BOUNDARY-CONDITIONS FOR FINITE-DIFFERENCE SCHEMES SOLVING HYPERBOLIC SYSTEMS - METHODOLOGY AND APPLICATION TO HIGH-ORDER COMPACT SCHEMES
CARPENTER, MH
GOTTLIEB, D
ABARBANEL, S
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1994, 111 (02) : 220 - 236
[5] A stable and conservative interface treatment of arbitrary spatial accuracy
Carpenter, MH
Nordström, J
Gottlieb, D
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1999, 148 (02) : 341 - 365
[6] Interface conditions for wave propagation through mesh refinement boundaries
Choi, DI
Brown, JD
Imbiriba, B
Centrella, J
MacNeice, P
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2004, 193 (02) : 398 - 425
[7] Accurate and stable grid interfaces for finite volume methods
Ferm, L
Lötstedt, P
[J]. APPLIED NUMERICAL MATHEMATICS, 2004, 49 (02) : 207 - 224
[8] Accurate time propagation for the Schrodinger equation with an explicitly time-dependent Hamiltonian
Kormann, Katharina
Holmgren, Sverker
Karlsson, Hans O.
[J]. JOURNAL OF CHEMICAL PHYSICS, 2008, 128 (18)
[9] A FOURIER METHOD SOLUTION FOR THE TIME-DEPENDENT SCHRODINGER-EQUATION AS A TOOL IN MOLECULAR-DYNAMICS
KOSLOFF, D
KOSLOFF, R
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1983, 52 (01) : 35 - 53
[10] A class of energy stable, high-order finite-difference interface schemes suitable for adaptive mesh refinement of hyperbolic problems
Kramer, R. M. J.
Pantano, C.
Pullin, D. I.
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 226 (02) : 1458 - 1484

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