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| 1 | Efficient Simulation of Wave Propagation with Implicit Finite Difference Schemes显示文摘Finite difference method is an important methodology in the approximation of waves.In this paper,we will study two implicit finite difference schemes for the simulation of waves.They are the weighted alternating direction implicit(ADI)scheme and the locally one-dimensional(LOD)scheme.The approximation errors,stability conditions,and dispersion relations for both schemes are investigated.Our analysis shows that the LOD implicit scheme has less dispersion error than that of the ADI scheme.Moreover,the unconditional stability for both schemes with arbitrary spatial accuracy is established for the first time.In order to improve computational efficiency,numerical algorithms based on message passing interface(MPI)are implemented.Numerical examples of wave propagation in a three-layer model and a standard complex model are presented.Our analysis and comparisons show that both ADI and LOD schemes are able to efficiently and accurately simulate wave propagation in complex media. | Wensheng Zhang Li Tong Eric T.Chung | 2012 | Numerical Mathematics(Theory,Methods and Applications)2012，5，2： | 2 |
| 2 | Multi-Product Expansion with Suzuki’s Method: Generalization显示文摘In this paper we discuss the extension to exponential splitting methods withrespect to time-dependent operators. We concentrate on the Suzuki’s method, whichincorporates ideas to the time-ordered exponential of [3, 11, 12, 34]. We formulate themethods with respect to higher order by using kernels for an extrapolation scheme. Theadvantages include more accurate and less computational intensive schemes to specialtime-dependent harmonic oscillator problems. The benefits of the higher order kernelsare given on different numerical examples. | Jürgen Geiser | 2011 | Numerical Mathematics(Theory,Methods and Applications)2011，4，1： | 0 |
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