Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow

1998 ◽  
Vol 143 (1) ◽  
pp. 90-124 ◽  
Author(s):  
Y. Morinishi ◽  
T.S. Lund ◽  
O.V. Vasilyev ◽  
P. Moin
Keyword(s):  
Finite Difference ◽  
Incompressible Flow ◽  
Higher Order ◽  
Difference Schemes ◽  
Finite Difference Schemes

Massively parallel structured direct solver for equations describing time-harmonic qP-polarized waves in TTI media

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. T69-T82 ◽  
Author(s):  
Shen Wang ◽  
Jianlin Xia ◽  
Maarten V. de Hoop ◽  
Xiaoye S. Li
Keyword(s):  
Finite Difference ◽  
Higher Order ◽  
Difference Schemes ◽  
Massively Parallel ◽  
Finite Difference Schemes ◽  
Variable Order ◽  
Nested Dissection ◽  
Partial Differential ◽  
Polarized Waves ◽  
Time Harmonic

We considered the discretization and approximate solutions of equations describing time-harmonic qP-polarized waves in 3D inhomogeneous anisotropic media. The anisotropy comprises general (tilted) transversely isotropic symmetries. We are concerned with solving these equations for a large number of different sources. We considered higher-order partial differential equations and variable-order finite-difference schemes to accommodate anisotropy on the one hand and allow higher-order accuracy — to control sampling rates for relatively high frequencies — on the other hand. We made use of a nested dissection based domain decomposition in a massively parallel multifrontal solver combined with hierarchically semiseparable matrix compression techniques. The higher-order partial differential operators and the variable-order finite-difference schemes require the introduction of separators with variable thickness in the nested dissection; the development of these and their integration with the multifrontal solver is the main focus of our study. The algorithm that we developed is a powerful tool for anisotropic full-waveform inversion.

scholarly journals Higher order schemes and Richardson extrapolation for singular perturbation problems

1989 ◽  
Vol 39 (1) ◽  
pp. 129-139 ◽  
Author(s):  
Dragoslav Herceg ◽  
Relja Vulanović ◽  
Nenad Petrović
Keyword(s):  
Finite Difference ◽  
Singular Perturbation ◽  
Fourth Order ◽  
Richardson Extrapolation ◽  
Higher Order ◽  
Difference Schemes ◽  
Singular Perturbation Problems ◽  
Finite Difference Schemes ◽  
Perturbation Problems ◽  
Uniform Accuracy

Semilinear singular perturbation problems are solved numerically by using finite–difference schemes on non-equidistant meshes which are dense in the layers. The fourth order uniform accuracy of the Hermitian approximation is improved by the Richardson extrapolation.

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