Cutting down on Fill Using Nested Dissection: Provably Good Elimination Orderings

1993 ◽  
pp. 31-55 ◽  
Author(s):  
Ajit Agrawal ◽  
Philip Klein ◽  
R. Ravi
Keyword(s):  
Nested Dissection

Incomplete Nested Dissection for Solving n by n Grid Problems

1978 ◽  
Vol 15 (4) ◽  
pp. 662-673 ◽  
Author(s):  
Alan George ◽  
William G. Poole, Jr. ◽  
Robert G. Voigt
Keyword(s):  
Nested Dissection

scholarly journals Numerical stability of nested dissection orderings

1980 ◽  
Vol 35 (152) ◽  
pp. 1235-1235 ◽  
Author(s):  
Indu Mati Anand
Keyword(s):  
Numerical Stability ◽  
Nested Dissection

scholarly journals Nested dissection solver for transport in 3D nano-electronic devices

2016 ◽  
Vol 15 (2) ◽  
pp. 708-720
Author(s):  
Y. Zhao ◽  
U. Hetmaniuk ◽  
S. R. Patil ◽  
J. Qi ◽  
M. P. Anantram
Keyword(s):  
Electronic Devices ◽  
Nested Dissection

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.

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